Groups G whose centre is cyclic (and only these) admit a faithful
irreducible representation
ρ: G→GL_{n}(ℂ). In the table below the groups
are sorted by the smallest dimension **n** and the
Frobenius-Schur indicator
**+** if ρ is orthogonal, **-** if ρ is symplectic, and nothing otherwise.

Jump to:
1,1+ (cyclic)
2+ (dihedral)
2- (dicyclic+3 more)
2
3+ (symmetries of platonic solids)
3

4+
4-
4
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5
6+
6-
6
7+
7
8+
8-
8
9+
9
10+
10-
10
11
12+
12-
12
13
14+
14-
14
15+
15
16+
18+
20+

d | ρ | Label | ID | ||
---|---|---|---|---|---|

SL_{2}(𝔽_{3}) | Special linear group on 𝔽_{3}^{2}; = Q_{8}⋊C_{3} = 2T = <2,3,3> = 1^{st} non-monomial group | 8 | 2- | SL(2,3) | 24,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

CSU_{2}(𝔽_{3}) | Conformal special unitary group on 𝔽_{3}^{2}; = Q_{8}.S_{3} | 16 | 2- | CSU(2,3) | 48,28 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

SL_{2}(𝔽_{5}) | Special linear group on 𝔽_{5}^{2}; = C_{2}.A_{5} = 2I = <2,3,5> | 24 | 2- | SL(2,5) | 120,5 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

M_{4}(2) | Modular maximal-cyclic group; = C_{8}⋊_{3}C_{2} | 8 | 2 | M4(2) | 16,6 |

SD_{16} | Semidihedral group; = Q_{8}⋊C_{2} = QD_{16} | 8 | 2 | SD16 | 16,8 |

C_{4}○D_{4} | Pauli group = central product of C_{4} and D_{4} | 8 | 2 | C4oD4 | 16,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}×S_{3} | Direct product of C_{3} and S_{3}; = U_{2}(𝔽_{2}) | 6 | 2 | C3xS3 | 18,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}⋊C_{8} | The semidirect product of C_{3} and C_{8} acting via C_{8}/C_{4}=C_{2} | 24 | 2 | C3:C8 | 24,1 |

C_{4}×S_{3} | Direct product of C_{4} and S_{3} | 12 | 2 | C4xS3 | 24,5 |

C_{3}⋊D_{4} | The semidirect product of C_{3} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 12 | 2 | C3:D4 | 24,8 |

C_{3}×D_{4} | Direct product of C_{3} and D_{4} | 12 | 2 | C3xD4 | 24,10 |

C_{3}×Q_{8} | Direct product of C_{3} and Q_{8} | 24 | 2 | C3xQ8 | 24,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×S_{3} | Direct product of C_{5} and S_{3} | 15 | 2 | C5xS3 | 30,1 |

C_{3}×D_{5} | Direct product of C_{3} and D_{5} | 15 | 2 | C3xD5 | 30,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}≀C_{2} | Wreath product of C_{4} by C_{2} | 8 | 2 | C4wrC2 | 32,11 |

C_{8}.C_{4} | 1^{st} non-split extension by C_{8} of C_{4} acting via C_{4}/C_{2}=C_{2} | 16 | 2 | C8.C4 | 32,15 |

M_{5}(2) | Modular maximal-cyclic group; = C_{16}⋊_{3}C_{2} | 16 | 2 | M5(2) | 32,17 |

SD_{32} | Semidihedral group; = C_{16}⋊_{2}C_{2} = QD_{32} | 16 | 2 | SD32 | 32,19 |

C_{8}○D_{4} | Central product of C_{8} and D_{4} | 16 | 2 | C8oD4 | 32,38 |

C_{4}○D_{8} | Central product of C_{4} and D_{8} | 16 | 2 | C4oD8 | 32,42 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}×Dic_{3} | Direct product of C_{3} and Dic_{3} | 12 | 2 | C3xDic3 | 36,6 |

S_{3}×C_{6} | Direct product of C_{6} and S_{3} | 12 | 2 | S3xC6 | 36,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}⋊_{2}C_{8} | The semidirect product of C_{5} and C_{8} acting via C_{8}/C_{4}=C_{2} | 40 | 2 | C5:2C8 | 40,1 |

C_{4}×D_{5} | Direct product of C_{4} and D_{5} | 20 | 2 | C4xD5 | 40,5 |

C_{5}⋊D_{4} | The semidirect product of C_{5} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 20 | 2 | C5:D4 | 40,8 |

C_{5}×D_{4} | Direct product of C_{5} and D_{4} | 20 | 2 | C5xD4 | 40,10 |

C_{5}×Q_{8} | Direct product of C_{5} and Q_{8} | 40 | 2 | C5xQ8 | 40,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{7} | Direct product of C_{7} and S_{3} | 21 | 2 | S3xC7 | 42,3 |

