B:=[];
G:=[];
# Design 1: autom. group order 4, simple, derived
B[1]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,7,8,11],[1,3,6,9,10,12],[1,4,5,8,9,13],[1,4,5,10,11,12],[1,4,8,9,12,13],[1,5,7,10,11,13],[1,6,7,8,9,11],[1,6,7,10,12,13],[2,3,8,11,12,13],[2,4,6,7,12,13],[2,4,6,9,10,11],[2,4,9,10,11,13],[2,5,6,8,10,13],[2,5,7,8,9,12],[2,5,7,9,10,12],[3,4,6,7,9,13],[3,4,7,8,10,11],[3,4,7,8,10,12],[3,5,6,8,10,13],[3,5,6,9,11,12],[3,5,7,9,11,13],[4,5,6,8,11,12]];
G[1]:=Group([(1,3,10,9)(2,8)(5,7,11,13)(6,12)]);
# Design 2: autom. group order 4, simple, derived
B[2]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,7,8,11],[1,3,6,9,12,13],[1,4,5,8,9,12],[1,4,5,10,11,13],[1,4,8,10,11,13],[1,5,7,9,10,12],[1,6,7,8,9,11],[1,6,7,10,12,13],[2,3,8,9,10,13],[2,4,6,9,10,12],[2,4,6,10,11,12],[2,4,7,8,12,13],[2,5,6,9,11,13],[2,5,7,8,12,13],[2,5,7,9,10,11],[3,4,6,7,8,10],[3,4,7,9,11,12],[3,4,7,9,11,13],[3,5,6,7,10,13],[3,5,6,8,11,12],[3,5,8,10,11,12],[4,5,6,8,9,13]];
G[2]:=Group([(1,7,12,10)(2,4,11,8)(5,9)(6,13)]);
# Design 3: autom. group order 4, simple
B[3]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,8,11,12],[1,3,6,9,10,13],[1,4,5,8,9,11],[1,4,5,10,12,13],[1,4,7,8,10,12],[1,5,7,9,11,13],[1,6,7,8,9,12],[1,6,7,10,11,13],[2,3,7,8,9,13],[2,4,6,7,8,13],[2,4,6,7,10,11],[2,4,9,10,11,13],[2,5,6,9,10,12],[2,5,7,9,10,12],[2,5,8,11,12,13],[3,4,6,9,11,12],[3,4,7,9,11,12],[3,4,8,10,12,13],[3,5,6,7,12,13],[3,5,6,8,10,11],[3,5,7,8,10,11],[4,5,6,8,9,13]];
G[3]:=Group([(2,4)(3,5)(6,7)(10,11),(1,8)(2,10)(4,11)(6,7)]);
# Design 4: autom. group order 4, simple
B[4]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,8,11,12],[1,3,6,8,9,13],[1,4,5,8,10,11],[1,4,5,9,12,13],[1,4,7,10,11,13],[1,5,7,9,10,12],[1,6,7,8,10,13],[1,6,7,9,11,12],[2,3,7,10,12,13],[2,4,6,7,11,13],[2,4,6,9,10,12],[2,4,7,8,9,12],[2,5,6,7,8,10],[2,5,8,9,11,13],[2,5,9,10,11,13],[3,4,6,9,10,11],[3,4,7,8,9,11],[3,4,8,10,12,13],[3,5,6,7,9,13],[3,5,6,10,11,12],[3,5,7,8,11,12],[4,5,6,8,12,13]];
G[4]:=Group([(2,5)(3,4)(6,7)(8,10)(9,11),(1,13)(3,11)(4,9)(6,10)(7,8)]);
# Design 5: autom. group order 4, simple
B[5]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,7,8,9],[1,3,6,10,11,12],[1,4,5,8,10,13],[1,4,6,9,11,13],[1,4,7,9,11,13],[1,5,7,8,12,13],[1,5,8,10,11,12],[1,6,7,9,10,12],[2,3,7,10,11,13],[2,4,5,9,10,12],[2,4,6,8,11,12],[2,4,7,8,11,12],[2,5,6,9,12,13],[2,5,9,10,11,13],[2,6,7,8,10,13],[3,4,6,8,10,13],[3,4,7,9,10,12],[3,4,8,9,12,13],[3,5,6,7,12,13],[3,5,6,8,9,11],[3,5,7,8,9,11],[4,5,6,7,10,11]];
G[5]:=Group([(1,2)(6,7)(8,9)(12,13),(1,8)(2,9)(4,11)(12,13)]);
# Design 6: autom. group order 4, simple, derived
B[6]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,7,8,11],[1,3,6,9,12,13],[1,4,5,8,9,12],[1,4,6,9,10,11],[1,4,8,10,11,13],[1,5,7,8,11,13],[1,5,7,9,10,12],[1,6,7,10,12,13],[2,3,8,9,10,13],[2,4,5,10,12,13],[2,4,6,10,11,12],[2,4,7,8,12,13],[2,5,6,9,11,13],[2,5,7,9,10,11],[2,6,7,8,9,12],[3,4,6,7,8,10],[3,4,7,9,11,12],[3,4,7,9,11,13],[3,5,6,7,10,13],[3,5,6,8,11,12],[3,5,8,10,11,12],[4,5,6,8,9,13]];
G[6]:=Group([(1,7,12,10)(2,4,11,8)(5,9)(6,13)]);
# Design 7: autom. group order 4, simple, derived
B[7]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,8,9,11],[1,3,6,10,12,13],[1,4,5,8,11,12],[1,4,6,9,10,13],[1,4,7,8,12,13],[1,5,7,9,10,11],[1,5,7,9,10,12],[1,6,7,8,11,13],[2,3,7,10,11,12],[2,4,5,8,10,13],[2,4,6,9,11,12],[2,4,7,9,12,13],[2,5,6,7,9,13],[2,5,8,10,11,13],[2,6,7,8,10,12],[3,4,6,7,8,10],[3,4,7,8,9,11],[3,4,9,10,11,13],[3,5,6,7,11,13],[3,5,6,8,9,12],[3,5,8,9,12,13],[4,5,6,10,11,12]];
G[7]:=Group([(1,2,8,9)(3,10)(4,13,12,7)(6,11)]);
# Design 8: autom. group order 4, simple, derived
B[8]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,7,8,9],[1,3,6,10,11,12],[1,4,5,8,10,13],[1,4,6,9,11,13],[1,4,8,10,12,13],[1,5,7,9,11,12],[1,5,7,9,12,13],[1,6,7,8,10,11],[2,3,7,10,12,13],[2,4,5,9,10,11],[2,4,7,8,11,13],[2,4,9,10,11,12],[2,5,6,8,11,12],[2,5,6,8,12,13],[2,6,7,9,10,13],[3,4,6,7,11,13],[3,4,6,8,9,12],[3,4,7,8,9,12],[3,5,6,9,10,13],[3,5,7,8,10,11],[3,5,8,9,11,13],[4,5,6,7,10,12]];
G[8]:=Group([(1,2)(6,7)(8,9)(11,13),(1,8)(2,9)(5,12)(6,7)]);
# Design 9: autom. group order 4, simple, derived
B[9]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,8,11,12],[1,3,8,9,10,13],[1,4,5,9,10,11],[1,4,6,7,9,12],[1,4,6,10,12,13],[1,5,7,8,9,12],[1,5,7,10,11,13],[1,6,7,8,11,13],[2,3,7,9,12,13],[2,4,5,8,11,13],[2,4,6,9,10,13],[2,4,7,8,9,11],[2,5,6,8,10,12],[2,5,7,10,12,13],[2,6,7,9,10,11],[3,4,6,7,8,13],[3,4,7,10,11,12],[3,4,8,10,11,12],[3,5,6,7,8,10],[3,5,6,9,11,12],[3,5,6,9,11,13],[4,5,8,9,12,13]];
G[9]:=Group([(1,5,11,10)(2,6,12,8)(4,9)(7,13)]);
# Design 10: autom. group order 4, simple
B[10]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,8,9,11,12],[1,3,6,8,10,13],[1,4,5,8,10,11],[1,4,6,7,9,12],[1,4,7,10,12,13],[1,5,6,9,11,13],[1,5,7,9,11,13],[1,6,7,8,10,12],[2,3,7,9,10,13],[2,4,5,9,10,12],[2,4,6,7,8,11],[2,4,6,10,11,13],[2,5,6,8,12,13],[2,5,7,8,12,13],[2,6,7,9,10,11],[3,4,6,9,12,13],[3,4,7,8,11,13],[3,4,8,9,11,12],[3,5,6,7,8,9],[3,5,6,10,11,12],[3,5,7,10,11,12],[4,5,8,9,10,13]];
G[10]:=Group([(1,2)(6,7)(8,9)(11,12),(1,11)(2,12)(4,10)(6,7)]);
# Design 11: autom. group order 4, simple
B[11]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,8,9,11,12],[1,3,6,8,10,13],[1,4,5,8,10,11],[1,4,6,7,8,12],[1,4,7,10,12,13],[1,5,6,9,11,13],[1,5,7,9,11,13],[1,6,7,9,10,12],[2,3,7,9,10,13],[2,4,5,9,10,12],[2,4,6,7,9,11],[2,4,6,10,11,13],[2,5,6,8,12,13],[2,5,7,8,12,13],[2,6,7,8,10,11],[3,4,6,9,12,13],[3,4,7,8,11,13],[3,4,8,9,11,12],[3,5,6,7,8,9],[3,5,6,10,11,12],[3,5,7,10,11,12],[4,5,8,9,10,13]];
G[11]:=Group([(1,2)(6,7)(8,9)(11,12),(1,11)(2,12)(4,10)(6,7)]);
# Design 12: autom. group order 4, simple, derived
B[12]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,6,7,8,11],[1,3,6,9,12,13],[1,4,5,7,9,12],[1,4,5,8,11,13],[1,4,9,10,11,13],[1,5,7,8,10,12],[1,6,7,10,11,13],[1,6,8,9,10,12],[2,3,7,9,10,11],[2,4,5,10,12,13],[2,4,6,7,12,13],[2,4,6,8,9,10],[2,5,6,10,11,12],[2,5,8,9,11,13],[2,7,8,9,12,13],[3,4,6,8,10,13],[3,4,7,10,11,12],[3,4,8,9,11,12],[3,5,6,7,9,13],[3,5,6,8,11,12],[3,5,7,8,10,13],[4,5,6,7,9,11]];
G[12]:=Group([(1,3,12,13)(2,11)(5,8,7,10)(6,9)]);
# Design 13: autom. group order 4, simple, derived
B[13]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,6,9,11,12],[1,3,6,7,10,13],[1,4,5,7,9,11],[1,4,5,8,12,13],[1,4,8,9,10,11],[1,5,7,8,12,13],[1,6,7,9,10,13],[1,6,8,10,11,12],[2,3,7,8,9,12],[2,4,5,10,11,13],[2,4,6,7,11,13],[2,4,6,8,10,12],[2,5,6,7,8,10],[2,5,9,10,12,13],[2,7,8,9,11,13],[3,4,6,9,12,13],[3,4,7,10,11,12],[3,4,8,9,10,13],[3,5,6,8,9,11],[3,5,6,8,11,13],[3,5,7,10,11,12],[4,5,6,7,9,12]];
G[13]:=Group([(1,8,11,10)(3,7,13,5)(4,9)(6,12)]);
# Design 14: autom. group order 4, simple, derived
B[14]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,6,7,8,11],[1,3,7,9,12,13],[1,4,5,8,9,12],[1,4,5,10,11,13],[1,4,6,9,11,13],[1,5,6,8,10,12],[1,6,7,9,10,12],[1,7,8,10,11,13],[2,3,8,9,10,11],[2,4,5,7,12,13],[2,4,6,7,9,10],[2,4,8,10,12,13],[2,5,6,9,11,13],[2,5,7,10,11,12],[2,6,8,9,12,13],[3,4,6,7,10,13],[3,4,6,8,11,12],[3,4,9,10,11,12],[3,5,6,7,11,12],[3,5,6,8,10,13],[3,5,7,8,9,13],[4,5,7,8,9,11]];
G[14]:=Group([(1,3,12,13)(2,11)(5,6,8,10)(7,9)]);
# Design 15: autom. group order 4, simple, derived
B[15]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,7,8,9,11],[1,3,7,10,12,13],[1,4,5,7,11,12],[1,4,5,8,9,13],[1,4,6,9,10,12],[1,5,6,8,11,13],[1,6,7,10,11,13],[1,6,8,9,10,12],[2,3,6,9,11,12],[2,4,5,10,12,13],[2,4,6,7,10,11],[2,4,6,8,12,13],[2,5,6,7,8,10],[2,5,9,10,11,13],[2,7,8,9,12,13],[3,4,6,7,9,13],[3,4,8,9,10,11],[3,4,8,10,11,13],[3,5,6,7,9,13],[3,5,6,8,11,12],[3,5,7,8,10,12],[4,5,7,9,11,12]];
G[15]:=Group([(1,5,13,8)(3,10,12,7)(4,9)(6,11)]);
# Design 16: autom. group order 4, simple, derived
B[16]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,6,7,11,12],[1,3,6,8,9,13],[1,4,5,7,9,11],[1,4,6,7,10,13],[1,4,9,10,12,13],[1,5,7,8,10,11],[1,5,8,9,12,13],[1,6,8,10,11,12],[2,3,7,9,10,12],[2,4,5,8,11,13],[2,4,6,8,9,10],[2,4,7,8,12,13],[2,5,6,8,10,12],[2,5,6,9,11,13],[2,7,9,10,11,13],[3,4,5,10,11,12],[3,4,6,10,11,13],[3,4,8,9,11,12],[3,5,6,7,12,13],[3,5,7,8,10,13],[3,6,7,8,9,11],[4,5,6,7,9,12]];
G[16]:=Group([(1,8,11,10)(3,4,13,9)(5,7)(6,12)]);
# Design 17: autom. group order 4, simple, derived
B[17]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,6,7,9,11],[1,3,6,8,12,13],[1,4,5,8,9,12],[1,4,6,10,11,13],[1,4,7,9,10,12],[1,5,7,9,11,13],[1,5,8,10,11,13],[1,6,7,8,10,12],[2,3,8,9,10,11],[2,4,5,7,12,13],[2,4,6,10,11,12],[2,4,7,8,11,13],[2,5,6,7,8,10],[2,5,6,9,12,13],[2,8,9,10,12,13],[3,4,5,10,11,12],[3,4,6,8,9,13],[3,4,7,9,10,13],[3,5,6,7,10,13],[3,5,7,8,11,12],[3,6,7,9,11,12],[4,5,6,8,9,11]];
G[17]:=Group([(1,3,12,13)(2,11)(4,7,9,10)(6,8)]);
# Design 18: autom. group order 4, simple, derived
B[18]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,6,7,9,11],[1,3,8,9,12,13],[1,4,5,10,11,12],[1,4,6,8,10,13],[1,4,6,9,11,12],[1,5,6,7,10,13],[1,5,7,8,9,13],[1,7,8,10,11,12],[2,3,7,8,10,11],[2,4,5,8,12,13],[2,4,6,8,9,10],[2,4,7,10,12,13],[2,5,6,8,11,12],[2,5,9,10,11,13],[2,6,7,9,12,13],[3,4,5,7,9,12],[3,4,6,7,11,13],[3,4,9,10,11,13],[3,5,6,7,10,12],[3,5,6,8,11,13],[3,6,8,9,10,12],[4,5,7,8,9,11]];
G[18]:=Group([(1,3,13,12)(2,11)(5,6,7,10)(8,9)]);
# Design 19: autom. group order 4, simple, derived
B[19]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,6,9,11,12],[1,3,7,8,9,11],[1,4,5,10,12,13],[1,4,6,7,10,11],[1,4,6,8,12,13],[1,5,6,7,8,10],[1,5,9,10,11,13],[1,7,8,9,12,13],[2,3,7,10,12,13],[2,4,5,7,11,13],[2,4,6,7,9,13],[2,4,8,9,10,11],[2,5,6,8,11,12],[2,5,7,8,10,12],[2,6,8,9,10,13],[3,4,5,8,9,13],[3,4,6,9,10,12],[3,4,8,10,11,12],[3,5,6,7,9,12],[3,5,6,8,11,13],[3,6,7,10,11,13],[4,5,7,9,11,12]];
G[19]:=Group([(2,7,12,10)(3,8,13,5)(4,9)(6,11)]);
# Design 20: autom. group order 4, simple, derived
B[20]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,11,12,13],[1,2,6,9,11,12],[1,3,7,10,11,13],[1,4,5,10,12,13],[1,4,6,7,9,10],[1,4,6,8,12,13],[1,5,6,8,9,11],[1,5,7,8,10,11],[1,7,8,9,12,13],[2,3,7,8,9,12],[2,4,5,7,11,13],[2,4,6,7,10,12],[2,4,8,9,10,11],[2,5,6,7,8,13],[2,5,9,10,12,13],[2,6,8,10,11,13],[3,4,5,8,9,13],[3,4,6,9,11,13],[3,4,8,10,11,12],[3,5,6,7,11,12],[3,5,6,8,10,12],[3,6,7,9,10,13],[4,5,7,9,11,12]];
G[20]:=Group([(2,12)(3,13)(5,8)(7,10),(1,11)(2,5,12,8)(3,7,13,10)(6,9)]);
# Design 21: autom. group order 4, simple, derived
B[21]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,8,12,13],[1,3,6,11,12,13],[1,4,6,9,10,11],[1,4,7,8,9,13],[1,5,7,8,10,12],[1,5,7,10,11,12],[1,6,7,9,10,13],[2,3,6,7,10,11],[2,3,8,9,10,12],[2,4,6,10,12,13],[2,4,7,10,12,13],[2,5,6,7,8,13],[2,5,9,11,12,13],[2,6,7,8,9,11],[3,4,5,9,10,13],[3,4,7,8,11,13],[3,4,7,9,11,12],[3,5,6,7,9,12],[3,5,8,10,11,13],[4,5,6,8,9,12],[4,5,6,8,10,11]];
G[21]:=Group([(3,5)(6,7)(8,11)(10,13),(1,12)(3,10)(5,13)(6,7)]);
# Design 22: autom. group order 4, simple, derived
B[22]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,8,12,13],[1,3,6,10,11,12],[1,4,6,10,11,13],[1,4,7,9,12,13],[1,5,7,8,10,13],[1,5,7,9,10,12],[1,6,7,8,9,11],[2,3,7,8,12,13],[2,3,7,10,11,12],[2,4,6,9,12,13],[2,4,7,10,11,13],[2,5,6,8,10,13],[2,5,6,9,10,12],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,9,10],[3,4,8,9,10,13],[3,5,6,7,11,13],[3,5,9,11,12,13],[4,5,6,7,8,12],[4,5,8,10,11,12]];
G[22]:=Group([(1,2)(6,7),(1,6,2,7)(3,9)(4,8)(5,11)]);
# Design 23: autom. group order 4, simple
B[23]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,7,9,12],[1,3,8,10,11,13],[1,4,6,7,10,11],[1,4,8,9,12,13],[1,5,6,10,12,13],[1,5,7,10,12,13],[1,6,7,8,9,11],[2,3,6,8,10,13],[2,3,7,9,10,12],[2,4,6,10,11,12],[2,4,7,8,12,13],[2,5,6,7,8,13],[2,5,9,10,11,12],[2,6,7,9,11,13],[3,4,5,9,11,13],[3,4,6,9,12,13],[3,4,7,10,11,13],[3,5,6,8,11,12],[3,5,7,8,11,12],[4,5,6,8,9,10],[4,5,7,8,9,10]];
G[23]:=Group([(3,4)(6,7)(9,11)(10,12),(2,13)(3,10)(4,12)(9,11)]);
# Design 24: autom. group order 4, simple
B[24]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,7,11,12],[1,3,8,10,11,13],[1,4,6,7,9,10],[1,4,8,9,12,13],[1,5,6,10,12,13],[1,5,7,10,12,13],[1,6,7,8,9,11],[2,3,6,8,10,13],[2,3,7,10,11,12],[2,4,6,9,10,12],[2,4,7,8,12,13],[2,5,6,7,8,13],[2,5,9,10,11,12],[2,6,7,9,11,13],[3,4,5,9,11,13],[3,4,6,11,12,13],[3,4,7,9,10,13],[3,5,6,8,9,12],[3,5,7,8,9,12],[4,5,6,8,10,11],[4,5,7,8,10,11]];
G[24]:=Group([(3,4)(6,7)(9,11)(10,12),(2,13)(3,10)(4,12)(9,11)]);
# Design 25: autom. group order 4, simple
B[25]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,7,9,12],[1,3,8,10,11,13],[1,4,6,7,10,11],[1,4,8,9,12,13],[1,5,6,10,12,13],[1,5,7,10,12,13],[1,6,7,8,9,11],[2,3,6,11,12,13],[2,3,7,11,12,13],[2,4,6,9,10,13],[2,4,7,9,10,13],[2,5,6,8,10,11],[2,5,7,8,9,12],[2,6,7,8,10,12],[3,4,5,8,10,12],[3,4,6,7,8,13],[3,4,9,10,11,12],[3,5,6,8,9,13],[3,5,7,9,10,11],[4,5,6,9,11,12],[4,5,7,8,11,13]];
G[25]:=Group([(3,4)(6,7)(9,11)(10,12),(2,13)(3,10)(4,12)(9,11)]);
# Design 26: autom. group order 4, simple
B[26]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,7,11,12],[1,3,8,10,11,13],[1,4,6,7,9,10],[1,4,8,9,12,13],[1,5,6,10,12,13],[1,5,7,10,12,13],[1,6,7,8,9,11],[2,3,6,9,12,13],[2,3,7,9,12,13],[2,4,6,10,11,13],[2,4,7,10,11,13],[2,5,6,8,9,10],[2,5,7,8,11,12],[2,6,7,8,10,12],[3,4,5,8,10,12],[3,4,6,7,8,13],[3,4,9,10,11,12],[3,5,6,8,11,13],[3,5,7,9,10,11],[4,5,6,9,11,12],[4,5,7,8,9,13]];
G[26]:=Group([(3,4)(6,7)(9,11)(10,12),(2,13)(3,10)(4,12)(9,11)]);
# Design 27: autom. group order 4, simple
B[27]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,8,10,13],[1,3,7,10,11,12],[1,4,6,11,12,13],[1,4,7,9,10,13],[1,5,6,9,10,12],[1,5,7,8,12,13],[1,6,7,8,9,11],[2,3,6,10,11,12],[2,3,7,9,12,13],[2,4,6,9,10,13],[2,4,7,8,10,12],[2,5,6,8,12,13],[2,5,7,10,11,13],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,8,13],[3,4,9,11,12,13],[3,5,6,7,9,12],[3,5,8,10,11,13],[4,5,6,7,10,11],[4,5,8,9,10,12]];
G[27]:=Group([(1,2)(3,5)(6,7)(8,11)(10,13),(1,6)(2,7)(3,8)(4,9)(5,11)(10,13)]);
# Design 28: autom. group order 4, simple
B[28]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,6,8,9,11],[1,3,5,11,12,13],[1,3,6,10,11,13],[1,4,5,9,10,13],[1,4,7,8,10,12],[1,5,7,9,12,13],[1,6,7,8,9,13],[1,6,7,10,11,12],[2,3,6,7,10,13],[2,3,7,9,10,12],[2,4,6,9,12,13],[2,4,7,9,11,13],[2,5,6,7,11,12],[2,5,8,10,11,13],[2,5,8,10,12,13],[3,4,6,8,12,13],[3,4,7,8,11,13],[3,4,9,10,11,12],[3,5,6,8,9,12],[3,5,7,8,9,11],[4,5,6,7,8,10],[4,5,6,9,10,11]];
G[28]:=Group([(2,5)(3,4)(6,7)(8,13)(11,12),(1,10)(3,8)(4,13)(6,12)(7,11)]);
# Design 29: autom. group order 4, simple, derived
B[29]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,6,9,11,13],[1,3,5,9,12,13],[1,3,6,8,10,12],[1,4,5,10,11,13],[1,4,7,8,10,13],[1,5,7,9,11,12],[1,6,7,8,9,11],[1,6,7,10,12,13],[2,3,6,10,11,13],[2,3,7,8,9,13],[2,4,6,7,9,12],[2,4,8,11,12,13],[2,5,6,7,10,11],[2,5,7,8,10,12],[2,5,9,10,12,13],[3,4,6,7,12,13],[3,4,7,9,10,11],[3,4,9,10,11,12],[3,5,6,8,11,12],[3,5,7,8,11,13],[4,5,6,8,9,10],[4,5,6,8,9,13]];