C_{3}×D_{7} | Direct product of C_{3} and D_{7} | 21 | 2 | C3xD7 | 42,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×D_{5} | Direct product of C_{5} and D_{5}; = AΣL_{1}(𝔽_{25}) | 10 | 2 | C5xD5 | 50,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}×D_{9} | Direct product of C_{3} and D_{9} | 18 | 2 | C3xD9 | 54,3 |

S_{3}×C_{9} | Direct product of C_{9} and S_{3} | 18 | 2 | S3xC9 | 54,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}⋊C_{8} | The semidirect product of C_{7} and C_{8} acting via C_{8}/C_{4}=C_{2} | 56 | 2 | C7:C8 | 56,1 |

C_{4}×D_{7} | Direct product of C_{4} and D_{7} | 28 | 2 | C4xD7 | 56,4 |

C_{7}⋊D_{4} | The semidirect product of C_{7} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 28 | 2 | C7:D4 | 56,7 |

C_{7}×D_{4} | Direct product of C_{7} and D_{4} | 28 | 2 | C7xD4 | 56,9 |

C_{7}×Q_{8} | Direct product of C_{7} and Q_{8} | 56 | 2 | C7xQ8 | 56,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×Dic_{3} | Direct product of C_{5} and Dic_{3} | 60 | 2 | C5xDic3 | 60,1 |

C_{3}×Dic_{5} | Direct product of C_{3} and Dic_{5} | 60 | 2 | C3xDic5 | 60,2 |

C_{6}×D_{5} | Direct product of C_{6} and D_{5} | 30 | 2 | C6xD5 | 60,10 |

S_{3}×C_{10} | Direct product of C_{10} and S_{3} | 30 | 2 | S3xC10 | 60,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.C_{8} | The non-split extension by D_{4} of C_{8} acting via C_{8}/C_{4}=C_{2} | 32 | 2 | D4.C8 | 64,31 |

D_{8}.C_{4} | 1^{st} non-split extension by D_{8} of C_{4} acting via C_{4}/C_{2}=C_{2} | 32 | 2 | D8.C4 | 64,40 |

C_{8}.C_{8} | 1^{st} non-split extension by C_{8} of C_{8} acting via C_{8}/C_{4}=C_{2} | 16 | 2 | C8.C8 | 64,45 |

C_{8}._{4}Q_{8} | 3^{rd} non-split extension by C_{8} of Q_{8} acting via Q_{8}/C_{4}=C_{2} | 32 | 2 | C8.4Q8 | 64,49 |

M_{6}(2) | Modular maximal-cyclic group; = C_{32}⋊_{3}C_{2} | 32 | 2 | M6(2) | 64,51 |

SD_{64} | Semidihedral group; = C_{32}⋊_{2}C_{2} = QD_{64} | 32 | 2 | SD64 | 64,53 |

C_{8}○D_{8} | Central product of C_{8} and D_{8} | 16 | 2 | C8oD8 | 64,124 |

D_{4}○C_{16} | Central product of D_{4} and C_{16} | 32 | 2 | D4oC16 | 64,185 |

C_{4}○D_{16} | Central product of C_{4} and D_{16} | 32 | 2 | C4oD16 | 64,189 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{11} | Direct product of C_{11} and S_{3} | 33 | 2 | S3xC11 | 66,1 |

C_{3}×D_{11} | Direct product of C_{3} and D_{11} | 33 | 2 | C3xD11 | 66,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×D_{5} | Direct product of C_{7} and D_{5} | 35 | 2 | C7xD5 | 70,1 |

C_{5}×D_{7} | Direct product of C_{5} and D_{7} | 35 | 2 | C5xD7 | 70,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{9}⋊C_{8} | The semidirect product of C_{9} and C_{8} acting via C_{8}/C_{4}=C_{2} | 72 | 2 | C9:C8 | 72,1 |

Q_{8}⋊C_{9} | The semidirect product of Q_{8} and C_{9} acting via C_{9}/C_{3}=C_{3} | 72 | 2 | Q8:C9 | 72,3 |

C_{4}×D_{9} | Direct product of C_{4} and D_{9} | 36 | 2 | C4xD9 | 72,5 |

C_{9}⋊D_{4} | The semidirect product of C_{9} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 36 | 2 | C9:D4 | 72,8 |

D_{4}×C_{9} | Direct product of C_{9} and D_{4} | 36 | 2 | D4xC9 | 72,10 |

Q_{8}×C_{9} | Direct product of C_{9} and Q_{8} | 72 | 2 | Q8xC9 | 72,11 |

C_{3}×C_{3}⋊C_{8} | Direct product of C_{3} and C_{3}⋊C_{8} | 24 | 2 | C3xC3:C8 | 72,12 |

C_{3}×SL_{2}(𝔽_{3}) | Direct product of C_{3} and SL_{2}(𝔽_{3}) | 24 | 2 | C3xSL(2,3) | 72,25 |