G[29]:=Group([(1,6,10,12)(2,5,9,11)(3,8)(7,13)]);
# Design 30: autom. group order 4, simple, derived
B[30]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,6,9,11,13],[1,3,5,8,12,13],[1,3,6,7,11,13],[1,4,6,8,10,13],[1,4,7,9,10,11],[1,5,7,9,12,13],[1,5,9,10,11,12],[1,6,7,8,10,12],[2,3,7,10,12,13],[2,3,10,11,12,13],[2,4,5,9,10,13],[2,4,7,8,11,12],[2,5,6,7,10,11],[2,5,6,8,9,12],[2,6,7,8,9,13],[3,4,6,7,9,12],[3,4,6,9,10,12],[3,4,8,9,11,13],[3,5,6,8,10,11],[3,5,7,8,9,11],[4,5,6,11,12,13],[4,5,7,8,10,13]];
G[30]:=Group([(1,6,10,11)(2,4,3,12)(5,9,13,8)]);
# Design 31: autom. group order 4, simple, derived
B[31]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,6,9,11,12],[1,3,5,10,11,13],[1,3,6,7,12,13],[1,4,7,9,10,12],[1,4,8,10,11,13],[1,5,6,9,11,13],[1,5,7,8,9,10],[1,6,7,8,12,13],[2,3,6,8,10,13],[2,3,7,9,11,13],[2,4,5,8,12,13],[2,4,7,9,11,13],[2,5,6,9,10,12],[2,5,7,10,12,13],[2,6,7,8,10,11],[3,4,6,7,8,9],[3,4,6,10,11,12],[3,4,9,10,12,13],[3,5,7,8,11,12],[3,5,8,9,11,12],[4,5,6,7,10,11],[4,5,6,8,9,13]];
G[31]:=Group([(1,2,11,12)(3,7)(4,9,8,6)(5,13)]);
# Design 32: autom. group order 4, simple, derived
B[32]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,6,9,11,13],[1,3,5,9,12,13],[1,3,7,8,12,13],[1,4,6,8,10,12],[1,4,6,9,11,13],[1,5,7,8,10,11],[1,5,7,9,10,11],[1,6,7,10,12,13],[2,3,6,7,10,11],[2,3,8,9,10,13],[2,4,5,10,12,13],[2,4,7,8,11,13],[2,5,6,7,9,12],[2,5,10,11,12,13],[2,6,7,8,9,12],[3,4,6,7,10,13],[3,4,7,9,11,12],[3,4,9,10,11,12],[3,5,6,8,11,12],[3,5,6,8,11,13],[4,5,6,8,9,10],[4,5,7,8,9,13]];
G[32]:=Group([(1,6,12,10)(2,5,11,9)(4,8)(7,13)]);
# Design 33: autom. group order 4, simple, derived
B[33]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,6,9,11,12],[1,3,5,10,11,13],[1,3,7,9,12,13],[1,4,6,8,10,13],[1,4,6,10,12,13],[1,5,7,8,10,11],[1,5,7,9,12,13],[1,6,7,8,9,11],[2,3,6,7,11,13],[2,3,8,9,10,13],[2,4,5,9,11,13],[2,4,7,8,12,13],[2,5,6,9,10,12],[2,5,7,8,10,12],[2,6,7,10,11,13],[3,4,6,7,8,9],[3,4,7,10,11,12],[3,4,9,10,11,12],[3,5,6,8,11,12],[3,5,6,8,12,13],[4,5,6,7,9,10],[4,5,8,9,11,13]];
G[33]:=Group([(1,5,11,10)(2,9,12,6)(3,13)(7,8)]);
# Design 34: autom. group order 4, simple, derived
B[34]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,8,9,11,13],[1,3,5,10,11,12],[1,3,6,7,9,12],[1,4,6,8,12,13],[1,4,7,9,10,13],[1,5,6,7,8,13],[1,5,10,11,12,13],[1,6,7,9,10,11],[2,3,6,10,11,13],[2,3,7,9,12,13],[2,4,5,9,10,13],[2,4,6,9,11,12],[2,5,6,7,11,13],[2,5,7,8,10,12],[2,6,7,8,10,12],[3,4,6,10,12,13],[3,4,7,8,10,11],[3,4,7,8,11,13],[3,5,6,8,9,11],[3,5,8,9,12,13],[4,5,6,8,9,10],[4,5,7,9,11,12]];
G[34]:=Group([(1,4,8,12)(2,11)(3,7,10,5)(6,13)]);
# Design 35: autom. group order 4, simple, derived
B[35]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,9,10,11,12],[1,3,5,8,11,13],[1,3,6,7,8,12],[1,4,6,9,11,13],[1,4,7,10,11,13],[1,5,6,9,12,13],[1,5,7,10,12,13],[1,6,7,8,9,10],[2,3,6,9,11,13],[2,3,7,10,11,13],[2,4,5,9,10,12],[2,4,6,7,12,13],[2,5,6,8,10,13],[2,5,7,8,9,13],[2,6,7,8,11,12],[3,4,6,7,9,10],[3,4,8,9,12,13],[3,4,8,10,12,13],[3,5,6,10,11,12],[3,5,7,9,11,12],[4,5,6,8,10,11],[4,5,7,8,9,11]];
G[35]:=Group([(6,7)(9,10),(1,8)(2,12)(5,13)(6,9,7,10)]);
# Design 36: autom. group order 4, simple, derived
B[36]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,9,10,11,12],[1,3,5,8,11,13],[1,3,6,7,8,12],[1,4,6,9,11,13],[1,4,7,10,11,13],[1,5,6,9,12,13],[1,5,7,10,12,13],[1,6,7,8,9,10],[2,3,6,10,11,13],[2,3,7,9,11,13],[2,4,5,9,10,12],[2,4,6,7,12,13],[2,5,6,8,10,13],[2,5,7,8,9,13],[2,6,7,8,11,12],[3,4,6,7,9,10],[3,4,8,9,12,13],[3,4,8,10,12,13],[3,5,6,9,11,12],[3,5,7,10,11,12],[4,5,6,8,10,11],[4,5,7,8,9,11]];
G[36]:=Group([(6,7)(9,10),(1,8)(2,12)(5,13)(6,9,7,10)]);
# Design 37: autom. group order 4, simple, derived
B[37]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,9,10,11,12],[1,3,5,8,11,13],[1,3,6,7,8,12],[1,4,6,9,11,13],[1,4,7,10,11,13],[1,5,6,10,12,13],[1,5,7,9,12,13],[1,6,7,8,9,10],[2,3,6,9,11,13],[2,3,7,10,11,13],[2,4,5,9,10,12],[2,4,6,7,12,13],[2,5,6,8,9,13],[2,5,7,8,10,13],[2,6,7,8,11,12],[3,4,6,7,9,10],[3,4,8,9,12,13],[3,4,8,10,12,13],[3,5,6,10,11,12],[3,5,7,9,11,12],[4,5,6,8,10,11],[4,5,7,8,9,11]];
G[37]:=Group([(6,7)(9,10),(1,8)(2,12)(5,13)(6,9,7,10)]);
# Design 38: autom. group order 4, simple, derived
B[38]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,9,10,11,12],[1,3,5,8,11,13],[1,3,6,7,8,12],[1,4,6,9,11,13],[1,4,7,10,11,13],[1,5,6,10,12,13],[1,5,7,9,12,13],[1,6,7,8,9,10],[2,3,6,10,11,13],[2,3,7,9,11,13],[2,4,5,9,10,12],[2,4,6,7,12,13],[2,5,6,8,9,13],[2,5,7,8,10,13],[2,6,7,8,11,12],[3,4,6,7,9,10],[3,4,8,9,12,13],[3,4,8,10,12,13],[3,5,6,9,11,12],[3,5,7,10,11,12],[4,5,6,8,10,11],[4,5,7,8,9,11]];
G[38]:=Group([(6,7)(9,10),(1,8)(2,12)(5,13)(6,9,7,10)]);
# Design 39: autom. group order 4, simple
B[39]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,7,8,13],[1,3,6,9,11,13],[1,3,7,9,11,12],[1,4,6,10,12,13],[1,4,8,9,10,12],[1,5,7,9,10,13],[1,5,8,11,12,13],[1,6,7,8,10,11],[2,3,6,10,12,13],[2,3,8,10,11,12],[2,4,6,9,11,13],[2,4,7,9,10,11],[2,5,7,11,12,13],[2,5,8,9,10,13],[2,6,7,8,9,12],[3,4,5,7,8,13],[3,4,7,10,12,13],[3,4,8,9,11,13],[3,5,6,7,9,12],[3,5,6,8,10,11],[4,5,6,7,10,11],[4,5,6,8,9,12]];
G[39]:=Group([(3,4)(7,8)(9,12)(10,11),(1,2)(7,8)(9,10)(11,12)]);
# Design 40: autom. group order 4, simple
B[40]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,7,8,13],[1,3,6,9,11,13],[1,3,7,9,11,12],[1,4,6,10,12,13],[1,4,8,9,10,12],[1,5,7,9,10,13],[1,5,8,11,12,13],[1,6,7,8,10,11],[2,3,6,10,12,13],[2,3,8,10,11,12],[2,4,6,9,11,13],[2,4,7,9,10,11],[2,5,7,11,12,13],[2,5,8,9,10,13],[2,6,7,8,9,12],[3,4,5,7,8,13],[3,4,7,10,12,13],[3,4,8,9,11,13],[3,5,6,7,10,11],[3,5,6,8,9,12],[4,5,6,7,9,12],[4,5,6,8,10,11]];
G[40]:=Group([(3,4)(7,8)(9,12)(10,11),(1,2)(7,8)(9,10)(11,12)]);
# Design 41: autom. group order 4, simple
B[41]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,5,10,11,13],[1,3,6,7,12,13],[1,3,8,9,10,12],[1,4,5,9,12,13],[1,4,6,8,10,13],[1,5,6,8,11,12],[1,6,7,8,9,11],[1,7,9,10,11,13],[2,3,6,9,10,13],[2,3,8,11,12,13],[2,4,6,7,11,13],[2,4,8,9,12,13],[2,5,6,8,9,11],[2,5,7,8,10,12],[2,6,7,9,10,12],[3,4,5,9,10,11],[3,4,6,9,11,12],[3,4,7,8,10,11],[3,5,6,8,10,13],[3,5,7,11,12,13],[4,5,6,7,10,12],[4,5,7,8,9,13]];
G[41]:=Group([(1,4,12,6)(2,9,7,8)(3,13,10,11)]);
# Design 42: autom. group order 4, simple, derived
B[42]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,11,12,13],[1,2,5,7,11,12],[1,3,6,7,9,13],[1,3,8,10,11,13],[1,4,6,10,12,13],[1,4,8,9,10,12],[1,5,6,8,11,13],[1,5,7,8,9,12],[1,6,7,9,10,11],[2,3,6,8,9,11],[2,3,9,10,12,13],[2,4,6,7,8,10],[2,4,8,9,11,13],[2,5,6,8,10,12],[2,5,7,10,11,13],[2,6,7,9,12,13],[3,4,5,7,10,13],[3,4,5,9,11,12],[3,4,6,7,11,12],[3,5,6,8,12,13],[3,7,8,10,11,12],[4,5,6,9,10,11],[4,5,7,8,9,13]];
G[42]:=Group([(1,5,12,7)(2,8,11,9)(3,6)(4,13)]);
# Design 43: autom. group order 4, simple, derived
B[43]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,9,13],[1,3,5,11,12,13],[1,3,6,8,11,13],[1,4,5,8,10,12],[1,4,6,7,10,13],[1,5,7,8,12,13],[1,6,9,10,11,12],[1,7,8,9,10,11],[2,3,7,10,12,13],[2,3,8,9,11,13],[2,4,5,10,11,13],[2,4,6,8,11,12],[2,5,6,7,9,12],[2,5,7,8,10,11],[2,6,8,10,12,13],[3,4,6,7,10,11],[3,4,7,8,9,12],[3,4,9,10,12,13],[3,5,6,7,11,12],[3,5,6,8,9,10],[4,5,6,8,9,13],[4,5,7,9,11,13]];
G[43]:=Group([(2,9)(3,11)(4,10)(5,12),(1,13)(2,4,9,10)(3,5,11,12)(6,7)]);
# Design 44: autom. group order 4, simple, derived
B[44]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,5,11,12,13],[1,3,6,7,9,13],[1,4,5,8,10,13],[1,4,6,8,9,12],[1,5,7,10,11,12],[1,6,7,8,10,12],[1,7,8,9,11,13],[2,3,7,8,11,12],[2,3,8,9,10,11],[2,4,5,7,12,13],[2,4,6,7,11,13],[2,5,6,7,8,10],[2,5,8,9,12,13],[2,6,9,10,12,13],[3,4,6,10,11,12],[3,4,7,9,10,13],[3,4,8,10,12,13],[3,5,6,7,9,12],[3,5,6,8,11,13],[4,5,6,8,9,11],[4,5,7,9,10,11]];
G[44]:=Group([(1,6)(3,13)(4,10)(5,11)(7,9)(8,12),(1,8)(4,7)(5,11)(6,12)(9,10)]);
# Design 45: autom. group order 4, simple, derived
B[45]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,9,13],[1,3,5,11,12,13],[1,3,6,8,11,13],[1,4,5,8,10,12],[1,4,6,7,10,13],[1,5,7,8,12,13],[1,6,9,10,11,12],[1,7,8,9,10,11],[2,3,7,10,12,13],[2,3,8,9,11,13],[2,4,5,10,11,13],[2,4,7,8,11,12],[2,5,6,7,9,12],[2,5,6,8,10,11],[2,6,8,10,12,13],[3,4,6,7,10,11],[3,4,6,8,9,12],[3,4,9,10,12,13],[3,5,6,7,11,12],[3,5,7,8,9,10],[4,5,6,8,9,13],[4,5,7,9,11,13]];
G[45]:=Group([(2,9)(3,11)(4,10)(5,12),(1,13)(2,4,9,10)(3,5,11,12)(6,7)]);
# Design 46: autom. group order 4, simple, derived
B[46]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,5,7,11,12],[1,3,6,7,10,13],[1,4,5,8,12,13],[1,4,9,10,12,13],[1,5,6,8,9,13],[1,6,7,8,11,12],[1,7,8,9,10,11],[2,3,6,8,9,12],[2,3,8,11,12,13],[2,4,5,7,11,13],[2,4,7,8,9,10],[2,5,6,8,10,11],[2,5,7,10,12,13],[2,6,7,9,12,13],[3,4,6,7,10,12],[3,4,6,9,11,13],[3,4,8,10,11,13],[3,5,7,8,9,13],[3,5,9,10,11,12],[4,5,6,7,9,11],[4,5,6,8,10,12]];
G[46]:=Group([(2,11)(3,7)(4,12)(5,8),(1,13)(2,3,11,7)(4,8,12,5)(6,10)]);
# Design 47: autom. group order 4, simple
B[47]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,7,11,12],[1,2,6,8,11,13],[1,3,5,9,11,12],[1,3,6,8,10,13],[1,4,5,8,12,13],[1,4,9,10,11,13],[1,5,6,7,10,11],[1,6,7,9,12,13],[1,7,8,9,10,12],[2,3,7,10,11,13],[2,3,8,9,12,13],[2,4,5,7,9,13],[2,4,6,9,10,12],[2,5,6,8,10,12],[2,5,10,11,12,13],[2,6,7,8,9,11],[3,4,6,7,10,12],[3,4,6,11,12,13],[3,4,8,9,10,11],[3,5,6,7,9,13],[3,5,7,8,11,12],[4,5,6,8,9,11],[4,5,7,8,10,13]];
G[47]:=Group([(1,11)(2,9)(3,8)(5,6)(7,10)(12,13),(1,12,11,13)(2,6,9,5)(3,10,8,7)]);
# Design 48: autom. group order 4, simple, derived
B[48]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,5,7,11,12],[1,3,6,7,10,13],[1,4,5,8,12,13],[1,4,9,10,12,13],[1,5,6,8,9,13],[1,6,7,8,11,12],[1,7,8,9,10,11],[2,3,8,9,10,12],[2,3,8,11,12,13],[2,4,5,7,11,13],[2,4,6,7,8,9],[2,5,6,8,10,11],[2,5,7,10,12,13],[2,6,7,9,12,13],[3,4,6,7,10,12],[3,4,6,9,11,13],[3,4,8,10,11,13],[3,5,6,9,11,12],[3,5,7,8,9,13],[4,5,6,8,10,12],[4,5,7,9,10,11]];
G[48]:=Group([(2,11)(3,7)(4,12)(5,8),(1,13)(2,3,11,7)(4,8,12,5)(6,10)]);
# Design 49: autom. group order 4, simple, derived
B[49]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,12],[1,3,5,11,12,13],[1,3,8,10,11,13],[1,4,5,6,10,13],[1,4,7,8,9,13],[1,5,7,9,10,12],[1,6,7,8,10,11],[1,6,8,9,12,13],[2,3,6,7,12,13],[2,3,8,10,12,13],[2,4,5,8,11,13],[2,4,8,9,10,12],[2,5,6,7,8,10],[2,5,7,9,11,13],[2,6,9,10,11,13],[3,4,6,7,9,13],[3,4,6,9,10,11],[3,4,7,10,11,12],[3,5,6,8,9,12],[3,5,7,8,9,11],[4,5,6,8,11,12],[4,5,7,10,12,13]];
G[49]:=Group([(1,8)(2,12)(3,6)(4,9)(7,13)(10,11),(1,10)(2,12)(3,7)(6,13)(8,11)]);
# Design 50: autom. group order 4, simple
B[50]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,5,11,12,13],[1,3,7,8,12,13],[1,4,5,7,9,13],[1,4,6,8,11,13],[1,5,6,8,10,12],[1,6,7,9,10,12],[1,7,8,9,10,11],[2,3,6,7,9,11],[2,3,8,10,11,13],[2,4,5,8,10,12],[2,4,7,10,12,13],[2,5,6,7,11,12],[2,5,7,8,9,13],[2,6,8,9,12,13],[3,4,6,8,9,10],[3,4,6,9,12,13],[3,4,7,10,11,12],[3,5,6,7,10,13],[3,5,8,9,11,12],[4,5,6,7,8,11],[4,5,9,10,11,13]];
G[50]:=Group([(1,6,12,13)(2,7,4,5)(3,11,10,9)]);
# Design 51: autom. group order 4, simple, derived
B[51]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,5,11,12,13],[1,3,7,10,12,13],[1,4,5,8,10,13],[1,4,6,8,9,12],[1,5,6,7,9,11],[1,6,7,8,10,12],[1,7,8,9,11,13],[2,3,7,8,11,12],[2,3,8,9,10,11],[2,4,5,7,12,13],[2,4,6,7,11,13],[2,5,6,7,8,10],[2,5,8,9,12,13],[2,6,9,10,12,13],[3,4,6,8,9,13],[3,4,6,10,11,12],[3,4,7,9,10,13],[3,5,6,7,9,12],[3,5,6,8,11,13],[4,5,7,9,10,11],[4,5,8,10,11,12]];
G[51]:=Group([(1,6)(3,13)(4,10)(5,11)(7,9)(8,12),(1,8)(4,7)(5,11)(6,12)(9,10)]);
# Design 52: autom. group order 4, simple, derived
B[52]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,12],[1,3,5,7,11,13],[1,3,8,9,12,13],[1,4,5,10,12,13],[1,4,6,9,10,13],[1,5,7,8,10,11],[1,6,7,8,9,13],[1,6,8,10,11,12],[2,3,6,8,10,13],[2,3,7,9,10,12],[2,4,5,8,11,13],[2,4,7,8,12,13],[2,5,6,8,10,12],[2,5,6,9,11,13],[2,7,9,10,11,13],[3,4,6,7,10,11],[3,4,6,8,9,11],[3,4,10,11,12,13],[3,5,6,7,12,13],[3,5,8,9,11,12],[4,5,6,7,9,12],[4,5,7,8,9,10]];
G[52]:=Group([(1,8,11,10)(3,4,13,9)(5,7)(6,12)]);
# Design 53: autom. group order 4, simple, derived
B[53]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,5,7,12,13],[1,3,8,10,12,13],[1,4,5,10,11,13],[1,4,6,7,9,12],[1,5,7,8,9,11],[1,6,7,8,10,12],[1,6,8,9,11,13],[2,3,6,8,11,12],[2,3,7,9,10,11],[2,4,5,8,12,13],[2,4,7,8,11,13],[2,5,6,7,8,10],[2,5,6,9,12,13],[2,7,9,10,12,13],[3,4,6,7,9,13],[3,4,6,10,11,12],[3,4,8,9,10,13],[3,5,6,7,11,13],[3,5,8,9,11,12],[4,5,6,8,9,10],[4,5,7,10,11,12]];
G[53]:=Group([(1,4,12,9)(2,11)(3,10,13,8)(6,7)]);
# Design 54: autom. group order 4, simple, derived
B[54]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,8,11,13],[1,3,5,6,12,13],[1,3,7,9,10,12],[1,4,5,10,11,13],[1,4,6,8,10,13],[1,5,8,9,11,12],[1,6,7,8,10,12],[1,6,7,9,11,13],[2,3,6,8,9,11],[2,3,7,10,11,13],[2,4,5,7,12,13],[2,4,6,10,11,12],[2,5,6,7,8,12],[2,5,8,9,10,13],[2,6,9,10,12,13],[3,4,6,8,9,13],[3,4,7,9,12,13],[3,4,8,10,11,12],[3,5,6,7,10,11],[3,5,8,11,12,13],[4,5,6,7,9,11],[4,5,7,8,9,10]];
G[54]:=Group([(1,3)(2,5)(4,6)(7,12)(8,13)(9,10),(1,9)(2,5)(3,10)(4,8)(6,13)]);
# Design 55: autom. group order 4, simple, derived
B[55]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,5,7,11,12],[1,3,6,8,9,10],[1,4,5,8,11,13],[1,4,6,7,10,13],[1,5,6,9,12,13],[1,6,7,8,11,12],[1,8,9,10,12,13],[2,3,6,7,12,13],[2,3,8,9,11,13],[2,4,5,10,12,13],[2,4,6,8,10,12],[2,5,6,8,11,13],[2,5,7,8,9,12],[2,6,7,9,10,11],[3,4,6,9,11,13],[3,4,7,9,12,13],[3,4,8,10,11,12],[3,5,6,10,11,12],[3,5,7,8,10,13],[4,5,6,7,8,9],[4,5,7,9,10,11]];
G[55]:=Group([(1,7,12,13)(2,5,4,8)(3,9,10,11)]);
# Design 56: autom. group order 4, simple, derived
B[56]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,8,11,13],[1,3,5,11,12,13],[1,3,7,10,12,13],[1,4,5,6,10,13],[1,4,6,8,9,12],[1,5,8,9,10,11],[1,6,7,8,10,12],[1,6,7,9,11,13],[2,3,6,8,11,13],[2,3,6,10,11,12],[2,4,5,7,12,13],[2,4,7,9,10,11],[2,5,6,7,8,10],[2,5,8,9,12,13],[2,6,9,10,12,13],[3,4,6,8,9,13],[3,4,7,9,10,13],[3,4,8,10,11,12],[3,5,6,7,9,11],[3,5,7,8,9,12],[4,5,6,7,11,12],[4,5,8,10,11,13]];
G[56]:=Group([(1,7)(2,11)(3,6)(4,9)(8,13)(10,12),(1,10)(2,11)(3,8)(6,13)(7,12)]);
# Design 57: autom. group order 4, simple, derived
B[57]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,6,11,12],[1,2,7,8,9,11],[1,3,5,7,11,13],[1,3,6,8,10,13],[1,4,7,10,11,13],[1,4,9,10,12,13],[1,5,6,8,10,12],[1,5,8,9,11,12],[1,6,7,9,12,13],[2,3,8,9,12,13],[2,3,10,11,12,13],[2,4,5,7,12,13],[2,4,6,8,9,13],[2,5,6,7,10,12],[2,5,8,10,11,13],[2,6,7,9,10,11],[3,4,5,9,11,12],[3,4,6,9,10,11],[3,4,7,8,10,12],[3,5,6,7,9,13],[3,6,7,8,11,12],[4,5,6,8,11,13],[4,5,7,8,9,10]];