C_{3}×Dic_{6} | Direct product of C_{3} and Dic_{6} | 24 | 2 | C3xDic6 | 72,26 |

S_{3}×C_{12} | Direct product of C_{12} and S_{3} | 24 | 2 | S3xC12 | 72,27 |

C_{3}×D_{12} | Direct product of C_{3} and D_{12} | 24 | 2 | C3xD12 | 72,28 |

C_{3}×C_{3}⋊D_{4} | Direct product of C_{3} and C_{3}⋊D_{4} | 12 | 2 | C3xC3:D4 | 72,30 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{13} | Direct product of C_{13} and S_{3} | 39 | 2 | S3xC13 | 78,3 |

C_{3}×D_{13} | Direct product of C_{3} and D_{13} | 39 | 2 | C3xD13 | 78,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}⋊_{2}C_{16} | The semidirect product of C_{5} and C_{16} acting via C_{16}/C_{8}=C_{2} | 80 | 2 | C5:2C16 | 80,1 |

C_{8}×D_{5} | Direct product of C_{8} and D_{5} | 40 | 2 | C8xD5 | 80,4 |

C_{8}⋊D_{5} | 3^{rd} semidirect product of C_{8} and D_{5} acting via D_{5}/C_{5}=C_{2} | 40 | 2 | C8:D5 | 80,5 |

C_{40}⋊C_{2} | 2^{nd} semidirect product of C_{40} and C_{2} acting faithfully | 40 | 2 | C40:C2 | 80,6 |

C_{4}.Dic_{5} | The non-split extension by C_{4} of Dic_{5} acting via Dic_{5}/C_{10}=C_{2} | 40 | 2 | C4.Dic5 | 80,10 |

C_{5}×M_{4}(2) | Direct product of C_{5} and M_{4}(2) | 40 | 2 | C5xM4(2) | 80,24 |

C_{5}×D_{8} | Direct product of C_{5} and D_{8} | 40 | 2 | C5xD8 | 80,25 |

C_{5}×SD_{16} | Direct product of C_{5} and SD_{16} | 40 | 2 | C5xSD16 | 80,26 |

C_{5}×Q_{16} | Direct product of C_{5} and Q_{16} | 80 | 2 | C5xQ16 | 80,27 |

C_{4}○D_{20} | Central product of C_{4} and D_{20} | 40 | 2 | C4oD20 | 80,38 |

C_{5}×C_{4}○D_{4} | Direct product of C_{5} and C_{4}○D_{4} | 40 | 2 | C5xC4oD4 | 80,48 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×Dic_{3} | Direct product of C_{7} and Dic_{3} | 84 | 2 | C7xDic3 | 84,3 |

C_{3}×Dic_{7} | Direct product of C_{3} and Dic_{7} | 84 | 2 | C3xDic7 | 84,4 |

C_{6}×D_{7} | Direct product of C_{6} and D_{7} | 42 | 2 | C6xD7 | 84,12 |

S_{3}×C_{14} | Direct product of C_{14} and S_{3} | 42 | 2 | S3xC14 | 84,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}⋊C_{8} | The semidirect product of C_{11} and C_{8} acting via C_{8}/C_{4}=C_{2} | 88 | 2 | C11:C8 | 88,1 |

C_{4}×D_{11} | Direct product of C_{4} and D_{11} | 44 | 2 | C4xD11 | 88,4 |

C_{11}⋊D_{4} | The semidirect product of C_{11} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 44 | 2 | C11:D4 | 88,7 |

D_{4}×C_{11} | Direct product of C_{11} and D_{4} | 44 | 2 | D4xC11 | 88,9 |

Q_{8}×C_{11} | Direct product of C_{11} and Q_{8} | 88 | 2 | Q8xC11 | 88,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×D_{9} | Direct product of C_{5} and D_{9} | 45 | 2 | C5xD9 | 90,1 |

C_{9}×D_{5} | Direct product of C_{9} and D_{5} | 45 | 2 | C9xD5 | 90,2 |

S_{3}×C_{15} | Direct product of C_{15} and S_{3} | 30 | 2 | S3xC15 | 90,6 |

C_{3}×D_{15} | Direct product of C_{3} and D_{15} | 30 | 2 | C3xD15 | 90,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×D_{7} | Direct product of C_{7} and D_{7}; = AΣL_{1}(𝔽_{49}) | 14 | 2 | C7xD7 | 98,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×Dic_{5} | Direct product of C_{5} and Dic_{5} | 20 | 2 | C5xDic5 | 100,6 |

D_{5}×C_{10} | Direct product of C_{10} and D_{5} | 20 | 2 | D5xC10 | 100,14 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{17} | Direct product of C_{17} and S_{3} | 51 | 2 | S3xC17 | 102,1 |

C_{3}×D_{17} | Direct product of C_{3} and D_{17} | 51 | 2 | C3xD17 | 102,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}⋊_{2}C_{8} | The semidirect product of C_{13} and C_{8} acting via C_{8}/C_{4}=C_{2} | 104 | 2 | C13:2C8 | 104,1 |