G[57]:=Group([(1,2)(3,4)(5,6)(7,8)(9,11)(10,12),(1,7)(2,8)(3,4)(5,10)(6,12)]);
# Design 58: autom. group order 4, simple, derived
B[58]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,6,11,12],[1,2,7,8,9,11],[1,3,5,7,12,13],[1,3,6,8,9,13],[1,4,8,9,12,13],[1,4,10,11,12,13],[1,5,6,7,10,12],[1,5,8,10,11,13],[1,6,7,9,10,11],[2,3,7,10,11,13],[2,3,9,10,12,13],[2,4,5,7,11,13],[2,4,6,8,10,13],[2,5,6,8,10,12],[2,5,8,9,11,12],[2,6,7,9,12,13],[3,4,5,9,11,12],[3,4,6,9,10,11],[3,4,7,8,10,12],[3,5,6,8,11,13],[3,6,7,8,11,12],[4,5,6,7,9,13],[4,5,7,8,9,10]];
G[58]:=Group([(1,2)(3,4)(5,6)(7,8)(9,11)(10,12),(1,7)(2,8)(5,12)(6,10)(9,11)]);
# Design 59: autom. group order 4, simple, derived
B[59]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,13],[1,3,5,8,12,13],[1,3,6,10,12,13],[1,4,6,7,8,9],[1,4,6,10,11,12],[1,5,7,10,11,13],[1,5,8,9,11,12],[1,7,8,9,10,13],[2,3,7,10,11,12],[2,3,8,9,10,11],[2,4,5,7,12,13],[2,4,8,10,12,13],[2,5,6,7,8,10],[2,5,6,9,11,13],[2,6,8,9,12,13],[3,4,5,8,11,13],[3,4,6,9,10,13],[3,4,7,9,11,13],[3,5,6,7,9,12],[3,6,7,8,11,12],[4,5,6,8,10,11],[4,5,7,9,10,12]];
G[59]:=Group([(1,3,12,13)(2,7)(4,11)(5,6,8,10)]);
# Design 60: autom. group order 4, simple
B[60]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,6,9,10,13],[1,3,5,10,11,13],[1,3,6,8,10,12],[1,4,6,9,11,13],[1,4,7,9,12,13],[1,5,6,8,11,12],[1,5,7,8,12,13],[1,7,8,9,10,11],[2,3,6,11,12,13],[2,3,8,9,12,13],[2,4,5,9,10,12],[2,4,6,7,8,11],[2,5,7,10,11,12],[2,5,8,9,11,13],[2,6,7,8,10,13],[3,4,5,8,10,13],[3,4,7,10,11,13],[3,4,8,9,11,12],[3,5,6,7,9,11],[3,6,7,9,10,12],[4,5,6,7,12,13],[4,5,6,8,9,10]];
G[60]:=Group([(2,3)(4,5)(8,9)(12,13),(1,7)(2,12)(3,13)(4,5)]);
# Design 61: autom. group order 4, simple
B[61]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,6,9,10,13],[1,3,5,10,11,13],[1,3,6,8,10,12],[1,4,6,8,11,13],[1,4,7,9,12,13],[1,5,6,9,11,12],[1,5,7,8,12,13],[1,7,8,9,10,11],[2,3,6,11,12,13],[2,3,8,9,12,13],[2,4,5,8,10,12],[2,4,6,7,9,11],[2,5,7,10,11,12],[2,5,8,9,11,13],[2,6,7,8,10,13],[3,4,5,9,10,13],[3,4,7,10,11,13],[3,4,8,9,11,12],[3,5,6,7,8,11],[3,6,7,9,10,12],[4,5,6,7,12,13],[4,5,6,8,9,10]];
G[61]:=Group([(2,3)(4,5)(8,9)(12,13),(1,7)(2,12)(3,13)(4,5)]);
# Design 62: autom. group order 4, simple
B[62]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,6,8,10,13],[1,3,5,10,11,13],[1,3,6,9,10,12],[1,4,6,9,11,13],[1,4,7,9,12,13],[1,5,6,8,11,12],[1,5,7,8,12,13],[1,7,8,9,10,11],[2,3,6,11,12,13],[2,3,8,9,12,13],[2,4,5,9,10,12],[2,4,6,7,8,11],[2,5,7,10,11,12],[2,5,8,9,11,13],[2,6,7,9,10,13],[3,4,5,8,10,13],[3,4,7,10,11,13],[3,4,8,9,11,12],[3,5,6,7,9,11],[3,6,7,8,10,12],[4,5,6,7,12,13],[4,5,6,8,9,10]];
G[62]:=Group([(2,3)(4,5)(8,9)(12,13),(1,7)(2,12)(3,13)(4,5)]);
# Design 63: autom. group order 4, simple
B[63]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,6,8,10,13],[1,3,5,10,11,13],[1,3,6,9,10,12],[1,4,6,8,11,13],[1,4,7,9,12,13],[1,5,6,9,11,12],[1,5,7,8,12,13],[1,7,8,9,10,11],[2,3,6,11,12,13],[2,3,8,9,12,13],[2,4,5,8,10,12],[2,4,6,7,9,11],[2,5,7,10,11,12],[2,5,8,9,11,13],[2,6,7,9,10,13],[3,4,5,9,10,13],[3,4,7,10,11,13],[3,4,8,9,11,12],[3,5,6,7,8,11],[3,6,7,8,10,12],[4,5,6,7,12,13],[4,5,6,8,9,10]];
G[63]:=Group([(2,3)(4,5)(8,9)(12,13),(1,7)(2,12)(3,13)(4,5)]);
# Design 64: autom. group order 4, simple
B[64]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,6,9,10,13],[1,3,5,10,11,13],[1,3,6,8,10,12],[1,4,6,9,11,12],[1,4,7,9,12,13],[1,5,6,8,11,13],[1,5,7,8,12,13],[1,7,8,9,10,11],[2,3,6,11,12,13],[2,3,8,9,12,13],[2,4,5,8,10,12],[2,4,8,9,11,13],[2,5,6,7,9,11],[2,5,7,10,11,12],[2,6,7,8,10,13],[3,4,5,9,10,13],[3,4,6,7,8,11],[3,4,7,10,11,13],[3,5,8,9,11,12],[3,6,7,9,10,12],[4,5,6,7,12,13],[4,5,6,8,9,10]];
G[64]:=Group([(2,3)(4,5)(8,9)(12,13),(1,7)(2,12)(3,13)(4,5)]);
# Design 65: autom. group order 4, simple
B[65]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,6,9,10,13],[1,3,5,10,11,13],[1,3,6,8,10,12],[1,4,6,8,11,12],[1,4,7,9,12,13],[1,5,6,9,11,13],[1,5,7,8,12,13],[1,7,8,9,10,11],[2,3,6,11,12,13],[2,3,8,9,12,13],[2,4,5,9,10,12],[2,4,8,9,11,13],[2,5,6,7,8,11],[2,5,7,10,11,12],[2,6,7,8,10,13],[3,4,5,8,10,13],[3,4,6,7,9,11],[3,4,7,10,11,13],[3,5,8,9,11,12],[3,6,7,9,10,12],[4,5,6,7,12,13],[4,5,6,8,9,10]];
G[65]:=Group([(2,3)(4,5)(8,9)(12,13),(1,7)(2,12)(3,13)(4,5)]);
# Design 66: autom. group order 4, simple
B[66]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,6,8,10,13],[1,3,5,10,11,13],[1,3,6,9,10,12],[1,4,6,9,11,12],[1,4,7,9,12,13],[1,5,6,8,11,13],[1,5,7,8,12,13],[1,7,8,9,10,11],[2,3,6,11,12,13],[2,3,8,9,12,13],[2,4,5,8,10,12],[2,4,8,9,11,13],[2,5,6,7,9,11],[2,5,7,10,11,12],[2,6,7,9,10,13],[3,4,5,9,10,13],[3,4,6,7,8,11],[3,4,7,10,11,13],[3,5,8,9,11,12],[3,6,7,8,10,12],[4,5,6,7,12,13],[4,5,6,8,9,10]];
G[66]:=Group([(2,3)(4,5)(8,9)(12,13),(1,7)(2,12)(3,13)(4,5)]);
# Design 67: autom. group order 4, simple
B[67]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,10,11,12],[1,2,6,8,10,13],[1,3,5,10,11,13],[1,3,6,9,10,12],[1,4,6,8,11,12],[1,4,7,9,12,13],[1,5,6,9,11,13],[1,5,7,8,12,13],[1,7,8,9,10,11],[2,3,6,11,12,13],[2,3,8,9,12,13],[2,4,5,9,10,12],[2,4,8,9,11,13],[2,5,6,7,8,11],[2,5,7,10,11,12],[2,6,7,9,10,13],[3,4,5,8,10,13],[3,4,6,7,9,11],[3,4,7,10,11,13],[3,5,8,9,11,12],[3,6,7,8,10,12],[4,5,6,7,12,13],[4,5,6,8,9,10]];
G[67]:=Group([(2,3)(4,5)(8,9)(12,13),(1,7)(2,12)(3,13)(4,5)]);
# Design 68: autom. group order 4, simple
B[68]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,13],[1,3,5,8,11,13],[1,3,6,7,10,12],[1,4,6,10,11,12],[1,4,7,8,12,13],[1,5,6,9,10,13],[1,5,7,8,9,11],[1,8,9,10,12,13],[2,3,7,9,12,13],[2,3,8,10,11,13],[2,4,5,9,12,13],[2,4,6,8,10,13],[2,5,6,8,11,12],[2,5,7,10,11,12],[2,6,7,8,9,10],[3,4,5,8,10,12],[3,4,6,9,11,13],[3,4,7,9,10,11],[3,5,6,7,12,13],[3,6,8,9,11,12],[4,5,6,7,8,9],[4,5,7,10,11,13]];
G[68]:=Group([(1,8,11,12)(2,10,7,3)(4,13,5,6)]);
# Design 69: autom. group order 4, simple, derived
B[69]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,5,11,12,13],[1,3,6,7,9,13],[1,4,6,8,9,12],[1,4,8,10,11,13],[1,5,7,8,9,13],[1,5,7,10,11,12],[1,6,7,8,10,12],[2,3,7,8,11,12],[2,3,8,9,10,11],[2,4,5,7,12,13],[2,4,6,7,11,13],[2,5,6,7,8,10],[2,5,8,9,12,13],[2,6,9,10,12,13],[3,4,5,6,10,12],[3,4,7,9,10,13],[3,4,8,10,12,13],[3,5,6,8,11,13],[3,6,7,9,11,12],[4,5,6,8,9,11],[4,5,7,9,10,11]];
G[69]:=Group([(1,6)(3,13)(4,10)(5,11)(7,9)(8,12),(1,8)(4,7)(5,11)(6,12)(9,10)]);
# Design 70: autom. group order 4, simple
B[70]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,13],[1,3,5,8,12,13],[1,3,8,10,11,13],[1,4,6,7,10,12],[1,4,6,9,10,13],[1,5,6,8,10,11],[1,5,7,9,11,12],[1,7,8,9,12,13],[2,3,6,9,12,13],[2,3,7,9,10,11],[2,4,5,8,11,12],[2,4,7,8,10,13],[2,5,6,8,9,13],[2,5,7,10,12,13],[2,6,8,10,11,12],[3,4,5,7,11,13],[3,4,6,11,12,13],[3,4,8,9,10,12],[3,5,6,7,10,12],[3,6,7,8,9,11],[4,5,6,7,8,9],[4,5,9,10,11,13]];
G[70]:=Group([(1,8,11,12)(2,9,13,10)(3,6,4,7)]);
# Design 71: autom. group order 4, simple, derived
B[71]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,13],[1,3,5,11,12,13],[1,3,7,10,11,13],[1,4,6,7,10,12],[1,4,8,9,10,13],[1,5,6,7,8,9],[1,5,8,10,12,13],[1,6,8,9,11,12],[2,3,6,8,10,11],[2,3,6,9,12,13],[2,4,5,8,11,13],[2,4,7,8,12,13],[2,5,6,8,10,12],[2,5,7,9,10,13],[2,7,9,10,11,12],[3,4,5,7,9,12],[3,4,6,10,12,13],[3,4,8,9,10,11],[3,5,7,8,11,12],[3,6,7,8,9,13],[4,5,6,7,10,11],[4,5,6,9,11,13]];
G[71]:=Group([(1,5,13,12)(2,4,6,9)(3,11)(8,10)]);
# Design 72: autom. group order 4, simple, derived
B[72]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,13],[1,3,5,11,12,13],[1,3,7,10,11,13],[1,4,6,7,8,12],[1,4,8,9,10,13],[1,5,6,7,9,10],[1,5,8,10,12,13],[1,6,8,9,11,12],[2,3,6,8,10,11],[2,3,6,9,12,13],[2,4,5,8,11,13],[2,4,7,10,12,13],[2,5,6,8,10,12],[2,5,7,8,9,13],[2,7,9,10,11,12],[3,4,5,7,9,12],[3,4,6,10,12,13],[3,4,8,9,10,11],[3,5,7,8,11,12],[3,6,7,8,9,13],[4,5,6,7,10,11],[4,5,6,9,11,13]];
G[72]:=Group([(1,5,13,12)(2,4,6,9)(3,11)(8,10)]);
# Design 73: autom. group order 4, simple, derived
B[73]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,12],[1,3,5,8,11,13],[1,3,7,10,12,13],[1,4,6,8,10,12],[1,4,8,9,11,13],[1,5,6,7,11,13],[1,5,7,8,9,10],[1,6,9,10,12,13],[2,3,6,8,9,13],[2,3,6,10,11,13],[2,4,5,9,12,13],[2,4,7,10,11,13],[2,5,6,7,8,12],[2,5,8,10,12,13],[2,7,8,9,10,11],[3,4,5,10,11,12],[3,4,6,7,9,10],[3,4,7,8,12,13],[3,5,7,9,11,12],[3,6,8,9,11,12],[4,5,6,7,9,13],[4,5,6,8,10,11]];
G[73]:=Group([(1,2,11,12)(3,10)(4,7,9,6)(5,13)]);
# Design 74: autom. group order 4, simple, derived
B[74]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,11,12,13],[1,2,6,9,11,12],[1,3,5,7,11,13],[1,3,8,10,11,13],[1,4,6,7,10,13],[1,4,7,9,10,12],[1,5,6,7,8,12],[1,5,8,9,12,13],[1,6,8,9,10,11],[2,3,6,9,12,13],[2,3,8,10,12,13],[2,4,5,6,8,11],[2,4,7,8,9,13],[2,5,7,8,10,12],[2,5,7,9,10,11],[2,6,7,10,11,13],[3,4,5,10,11,12],[3,4,6,8,9,10],[3,4,7,9,11,12],[3,5,6,7,9,13],[3,6,7,8,11,12],[4,5,6,10,12,13],[4,5,8,9,11,13]];
G[74]:=Group([(1,6)(2,10)(3,13)(5,7)(8,12)(9,11),(1,9)(2,8)(3,13)(6,11)(10,12)]);
# Design 75: autom. group order 4, simple
B[75]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,7,9],[1,2,4,9,10,11],[1,2,6,8,10,12],[1,3,5,10,11,13],[1,3,8,9,11,12],[1,4,6,7,12,13],[1,4,8,10,11,13],[1,5,6,9,11,12],[1,5,7,8,12,13],[1,6,7,9,10,13],[2,3,6,11,12,13],[2,3,7,10,12,13],[2,4,5,11,12,13],[2,4,6,8,9,13],[2,5,6,7,10,11],[2,5,8,9,10,13],[2,7,8,9,11,12],[3,4,5,8,10,12],[3,4,6,9,10,12],[3,4,7,9,11,13],[3,5,6,8,9,13],[3,6,7,8,10,11],[4,5,6,7,8,11],[4,5,7,9,10,12]];
G[75]:=Group([(1,11,12,13)(2,7,10,9)(3,6,4,8)]);
# Design 76: autom. group order 4, simple
B[76]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,13],[1,3,5,8,11,12],[1,3,7,9,12,13],[1,4,6,8,10,13],[1,4,7,9,10,11],[1,5,6,8,9,13],[1,5,7,10,12,13],[1,6,8,10,11,12],[2,3,6,9,10,13],[2,3,8,10,11,13],[2,4,5,8,12,13],[2,4,6,7,10,12],[2,5,6,9,11,12],[2,5,7,8,10,11],[2,7,8,9,12,13],[3,4,5,7,11,13],[3,4,6,11,12,13],[3,4,8,9,10,12],[3,5,6,7,10,12],[3,6,7,8,9,11],[4,5,6,7,8,9],[4,5,9,10,11,13]];
G[76]:=Group([(1,9,13,10)(2,8,11,12)(3,6,4,7)]);
# Design 77: autom. group order 4, simple, derived
B[77]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,5,7,12,13],[1,3,8,10,12,13],[1,4,6,7,8,9],[1,4,8,10,11,12],[1,5,6,8,11,13],[1,5,7,9,11,12],[1,6,7,9,10,13],[2,3,6,8,11,12],[2,3,7,9,10,11],[2,4,5,10,12,13],[2,4,6,7,12,13],[2,5,6,7,8,10],[2,5,8,9,11,13],[2,7,8,9,12,13],[3,4,5,7,11,13],[3,4,6,9,11,13],[3,4,8,9,10,13],[3,5,6,8,9,12],[3,6,7,10,11,12],[4,5,6,9,10,12],[4,5,7,8,10,11]];
G[77]:=Group([(1,3,12,13)(2,6)(4,11)(5,8,7,10)]);
# Design 78: autom. group order 4, simple, derived
B[78]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,8,11],[1,3,5,7,12,13],[1,3,8,10,12,13],[1,4,6,9,12,13],[1,4,7,10,11,13],[1,5,6,8,11,13],[1,5,7,9,10,11],[1,6,8,9,10,12],[2,3,6,9,11,13],[2,3,8,10,11,13],[2,4,5,8,12,13],[2,4,7,9,10,13],[2,5,6,10,11,12],[2,5,7,8,9,12],[2,6,7,10,12,13],[3,4,5,10,11,12],[3,4,6,7,11,12],[3,4,6,8,9,10],[3,5,6,7,9,13],[3,7,8,9,11,12],[4,5,6,7,8,10],[4,5,8,9,11,13]];
G[78]:=Group([(1,8,12,10)(2,5,11,7)(3,13)(6,9)]);
# Design 79: autom. group order 4, simple, derived
B[79]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,5,11,12,13],[1,3,7,8,9,12],[1,4,6,7,9,13],[1,4,6,8,11,13],[1,5,6,9,10,12],[1,5,7,8,10,11],[1,6,8,10,12,13],[2,3,6,7,10,13],[2,3,6,8,11,12],[2,4,5,8,12,13],[2,4,9,10,12,13],[2,5,6,7,11,12],[2,5,7,8,9,13],[2,6,8,9,10,11],[3,4,5,10,11,13],[3,4,6,7,10,12],[3,4,8,9,10,11],[3,5,6,8,9,13],[3,7,9,11,12,13],[4,5,6,7,9,11],[4,5,7,8,10,12]];
G[79]:=Group([(1,3,11,6)(2,13)(4,5,12,8)(7,10)]);
# Design 80: autom. group order 4, simple, derived
B[80]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,5,11,12,13],[1,3,8,9,10,12],[1,4,6,7,9,13],[1,4,6,8,11,13],[1,5,6,7,9,12],[1,5,7,8,10,11],[1,6,8,10,12,13],[2,3,6,7,10,13],[2,3,6,8,11,12],[2,4,5,8,12,13],[2,4,9,10,12,13],[2,5,6,7,11,12],[2,5,7,8,9,13],[2,6,8,9,10,11],[3,4,5,10,11,13],[3,4,6,7,10,12],[3,4,7,8,9,11],[3,5,6,8,9,13],[3,7,9,11,12,13],[4,5,6,9,10,11],[4,5,7,8,10,12]];
G[80]:=Group([(1,3,11,6)(2,13)(4,5,12,8)(7,10)]);
# Design 81: autom. group order 4, simple
B[81]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,5,7,12,13],[1,3,8,10,11,13],[1,4,6,7,9,11],[1,4,6,10,12,13],[1,5,6,8,11,12],[1,5,8,9,12,13],[1,6,7,8,9,10],[2,3,6,7,10,12],[2,3,9,11,12,13],[2,4,5,6,8,13],[2,4,7,8,12,13],[2,5,6,9,10,13],[2,5,7,8,9,11],[2,6,8,10,11,12],[3,4,5,8,10,11],[3,4,6,9,11,13],[3,4,8,9,10,12],[3,5,6,7,11,12],[3,6,7,8,9,13],[4,5,7,9,10,12],[4,5,7,10,11,13]];
G[81]:=Group([(1,7,13,8)(2,12,9,10)(4,5,6,11)]);
# Design 82: autom. group order 4, simple
B[82]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,11,12,13],[1,2,6,9,11,12],[1,3,6,7,10,13],[1,3,7,11,12,13],[1,4,5,7,10,11],[1,4,5,8,9,12],[1,5,8,10,12,13],[1,6,7,8,9,11],[1,6,8,9,10,13],[2,3,6,8,12,13],[2,3,8,9,10,11],[2,4,7,8,10,13],[2,4,9,10,11,13],[2,5,6,7,8,11],[2,5,6,7,10,12],[2,5,7,9,12,13],[3,4,5,6,9,13],[3,4,6,10,11,12],[3,4,7,8,9,12],[3,5,7,9,11,13],[3,5,8,10,11,12],[4,5,6,8,11,13],[4,6,7,9,10,12]];
G[82]:=Group([(1,2,5,12)(3,7,8,11)(4,6,10,13)]);
# Design 83: autom. group order 4, simple
B[83]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,6,11,12],[1,2,7,8,9,11],[1,3,6,7,9,13],[1,3,7,11,12,13],[1,4,5,7,10,13],[1,4,9,10,11,12],[1,5,6,8,10,12],[1,5,8,9,12,13],[1,6,8,10,11,13],[2,3,6,8,12,13],[2,3,9,10,11,12],[2,4,5,8,11,13],[2,4,8,9,10,13],[2,5,6,7,10,12],[2,5,7,9,12,13],[2,6,7,10,11,13],[3,4,5,11,12,13],[3,4,6,9,10,13],[3,4,7,8,10,12],[3,5,6,8,9,11],[3,5,7,8,10,11],[4,5,6,7,9,11],[4,6,7,8,9,12]];
G[83]:=Group([(1,2)(3,4)(5,6)(7,8)(9,11)(10,12),(1,7)(2,8)(5,10)(6,12)(9,11)]);
# Design 84: autom. group order 4, simple
B[84]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,6,11,12],[1,2,7,8,9,11],[1,3,6,7,11,13],[1,3,7,9,12,13],[1,4,5,7,10,13],[1,4,9,10,11,12],[1,5,6,8,10,12],[1,5,8,11,12,13],[1,6,8,9,10,13],[2,3,6,8,12,13],[2,3,9,10,11,12],[2,4,5,8,9,13],[2,4,8,10,11,13],[2,5,6,7,10,12],[2,5,7,11,12,13],[2,6,7,9,10,13],[3,4,5,9,12,13],[3,4,6,10,11,13],[3,4,7,8,10,12],[3,5,6,8,9,11],[3,5,7,8,10,11],[4,5,6,7,9,11],[4,6,7,8,9,12]];
G[84]:=Group([(1,2)(3,4)(5,6)(7,8)(9,11)(10,12),(1,7)(2,8)(5,10)(6,12)(9,11)]);
# Design 85: autom. group order 4, simple, derived
B[85]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,6,11,12],[1,2,7,8,9,11],[1,3,6,7,11,13],[1,3,7,9,12,13],[1,4,5,7,10,13],[1,4,9,10,12,13],[1,5,6,8,10,12],[1,5,8,11,12,13],[1,6,8,9,10,11],[2,3,6,8,12,13],[2,3,10,11,12,13],[2,4,5,8,9,13],[2,4,8,10,11,13],[2,5,6,7,10,12],[2,5,7,9,11,12],[2,6,7,9,10,13],[3,4,5,9,11,12],[3,4,6,9,10,11],[3,4,7,8,10,12],[3,5,6,8,9,13],[3,5,7,8,10,11],[4,5,6,7,11,13],[4,6,7,8,9,12]];
G[85]:=Group([(1,2)(3,4)(5,6)(7,8)(9,11)(10,12),(1,7)(2,8)(5,10)(6,12)(9,11)]);