C_{4}×D_{13} | Direct product of C_{4} and D_{13} | 52 | 2 | C4xD13 | 104,5 |

C_{13}⋊D_{4} | The semidirect product of C_{13} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 52 | 2 | C13:D4 | 104,8 |

D_{4}×C_{13} | Direct product of C_{13} and D_{4} | 52 | 2 | D4xC13 | 104,10 |

Q_{8}×C_{13} | Direct product of C_{13} and Q_{8} | 104 | 2 | Q8xC13 | 104,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}×Dic_{9} | Direct product of C_{3} and Dic_{9} | 36 | 2 | C3xDic9 | 108,6 |

C_{9}×Dic_{3} | Direct product of C_{9} and Dic_{3} | 36 | 2 | C9xDic3 | 108,7 |

C_{6}×D_{9} | Direct product of C_{6} and D_{9} | 36 | 2 | C6xD9 | 108,23 |

S_{3}×C_{18} | Direct product of C_{18} and S_{3} | 36 | 2 | S3xC18 | 108,24 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{11} | Direct product of C_{11} and D_{5} | 55 | 2 | D5xC11 | 110,3 |

C_{5}×D_{11} | Direct product of C_{5} and D_{11} | 55 | 2 | C5xD11 | 110,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}⋊C_{16} | The semidirect product of C_{7} and C_{16} acting via C_{16}/C_{8}=C_{2} | 112 | 2 | C7:C16 | 112,1 |

C_{8}×D_{7} | Direct product of C_{8} and D_{7} | 56 | 2 | C8xD7 | 112,3 |

C_{8}⋊D_{7} | 3^{rd} semidirect product of C_{8} and D_{7} acting via D_{7}/C_{7}=C_{2} | 56 | 2 | C8:D7 | 112,4 |

C_{56}⋊C_{2} | 2^{nd} semidirect product of C_{56} and C_{2} acting faithfully | 56 | 2 | C56:C2 | 112,5 |

C_{4}.Dic_{7} | The non-split extension by C_{4} of Dic_{7} acting via Dic_{7}/C_{14}=C_{2} | 56 | 2 | C4.Dic7 | 112,9 |

C_{7}×M_{4}(2) | Direct product of C_{7} and M_{4}(2) | 56 | 2 | C7xM4(2) | 112,23 |

C_{7}×D_{8} | Direct product of C_{7} and D_{8} | 56 | 2 | C7xD8 | 112,24 |

C_{7}×SD_{16} | Direct product of C_{7} and SD_{16} | 56 | 2 | C7xSD16 | 112,25 |

C_{7}×Q_{16} | Direct product of C_{7} and Q_{16} | 112 | 2 | C7xQ16 | 112,26 |

C_{4}○D_{28} | Central product of C_{4} and D_{28} | 56 | 2 | C4oD28 | 112,30 |

C_{7}×C_{4}○D_{4} | Direct product of C_{7} and C_{4}○D_{4} | 56 | 2 | C7xC4oD4 | 112,40 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{19} | Direct product of C_{19} and S_{3} | 57 | 2 | S3xC19 | 114,3 |

C_{3}×D_{19} | Direct product of C_{3} and D_{19} | 57 | 2 | C3xD19 | 114,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×D_{9} | Direct product of C_{7} and D_{9} | 63 | 2 | C7xD9 | 126,3 |

C_{9}×D_{7} | Direct product of C_{9} and D_{7} | 63 | 2 | C9xD7 | 126,4 |

S_{3}×C_{21} | Direct product of C_{21} and S_{3} | 42 | 2 | S3xC21 | 126,12 |

C_{3}×D_{21} | Direct product of C_{3} and D_{21} | 42 | 2 | C3xD21 | 126,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{8}≀C_{2} | Wreath product of C_{8} by C_{2} | 16 | 2 | C8wrC2 | 128,67 |

C_{16}._{3}C_{8} | 1^{st} non-split extension by C_{16} of C_{8} acting via C_{8}/C_{4}=C_{2} | 32 | 2 | C16.3C8 | 128,105 |

D_{4}.C_{16} | The non-split extension by D_{4} of C_{16} acting via C_{16}/C_{8}=C_{2} | 64 | 2 | D4.C16 | 128,133 |

D_{16}.C_{4} | 1^{st} non-split extension by D_{16} of C_{4} acting via C_{4}/C_{2}=C_{2} | 64 | 2 | D16.C4 | 128,149 |

C_{8}.C_{16} | 1^{st} non-split extension by C_{8} of C_{16} acting via C_{16}/C_{8}=C_{2} | 32 | 2 | C8.C16 | 128,154 |

C_{32}.C_{4} | 1^{st} non-split extension by C_{32} of C_{4} acting via C_{4}/C_{2}=C_{2} | 64 | 2 | C32.C4 | 128,157 |

M_{7}(2) | Modular maximal-cyclic group; = C_{64}⋊_{3}C_{2} | 64 | 2 | M7(2) | 128,160 |

SD_{128} | Semidihedral group; = C_{64}⋊_{2}C_{2} = QD_{128} | 64 | 2 | SD128 | 128,162 |

C_{16}○D_{8} | Central product of C_{16} and D_{8} | 32 | 2 | C16oD8 | 128,902 |

C_{8}○D_{16} | Central product of C_{8} and D_{16} | 32 | 2 | C8oD16 | 128,910 |

D_{4}○C_{32} | Central product of D_{4} and C_{32} | 64 | 2 | D4oC32 | 128,990 |

C_{4}○D_{32} | Central product of C_{4} and D_{32} | 64 | 2 | C4oD32 | 128,994 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{13} | Direct product of C_{13} and D_{5} | 65 | 2 | D5xC13 | 130,1 |

C_{5}×D_{13} | Direct product of C_{5} and D_{13} | 65 | 2 | C5xD13 | 130,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×Dic_{3} | Direct product of C_{11} and Dic_{3} | 132 | 2 | C11xDic3 | 132,1 |

C_{3}×Dic_{11} | Direct product of C_{3} and Dic_{11} | 132 | 2 | C3xDic11 | 132,2 |

C_{6}×D_{11} | Direct product of C_{6} and D_{11} | 66 | 2 | C6xD11 | 132,7 |

S_{3}×C_{22} | Direct product of C_{22} and S_{3} | 66 | 2 | S3xC22 | 132,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}⋊_{3}C_{8} | The semidirect product of C_{17} and C_{8} acting via C_{8}/C_{4}=C_{2} | 136 | 2 | C17:3C8 | 136,1 |

C_{4}×D_{17} | Direct product of C_{4} and D_{17} | 68 | 2 | C4xD17 | 136,5 |

C_{17}⋊D_{4} | The semidirect product of C_{17} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 68 | 2 | C17:D4 | 136,8 |

D_{4}×C_{17} | Direct product of C_{17} and D_{4} | 68 | 2 | D4xC17 | 136,10 |

Q_{8}×C_{17} | Direct product of C_{17} and Q_{8} | 136 | 2 | Q8xC17 | 136,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{23} | Direct product of C_{23} and S_{3} | 69 | 2 | S3xC23 | 138,1 |

C_{3}×D_{23} | Direct product of C_{3} and D_{23} | 69 | 2 | C3xD23 | 138,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×Dic_{5} | Direct product of C_{7} and Dic_{5} | 140 | 2 | C7xDic5 | 140,1 |

C_{5}×Dic_{7} | Direct product of C_{5} and Dic_{7} | 140 | 2 | C5xDic7 | 140,2 |

C_{10}×D_{7} | Direct product of C_{10} and D_{7} | 70 | 2 | C10xD7 | 140,8 |

D_{5}×C_{14} | Direct product of C_{14} and D_{5} | 70 | 2 | D5xC14 | 140,9 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{25} | Direct product of C_{25} and S_{3} | 75 | 2 | S3xC25 | 150,1 |

C_{3}×D_{25} | Direct product of C_{3} and D_{25} | 75 | 2 | C3xD25 | 150,2 |

D_{5}×C_{15} | Direct product of C_{15} and D_{5} | 30 | 2 | D5xC15 | 150,8 |

C_{5}×D_{15} | Direct product of C_{5} and D_{15} | 30 | 2 | C5xD15 | 150,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{19}⋊C_{8} | The semidirect product of C_{19} and C_{8} acting via C_{8}/C_{4}=C_{2} | 152 | 2 | C19:C8 | 152,1 |

C_{4}×D_{19} | Direct product of C_{4} and D_{19} | 76 | 2 | C4xD19 | 152,4 |

C_{19}⋊D_{4} | The semidirect product of C_{19} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 76 | 2 | C19:D4 | 152,7 |

D_{4}×C_{19} | Direct product of C_{19} and D_{4} | 76 | 2 | D4xC19 | 152,9 |

Q_{8}×C_{19} | Direct product of C_{19} and Q_{8} | 152 | 2 | Q8xC19 | 152,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×D_{7} | Direct product of C_{11} and D_{7} | 77 | 2 | C11xD7 | 154,1 |

C_{7}×D_{11} | Direct product of C_{7} and D_{11} | 77 | 2 | C7xD11 | 154,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{13} | Direct product of C_{13} and Dic_{3} | 156 | 2 | Dic3xC13 | 156,3 |

C_{3}×Dic_{13} | Direct product of C_{3} and Dic_{13} | 156 | 2 | C3xDic13 | 156,4 |

C_{6}×D_{13} | Direct product of C_{6} and D_{13} | 78 | 2 | C6xD13 | 156,15 |

S_{3}×C_{26} | Direct product of C_{26} and S_{3} | 78 | 2 | S3xC26 | 156,16 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{9}×D_{9} | Direct product of C_{9} and D_{9} | 18 | 2 | C9xD9 | 162,3 |