# Design 86: autom. group order 4, simple
B[86]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,11,12,13],[1,2,6,7,9,11],[1,3,6,8,12,13],[1,3,6,9,10,12],[1,4,5,8,9,13],[1,4,7,9,11,12],[1,5,6,10,11,13],[1,5,7,8,10,11],[1,7,8,10,12,13],[2,3,7,10,11,12],[2,3,8,9,11,13],[2,4,5,7,10,13],[2,4,6,8,10,12],[2,5,6,11,12,13],[2,5,8,9,10,12],[2,6,7,8,9,13],[3,4,5,8,11,12],[3,4,6,7,10,13],[3,4,9,10,11,13],[3,5,6,7,8,11],[3,5,7,9,12,13],[4,5,6,7,9,12],[4,6,8,9,10,11]];
G[86]:=Group([(1,9)(2,12)(3,7)(4,5)(8,13)(10,11),(1,10,9,11)(2,13,12,8)(3,4,7,5)]);
# Design 87: autom. group order 4, simple, derived
B[87]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,6,7,12,13],[1,3,6,8,9,13],[1,4,5,7,10,13],[1,4,8,9,10,12],[1,5,6,7,11,12],[1,5,8,10,11,12],[1,7,8,9,11,13],[2,3,7,8,11,12],[2,3,7,9,10,11],[2,4,5,8,12,13],[2,4,6,8,11,13],[2,5,6,7,8,10],[2,5,7,9,12,13],[2,6,9,10,12,13],[3,4,5,9,11,13],[3,4,6,10,11,12],[3,4,7,10,12,13],[3,5,6,8,9,12],[3,5,8,10,11,13],[4,5,6,7,9,11],[4,6,7,8,9,10]];
G[87]:=Group([(1,6)(3,13)(4,10)(5,11)(7,12)(8,9),(1,7)(4,8)(5,11)(6,12)(9,10)]);
# Design 88: autom. group order 4, simple, derived
B[88]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,11,12,13],[1,2,6,9,11,12],[1,3,6,7,10,11],[1,3,8,9,11,13],[1,4,5,8,9,12],[1,4,6,7,8,13],[1,5,6,10,12,13],[1,5,7,8,10,11],[1,7,9,10,12,13],[2,3,6,7,12,13],[2,3,8,10,11,12],[2,4,5,7,10,12],[2,4,8,9,10,13],[2,5,6,8,11,13],[2,5,7,9,11,13],[2,6,7,8,9,10],[3,4,5,10,11,13],[3,4,6,9,10,13],[3,4,7,9,11,12],[3,5,6,8,9,12],[3,5,7,8,12,13],[4,5,6,7,9,11],[4,6,8,10,11,12]];
G[88]:=Group([(1,10,11,12)(2,13,7,8)(3,4,9,5)]);
# Design 89: autom. group order 4, simple, derived
B[89]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,12],[1,3,6,7,11,13],[1,3,8,10,11,13],[1,4,5,8,12,13],[1,4,8,9,10,11],[1,5,6,7,8,10],[1,5,6,9,12,13],[1,7,9,10,12,13],[2,3,6,9,10,13],[2,3,7,8,9,12],[2,4,5,10,11,13],[2,4,7,10,12,13],[2,5,6,8,10,12],[2,5,7,8,11,13],[2,6,8,9,11,13],[3,4,5,7,9,13],[3,4,6,8,12,13],[3,4,6,10,11,12],[3,5,7,10,11,12],[3,5,8,9,11,12],[4,5,6,7,9,11],[4,6,7,8,9,10]];
G[89]:=Group([(2,12)(3,13)(4,9)(8,10),(1,11)(2,3,12,13)(4,10,9,8)(6,7)]);
# Design 90: autom. group order 4, simple, derived
B[90]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,6,7,12,13],[1,3,8,10,12,13],[1,4,5,7,10,13],[1,4,8,9,10,12],[1,5,6,7,11,12],[1,5,6,8,9,11],[1,7,8,9,11,13],[2,3,7,8,11,12],[2,3,7,9,10,11],[2,4,5,8,12,13],[2,4,6,8,11,13],[2,5,6,7,8,10],[2,5,7,9,12,13],[2,6,9,10,12,13],[3,4,5,9,11,13],[3,4,6,7,9,13],[3,4,6,10,11,12],[3,5,6,8,9,12],[3,5,8,10,11,13],[4,5,7,10,11,12],[4,6,7,8,9,10]];
G[90]:=Group([(1,6)(3,13)(4,10)(5,11)(7,12)(8,9),(1,7)(4,8)(5,11)(6,12)(9,10)]);
# Design 91: autom. group order 4, simple
B[91]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,7,11,12],[1,2,9,10,11,12],[1,3,6,7,9,13],[1,3,8,11,12,13],[1,4,5,6,11,13],[1,4,8,9,10,13],[1,5,6,8,10,11],[1,5,7,8,9,12],[1,6,7,10,12,13],[2,3,6,11,12,13],[2,3,7,8,10,13],[2,4,5,8,12,13],[2,4,6,9,10,13],[2,5,6,7,9,12],[2,5,8,9,11,13],[2,6,7,8,10,11],[3,4,5,7,10,11],[3,4,6,8,9,12],[3,4,9,10,11,12],[3,5,6,8,10,12],[3,5,7,9,11,13],[4,5,7,10,12,13],[4,6,7,8,9,11]];
G[91]:=Group([(1,2)(3,4)(5,7)(6,8)(9,12)(10,11),(1,6)(2,8)(3,10)(4,11)(9,12)]);
# Design 92: autom. group order 4, simple
B[92]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,7,11,12],[1,2,9,10,11,12],[1,3,6,7,11,13],[1,3,8,9,12,13],[1,4,5,6,12,13],[1,4,8,10,11,13],[1,5,6,8,10,12],[1,5,7,8,9,11],[1,6,7,9,10,13],[2,3,6,9,12,13],[2,3,7,8,10,13],[2,4,5,8,9,13],[2,4,6,10,11,13],[2,5,6,7,9,11],[2,5,8,11,12,13],[2,6,7,8,10,12],[3,4,5,7,10,12],[3,4,6,8,9,11],[3,4,9,10,11,12],[3,5,6,8,10,11],[3,5,7,11,12,13],[4,5,7,9,10,13],[4,6,7,8,9,12]];
G[92]:=Group([(1,2)(3,4)(5,7)(6,8)(9,11)(10,12),(1,6)(2,8)(3,10)(4,12)(9,11)]);
# Design 93: autom. group order 4, simple, derived
B[93]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,12],[1,3,6,9,10,13],[1,3,7,8,9,11],[1,4,5,8,12,13],[1,4,6,7,11,13],[1,5,6,7,12,13],[1,5,6,8,10,11],[1,8,9,10,12,13],[2,3,6,8,12,13],[2,3,7,10,12,13],[2,4,5,10,11,13],[2,4,6,8,9,12],[2,5,6,7,8,10],[2,5,8,9,11,13],[2,6,7,9,11,13],[3,4,5,7,9,13],[3,4,6,10,11,12],[3,4,8,10,11,13],[3,5,6,9,11,12],[3,5,7,8,11,12],[4,5,7,9,10,12],[4,6,7,8,9,10]];
G[93]:=Group([(1,3,11,13)(2,12)(4,6,9,8)(7,10)]);
# Design 94: autom. group order 4, simple, derived
B[94]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,6,9,10,11],[1,3,7,8,11,12],[1,4,5,8,12,13],[1,4,6,8,11,13],[1,5,6,7,8,10],[1,5,6,9,12,13],[1,7,9,10,12,13],[2,3,6,7,12,13],[2,3,8,10,12,13],[2,4,5,10,11,13],[2,4,6,7,9,12],[2,5,6,8,10,12],[2,5,7,8,9,11],[2,6,8,9,11,13],[3,4,5,7,9,13],[3,4,6,10,11,12],[3,4,8,9,10,13],[3,5,6,7,11,13],[3,5,8,9,11,12],[4,5,7,10,11,12],[4,6,7,8,9,10]];
G[94]:=Group([(2,12)(3,13)(4,9)(8,10),(1,11)(2,4,12,9)(3,10,13,8)(6,7)]);
# Design 95: autom. group order 4, simple, derived
B[95]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,12],[1,3,6,8,11,13],[1,3,7,10,11,13],[1,4,5,8,12,13],[1,4,6,10,12,13],[1,5,6,8,9,11],[1,5,7,9,12,13],[1,6,7,8,9,10],[2,3,6,8,12,13],[2,3,9,11,12,13],[2,4,5,8,10,11],[2,4,7,8,9,13],[2,5,6,7,11,13],[2,5,6,9,10,13],[2,6,7,8,10,12],[3,4,5,7,10,13],[3,4,6,7,9,11],[3,4,6,9,10,12],[3,5,7,8,9,12],[3,5,8,10,11,12],[4,5,6,7,11,12],[4,8,9,10,11,13]];
G[95]:=Group([(2,12)(3,13)(6,8)(7,10),(1,11)(2,6,12,8)(3,7,13,10)(4,5)]);
# Design 96: autom. group order 4, simple
B[96]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,13],[1,3,6,9,12,13],[1,3,10,11,12,13],[1,4,5,8,11,13],[1,4,6,7,9,10],[1,5,6,8,10,13],[1,5,7,8,11,12],[1,7,8,9,10,12],[2,3,6,8,12,13],[2,3,7,8,10,11],[2,4,8,10,12,13],[2,4,9,10,11,13],[2,5,6,7,10,12],[2,5,6,8,9,11],[2,5,7,9,12,13],[3,4,5,7,10,13],[3,4,5,8,9,12],[3,4,6,7,11,12],[3,5,7,9,11,13],[3,6,8,9,10,11],[4,5,6,10,11,12],[4,6,7,8,9,13]];
G[96]:=Group([(1,3,13,5)(2,12,7,8)(4,6,9,11)]);
# Design 97: autom. group order 4, simple, derived
B[97]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,12],[1,3,6,7,11,13],[1,3,8,10,11,13],[1,4,5,8,12,13],[1,4,8,9,10,11],[1,5,6,7,8,10],[1,5,6,9,12,13],[1,7,9,10,12,13],[2,3,6,8,9,13],[2,3,7,9,10,12],[2,4,6,10,11,13],[2,4,7,8,12,13],[2,5,6,8,10,12],[2,5,7,10,11,13],[2,5,8,9,11,13],[3,4,5,7,9,13],[3,4,5,10,11,12],[3,4,6,10,12,13],[3,5,7,8,11,12],[3,6,8,9,11,12],[4,5,6,7,9,11],[4,6,7,8,9,10]];
G[97]:=Group([(2,12)(3,13)(4,9)(8,10),(1,11)(2,3,12,13)(4,8,9,10)(6,7)]);
# Design 98: autom. group order 4, simple, derived
B[98]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,12],[1,3,6,8,10,13],[1,3,7,9,10,11],[1,4,5,8,12,13],[1,4,7,8,11,13],[1,5,6,8,10,11],[1,5,6,9,12,13],[1,7,9,10,12,13],[2,3,6,11,12,13],[2,3,8,10,12,13],[2,4,6,7,10,13],[2,4,8,9,10,12],[2,5,6,7,8,9],[2,5,7,10,11,13],[2,5,8,9,11,13],[3,4,5,7,9,13],[3,4,5,10,11,12],[3,4,6,9,11,13],[3,5,7,8,11,12],[3,6,7,8,9,12],[4,5,6,7,10,12],[4,6,8,9,10,11]];
G[98]:=Group([(2,8,12,10)(3,4,13,9)(5,7)(6,11)]);
# Design 99: autom. group order 4, simple, derived
B[99]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,8,13],[1,3,6,9,11,13],[1,3,10,11,12,13],[1,4,5,7,10,11],[1,4,8,9,10,13],[1,5,6,8,11,12],[1,5,7,8,12,13],[1,6,7,9,10,12],[2,3,6,7,11,12],[2,3,8,9,12,13],[2,4,6,10,11,13],[2,4,7,10,12,13],[2,5,6,8,9,10],[2,5,7,9,11,13],[2,5,8,10,11,12],[3,4,5,7,9,12],[3,4,5,8,11,13],[3,4,6,8,10,12],[3,5,6,7,10,13],[3,7,8,9,10,11],[4,5,6,9,12,13],[4,6,7,8,9,11]];
G[99]:=Group([(1,2,5,8)(3,10,12,7)(4,9,11,13)]);
# Design 100: autom. group order 4, simple, derived
B[100]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,7,8,11,12],[1,3,7,9,10,11],[1,4,5,8,12,13],[1,4,6,8,11,13],[1,5,6,7,8,10],[1,5,7,9,12,13],[1,6,9,10,12,13],[2,3,6,7,12,13],[2,3,6,8,9,13],[2,4,7,10,11,13],[2,4,8,9,10,12],[2,5,6,7,11,12],[2,5,7,8,9,13],[2,5,8,10,11,12],[3,4,5,6,10,12],[3,4,5,9,11,13],[3,4,7,10,12,13],[3,5,8,10,11,13],[3,6,8,9,11,12],[4,5,6,7,9,11],[4,6,7,8,9,10]];
G[100]:=Group([(2,6)(3,13)(4,10)(5,11)(7,12)(8,9),(2,7)(4,8)(5,11)(6,12)(9,10)]);
# Design 101: autom. group order 4, simple, derived
B[101]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,10,11,13],[1,3,7,8,11,12],[1,3,7,9,10,11],[1,4,5,8,12,13],[1,4,6,8,11,13],[1,5,6,7,8,10],[1,5,7,9,12,13],[1,6,9,10,12,13],[2,3,6,7,12,13],[2,3,8,10,12,13],[2,4,7,10,11,13],[2,4,8,9,10,12],[2,5,6,7,11,12],[2,5,6,8,9,11],[2,5,7,8,9,13],[3,4,5,6,10,12],[3,4,5,9,11,13],[3,4,6,7,9,13],[3,5,8,10,11,13],[3,6,8,9,11,12],[4,5,7,10,11,12],[4,6,7,8,9,10]];
G[101]:=Group([(2,6)(3,13)(4,10)(5,11)(7,12)(8,9),(2,7)(4,8)(5,11)(6,12)(9,10)]);
# Design 102: autom. group order 4, simple, derived
B[102]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,11,12,13],[1,2,7,9,11,12],[1,3,6,7,10,13],[1,3,6,9,11,13],[1,4,5,10,12,13],[1,4,8,9,10,11],[1,5,6,8,12,13],[1,5,7,8,10,11],[1,6,7,8,9,12],[2,3,6,8,10,11],[2,3,7,8,12,13],[2,4,6,7,10,12],[2,4,8,9,10,13],[2,5,6,8,11,13],[2,5,6,9,10,12],[2,5,7,9,11,13],[3,4,5,7,9,13],[3,4,5,8,11,12],[3,4,6,9,11,12],[3,5,7,10,11,12],[3,8,9,10,12,13],[4,5,6,7,8,9],[4,6,7,10,11,13]];
G[102]:=Group([(1,7,12,9)(2,6,11,8)(3,10)(5,13)]);
# Design 103: autom. group order 4, simple
B[103]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,6,10,12,13],[1,3,9,11,12,13],[1,4,5,8,10,13],[1,4,6,7,9,10],[1,5,6,8,11,13],[1,5,7,8,11,12],[1,6,7,8,9,12],[2,3,6,7,8,11],[2,3,8,10,12,13],[2,4,6,8,12,13],[2,4,6,9,11,13],[2,5,6,7,10,12],[2,5,7,9,12,13],[2,5,8,9,10,11],[3,4,5,7,11,13],[3,4,5,8,9,12],[3,4,7,10,11,12],[3,5,6,7,9,13],[3,6,8,9,10,11],[4,5,6,10,11,12],[4,7,8,9,10,13]];
G[103]:=Group([(1,3,13,5)(2,12,7,8)(4,10,9,11)]);
# Design 104: autom. group order 4, simple, derived
B[104]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,6,9,12,13],[1,3,8,10,12,13],[1,4,5,8,12,13],[1,4,6,7,8,11],[1,5,6,7,11,12],[1,5,8,9,10,11],[1,6,7,9,10,13],[2,3,6,8,9,11],[2,3,7,10,11,12],[2,4,6,8,10,13],[2,4,7,9,12,13],[2,5,6,8,10,12],[2,5,6,11,12,13],[2,5,7,8,9,13],[3,4,5,7,10,12],[3,4,5,9,11,13],[3,4,6,10,11,13],[3,5,7,8,11,13],[3,6,7,8,9,12],[4,5,6,7,9,10],[4,8,9,10,11,12]];
G[104]:=Group([(1,6,13,9)(2,5,11,4)(3,12)(7,10)]);
# Design 105: autom. group order 4, simple, derived
B[105]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,6,7,12],[1,3,5,8,9,10],[1,3,5,11,12,13],[1,4,5,10,11,13],[1,4,6,7,9,11],[1,6,7,8,10,13],[1,6,8,9,12,13],[1,7,8,10,11,12],[2,3,6,7,11,13],[2,3,6,8,10,12],[2,4,5,8,10,13],[2,4,8,9,11,12],[2,5,7,8,9,13],[2,5,7,10,11,12],[2,6,9,10,11,13],[3,4,6,10,12,13],[3,4,7,8,11,13],[3,4,7,9,10,12],[3,5,6,8,9,11],[3,5,7,9,12,13],[4,5,6,7,9,10],[4,5,6,8,11,12]];
G[105]:=Group([(1,2,11,8)(3,9,12,7)(4,10)(5,13)]);
# Design 106: autom. group order 4, simple, derived
B[106]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,6,10,12],[1,3,5,7,8,10],[1,3,5,11,12,13],[1,4,5,7,9,13],[1,4,8,9,10,11],[1,6,7,8,11,13],[1,6,7,9,11,12],[1,6,8,10,12,13],[2,3,6,8,9,11],[2,3,7,9,12,13],[2,4,6,7,8,12],[2,4,6,10,11,13],[2,5,7,8,11,13],[2,5,7,10,11,12],[2,5,8,9,10,13],[3,4,5,6,11,13],[3,4,7,10,11,12],[3,4,8,10,12,13],[3,5,6,8,9,12],[3,6,7,9,10,13],[4,5,6,7,9,10],[4,5,8,9,11,12]];
G[106]:=Group([(1,2)(3,4)(5,6)(7,8)(10,12)(11,13),(1,5)(2,6)(7,13)(8,11)(10,12)]);
# Design 107: autom. group order 4, simple, derived
B[107]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,10,12],[1,2,5,7,9,13],[1,3,5,6,8,12],[1,3,5,10,11,13],[1,4,6,7,10,12],[1,4,6,8,11,13],[1,5,7,8,10,13],[1,6,9,11,12,13],[1,7,8,9,11,12],[2,3,6,7,12,13],[2,3,6,8,9,11],[2,4,5,9,12,13],[2,4,7,8,11,13],[2,5,6,7,10,11],[2,5,8,10,11,12],[2,6,8,10,12,13],[3,4,5,11,12,13],[3,4,7,10,11,12],[3,4,8,9,10,13],[3,5,7,8,9,12],[3,6,7,9,10,13],[4,5,6,7,9,11],[4,5,6,8,9,10]];
G[107]:=Group([(2,9)(3,11)(4,12)(5,13),(1,10)(2,3,9,11)(4,13,12,5)(6,8)]);
# Design 108: autom. group order 4, simple, derived
B[108]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,7,12,13],[1,3,5,6,10,12],[1,3,5,8,9,11],[1,4,6,8,9,13],[1,4,7,10,11,12],[1,5,6,7,11,13],[1,6,8,10,11,13],[1,7,8,9,10,12],[2,3,6,7,10,13],[2,3,6,8,11,12],[2,4,5,8,10,13],[2,4,6,9,11,12],[2,5,7,8,11,12],[2,5,9,10,11,13],[2,6,7,8,9,10],[3,4,5,7,9,10],[3,4,7,8,11,13],[3,4,10,11,12,13],[3,5,8,9,12,13],[3,6,7,9,12,13],[4,5,6,7,9,11],[4,5,6,8,10,12]];
G[108]:=Group([(1,2,13,12)(3,10)(4,5,9,7)(6,11)]);
# Design 109: autom. group order 4, simple, derived
B[109]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,7,12,13],[1,3,5,6,7,10],[1,3,5,8,11,12],[1,4,6,8,11,13],[1,4,8,9,10,12],[1,5,9,10,11,13],[1,6,7,8,9,13],[1,6,7,10,11,12],[2,3,6,8,9,11],[2,3,6,10,12,13],[2,4,5,7,9,10],[2,4,6,10,11,13],[2,5,6,8,9,12],[2,5,7,8,11,13],[2,7,8,10,11,12],[3,4,5,11,12,13],[3,4,7,8,10,13],[3,4,7,9,11,12],[3,5,8,9,10,13],[3,6,7,9,12,13],[4,5,6,7,9,11],[4,5,6,8,10,12]];
G[109]:=Group([(1,2,8,10)(3,7,12,9)(4,11)(6,13)]);
# Design 110: autom. group order 4, simple, derived
B[110]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,7,12,13],[1,3,5,6,10,12],[1,3,5,8,9,11],[1,4,6,9,11,13],[1,4,7,10,11,12],[1,5,7,8,10,13],[1,6,7,8,9,12],[1,6,8,10,11,13],[2,3,6,7,9,10],[2,3,7,8,11,13],[2,4,5,10,11,13],[2,4,8,9,10,12],[2,5,6,7,11,12],[2,5,6,8,9,13],[2,6,8,10,11,12],[3,4,5,8,11,12],[3,4,6,7,10,13],[3,4,6,8,12,13],[3,5,9,10,12,13],[3,7,9,11,12,13],[4,5,6,7,9,11],[4,5,7,8,9,10]];
G[110]:=Group([(1,2)(5,7)(6,8)(10,11)(12,13),(1,12)(2,13)(4,9)(6,10)(8,11)]);
# Design 111: autom. group order 4, simple, derived
B[111]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,7,12,13],[1,3,5,6,10,12],[1,3,5,8,9,11],[1,4,7,10,11,12],[1,4,8,9,10,13],[1,5,6,7,11,13],[1,6,7,8,9,12],[1,6,8,10,11,13],[2,3,6,8,11,12],[2,3,7,10,11,13],[2,4,5,8,11,13],[2,4,6,9,11,12],[2,5,6,9,10,13],[2,5,7,8,10,12],[2,6,7,8,9,10],[3,4,5,7,9,10],[3,4,6,7,8,13],[3,4,6,10,12,13],[3,5,8,9,12,13],[3,7,9,11,12,13],[4,5,6,7,9,11],[4,5,8,10,11,12]];
G[111]:=Group([(2,5)(4,6)(7,12)(8,10)(9,11),(1,13)(2,7)(4,11)(5,12)(6,9)(8,10)]);
# Design 112: autom. group order 4, simple, derived
B[112]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,10,12],[1,2,5,7,9,13],[1,3,5,6,8,12],[1,3,6,7,10,11],[1,4,5,10,12,13],[1,4,6,8,11,13],[1,5,7,8,10,13],[1,6,9,11,12,13],[1,7,8,9,11,12],[2,3,5,9,11,13],[2,3,8,10,12,13],[2,4,6,8,9,12],[2,4,7,8,11,13],[2,5,6,7,11,12],[2,5,6,8,10,11],[2,6,7,10,12,13],[3,4,5,11,12,13],[3,4,6,7,9,13],[3,4,7,10,11,12],[3,5,7,8,9,12],[3,6,8,9,10,13],[4,5,6,7,9,10],[4,5,8,9,10,11]];
G[112]:=Group([(2,9)(3,11)(4,12)(5,13),(1,10)(2,4,9,12)(3,5,11,13)(6,8)]);
# Design 113: autom. group order 4, simple, derived
B[113]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,6,9,11,12],[1,2,7,10,11,12],[1,3,6,10,11,13],[1,3,8,9,11,13],[1,4,5,11,12,13],[1,4,6,7,10,13],[1,4,6,8,9,12],[1,5,7,8,9,10],[1,5,7,8,12,13],[2,3,7,8,12,13],[2,3,9,10,12,13],[2,4,5,7,9,11],[2,4,6,8,10,12],[2,4,8,9,11,13],[2,5,6,7,11,13],[2,5,6,8,10,13],[3,4,5,8,10,11],[3,4,6,7,9,13],[3,4,7,10,11,12],[3,5,6,7,9,12],[3,5,6,8,11,12],[4,5,9,10,12,13],[6,7,8,9,10,11]];
G[113]:=Group([(2,3)(7,8)(9,10)(12,13),(1,5)(2,12,3,13)(6,11)(7,9,8,10)]);