C_{3}×D_{27} | Direct product of C_{3} and D_{27} | 54 | 2 | C3xD27 | 162,7 |

S_{3}×C_{27} | Direct product of C_{27} and S_{3} | 54 | 2 | S3xC27 | 162,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{17} | Direct product of C_{17} and D_{5} | 85 | 2 | D5xC17 | 170,1 |

C_{5}×D_{17} | Direct product of C_{5} and D_{17} | 85 | 2 | C5xD17 | 170,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{29} | Direct product of C_{29} and S_{3} | 87 | 2 | S3xC29 | 174,1 |

C_{3}×D_{29} | Direct product of C_{3} and D_{29} | 87 | 2 | C3xD29 | 174,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}⋊C_{16} | The semidirect product of C_{11} and C_{16} acting via C_{16}/C_{8}=C_{2} | 176 | 2 | C11:C16 | 176,1 |

C_{8}×D_{11} | Direct product of C_{8} and D_{11} | 88 | 2 | C8xD11 | 176,3 |

C_{88}⋊C_{2} | 4^{th} semidirect product of C_{88} and C_{2} acting faithfully | 88 | 2 | C88:C2 | 176,4 |

C_{8}⋊D_{11} | 2^{nd} semidirect product of C_{8} and D_{11} acting via D_{11}/C_{11}=C_{2} | 88 | 2 | C8:D11 | 176,5 |

C_{44}.C_{4} | 1^{st} non-split extension by C_{44} of C_{4} acting via C_{4}/C_{2}=C_{2} | 88 | 2 | C44.C4 | 176,9 |

C_{11}×M_{4}(2) | Direct product of C_{11} and M_{4}(2) | 88 | 2 | C11xM4(2) | 176,23 |

C_{11}×D_{8} | Direct product of C_{11} and D_{8} | 88 | 2 | C11xD8 | 176,24 |

C_{11}×SD_{16} | Direct product of C_{11} and SD_{16} | 88 | 2 | C11xSD16 | 176,25 |

C_{11}×Q_{16} | Direct product of C_{11} and Q_{16} | 176 | 2 | C11xQ16 | 176,26 |

D_{44}⋊_{5}C_{2} | The semidirect product of D_{44} and C_{2} acting through Inn(D_{44}) | 88 | 2 | D44:5C2 | 176,30 |

C_{11}×C_{4}○D_{4} | Direct product of C_{11} and C_{4}○D_{4} | 88 | 2 | C11xC4oD4 | 176,40 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×Dic_{9} | Direct product of C_{5} and Dic_{9} | 180 | 2 | C5xDic9 | 180,1 |

C_{9}×Dic_{5} | Direct product of C_{9} and Dic_{5} | 180 | 2 | C9xDic5 | 180,2 |

D_{5}×C_{18} | Direct product of C_{18} and D_{5} | 90 | 2 | D5xC18 | 180,9 |

C_{10}×D_{9} | Direct product of C_{10} and D_{9} | 90 | 2 | C10xD9 | 180,10 |

Dic_{3}×C_{15} | Direct product of C_{15} and Dic_{3} | 60 | 2 | Dic3xC15 | 180,14 |

C_{3}×Dic_{15} | Direct product of C_{3} and Dic_{15} | 60 | 2 | C3xDic15 | 180,15 |

S_{3}×C_{30} | Direct product of C_{30} and S_{3} | 60 | 2 | S3xC30 | 180,33 |

C_{6}×D_{15} | Direct product of C_{6} and D_{15} | 60 | 2 | C6xD15 | 180,34 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}×D_{7} | Direct product of C_{13} and D_{7} | 91 | 2 | C13xD7 | 182,1 |

C_{7}×D_{13} | Direct product of C_{7} and D_{13} | 91 | 2 | C7xD13 | 182,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{23}⋊C_{8} | The semidirect product of C_{23} and C_{8} acting via C_{8}/C_{4}=C_{2} | 184 | 2 | C23:C8 | 184,1 |

C_{4}×D_{23} | Direct product of C_{4} and D_{23} | 92 | 2 | C4xD23 | 184,4 |

C_{23}⋊D_{4} | The semidirect product of C_{23} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 92 | 2 | C23:D4 | 184,7 |

D_{4}×C_{23} | Direct product of C_{23} and D_{4} | 92 | 2 | D4xC23 | 184,9 |

Q_{8}×C_{23} | Direct product of C_{23} and Q_{8} | 184 | 2 | Q8xC23 | 184,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{31} | Direct product of C_{31} and S_{3} | 93 | 2 | S3xC31 | 186,3 |

C_{3}×D_{31} | Direct product of C_{3} and D_{31} | 93 | 2 | C3xD31 | 186,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{19} | Direct product of C_{19} and D_{5} | 95 | 2 | D5xC19 | 190,1 |

C_{5}×D_{19} | Direct product of C_{5} and D_{19} | 95 | 2 | C5xD19 | 190,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×Dic_{7} | Direct product of C_{7} and Dic_{7} | 28 | 2 | C7xDic7 | 196,5 |

D_{7}×C_{14} | Direct product of C_{14} and D_{7} | 28 | 2 | D7xC14 | 196,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×D_{9} | Direct product of C_{11} and D_{9} | 99 | 2 | C11xD9 | 198,1 |

C_{9}×D_{11} | Direct product of C_{9} and D_{11} | 99 | 2 | C9xD11 | 198,2 |

S_{3}×C_{33} | Direct product of C_{33} and S_{3} | 66 | 2 | S3xC33 | 198,6 |

C_{3}×D_{33} | Direct product of C_{3} and D_{33} | 66 | 2 | C3xD33 | 198,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{25}⋊_{2}C_{8} | The semidirect product of C_{25} and C_{8} acting via C_{8}/C_{4}=C_{2} | 200 | 2 | C25:2C8 | 200,1 |

C_{4}×D_{25} | Direct product of C_{4} and D_{25} | 100 | 2 | C4xD25 | 200,5 |

C_{25}⋊D_{4} | The semidirect product of C_{25} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 100 | 2 | C25:D4 | 200,8 |

D_{4}×C_{25} | Direct product of C_{25} and D_{4} | 100 | 2 | D4xC25 | 200,10 |

Q_{8}×C_{25} | Direct product of C_{25} and Q_{8} | 200 | 2 | Q8xC25 | 200,11 |

C_{5}×C_{5}⋊_{2}C_{8} | Direct product of C_{5} and C_{5}⋊_{2}C_{8} | 40 | 2 | C5xC5:2C8 | 200,15 |

C_{5}×Dic_{10} | Direct product of C_{5} and Dic_{10} | 40 | 2 | C5xDic10 | 200,27 |

D_{5}×C_{20} | Direct product of C_{20} and D_{5} | 40 | 2 | D5xC20 | 200,28 |

C_{5}×D_{20} | Direct product of C_{5} and D_{20} | 40 | 2 | C5xD20 | 200,29 |

C_{5}×C_{5}⋊D_{4} | Direct product of C_{5} and C_{5}⋊D_{4} | 20 | 2 | C5xC5:D4 | 200,31 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{17} | Direct product of C_{17} and Dic_{3} | 204 | 2 | Dic3xC17 | 204,1 |

C_{3}×Dic_{17} | Direct product of C_{3} and Dic_{17} | 204 | 2 | C3xDic17 | 204,2 |

C_{6}×D_{17} | Direct product of C_{6} and D_{17} | 102 | 2 | C6xD17 | 204,9 |

S_{3}×C_{34} | Direct product of C_{34} and S_{3} | 102 | 2 | S3xC34 | 204,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}⋊_{2}C_{16} | The semidirect product of C_{13} and C_{16} acting via C_{16}/C_{8}=C_{2} | 208 | 2 | C13:2C16 | 208,1 |

C_{8}×D_{13} | Direct product of C_{8} and D_{13} | 104 | 2 | C8xD13 | 208,4 |

C_{8}⋊D_{13} | 3^{rd} semidirect product of C_{8} and D_{13} acting via D_{13}/C_{13}=C_{2} | 104 | 2 | C8:D13 | 208,5 |

C_{104}⋊C_{2} | 2^{nd} semidirect product of C_{104} and C_{2} acting faithfully | 104 | 2 | C104:C2 | 208,6 |

C_{52}._{4}C_{4} | 1^{st} non-split extension by C_{52} of C_{4} acting via C_{4}/C_{2}=C_{2} | 104 | 2 | C52.4C4 | 208,10 |

C_{13}×M_{4}(2) | Direct product of C_{13} and M_{4}(2) | 104 | 2 | C13xM4(2) | 208,24 |

C_{13}×D_{8} | Direct product of C_{13} and D_{8} | 104 | 2 | C13xD8 | 208,25 |

C_{13}×SD_{16} | Direct product of C_{13} and SD_{16} | 104 | 2 | C13xSD16 | 208,26 |

C_{13}×Q_{16} | Direct product of C_{13} and Q_{16} | 208 | 2 | C13xQ16 | 208,27 |

D_{52}⋊_{5}C_{2} | The semidirect product of D_{52} and C_{2} acting through Inn(D_{52}) | 104 | 2 | D52:5C2 | 208,38 |

C_{13}×C_{4}○D_{4} | Direct product of C_{13} and C_{4}○D_{4} | 104 | 2 | C13xC4oD4 | 208,48 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×C_{15} | Direct product of C_{15} and D_{7} | 105 | 2 | D7xC15 | 210,5 |

D_{5}×C_{21} | Direct product of C_{21} and D_{5} | 105 | 2 | D5xC21 | 210,6 |

C_{3}×D_{35} | Direct product of C_{3} and D_{35} | 105 | 2 | C3xD35 | 210,7 |

S_{3}×C_{35} | Direct product of C_{35} and S_{3} | 105 | 2 | S3xC35 | 210,8 |

C_{5}×D_{21} | Direct product of C_{5} and D_{21} | 105 | 2 | C5xD21 | 210,9 |

C_{7}×D_{15} | Direct product of C_{7} and D_{15} | 105 | 2 | C7xD15 | 210,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×Dic_{5} | Direct product of C_{11} and Dic_{5} | 220 | 2 | C11xDic5 | 220,3 |

C_{5}×Dic_{11} | Direct product of C_{5} and Dic_{11} | 220 | 2 | C5xDic11 | 220,4 |

C_{10}×D_{11} | Direct product of C_{10} and D_{11} | 110 | 2 | C10xD11 | 220,12 |

D_{5}×C_{22} | Direct product of C_{22} and D_{5} | 110 | 2 | D5xC22 | 220,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{37} | Direct product of C_{37} and S_{3} | 111 | 2 | S3xC37 | 222,3 |

C_{3}×D_{37} | Direct product of C_{3} and D_{37} | 111 | 2 | C3xD37 | 222,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{19} | Direct product of C_{19} and Dic_{3} | 228 | 2 | Dic3xC19 | 228,3 |

C_{3}×Dic_{19} | Direct product of C_{3} and Dic_{19} | 228 | 2 | C3xDic19 | 228,4 |

C_{6}×D_{19} | Direct product of C_{6} and D_{19} | 114 | 2 | C6xD19 | 228,12 |

S_{3}×C_{38} | Direct product of C_{38} and S_{3} | 114 | 2 | S3xC38 | 228,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{23} | Direct product of C_{23} and D_{5} | 115 | 2 | D5xC23 | 230,1 |

C_{5}×D_{23} | Direct product of C_{5} and D_{23} | 115 | 2 | C5xD23 | 230,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{29}⋊_{2}C_{8} | The semidirect product of C_{29} and C_{8} acting via C_{8}/C_{4}=C_{2} | 232 | 2 | C29:2C8 | 232,1 |

C_{4}×D_{29} | Direct product of C_{4} and D_{29} | 116 | 2 | C4xD29 | 232,5 |

C_{29}⋊D_{4} | The semidirect product of C_{29} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 116 | 2 | C29:D4 | 232,8 |

D_{4}×C_{29} | Direct product of C_{29} and D_{4} | 116 | 2 | D4xC29 | 232,10 |

Q_{8}×C_{29} | Direct product of C_{29} and Q_{8} | 232 | 2 | Q8xC29 | 232,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}×D_{9} | Direct product of C_{13} and D_{9} | 117 | 2 | C13xD9 | 234,3 |

C_{9}×D_{13} | Direct product of C_{9} and D_{13} | 117 | 2 | C9xD13 | 234,4 |

S_{3}×C_{39} | Direct product of C_{39} and S_{3} | 78 | 2 | S3xC39 | 234,12 |

C_{3}×D_{39} | Direct product of C_{3} and D_{39} | 78 | 2 | C3xD39 | 234,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×C_{17} | Direct product of C_{17} and D_{7} | 119 | 2 | D7xC17 | 238,1 |

C_{7}×D_{17} | Direct product of C_{7} and D_{17} | 119 | 2 | C7xD17 | 238,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×D_{11} | Direct product of C_{11} and D_{11}; = AΣL_{1}(𝔽_{121}) | 22 | 2 | C11xD11 | 242,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{41} | Direct product of C_{41} and S_{3} | 123 | 2 | S3xC41 | 246,1 |

C_{3}×D_{41} | Direct product of C_{3} and D_{41} | 123 | 2 | C3xD41 | 246,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{31}⋊C_{8} | The semidirect product of C_{31} and C_{8} acting via C_{8}/C_{4}=C_{2} | 248 | 2 | C31:C8 | 248,1 |

C_{4}×D_{31} | Direct product of C_{4} and D_{31} | 124 | 2 | C4xD31 | 248,4 |

C_{31}⋊D_{4} | The semidirect product of C_{31} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 124 | 2 | C31:D4 | 248,7 |

D_{4}×C_{31} | Direct product of C_{31} and D_{4} | 124 | 2 | D4xC31 | 248,9 |

Q_{8}×C_{31} | Direct product of C_{31} and Q_{8} | 248 | 2 | Q8xC31 | 248,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×D_{25} | Direct product of C_{5} and D_{25} | 50 | 2 | C5xD25 | 250,3 |

D_{5}×C_{25} | Direct product of C_{25} and D_{5} | 50 | 2 | D5xC25 | 250,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×Dic_{9} | Direct product of C_{7} and Dic_{9} | 252 | 2 | C7xDic9 | 252,3 |

C_{9}×Dic_{7} | Direct product of C_{9} and Dic_{7} | 252 | 2 | C9xDic7 | 252,4 |

D_{7}×C_{18} | Direct product of C_{18} and D_{7} | 126 | 2 | D7xC18 | 252,12 |

C_{14}×D_{9} | Direct product of C_{14} and D_{9} | 126 | 2 | C14xD9 | 252,13 |

Dic_{3}×C_{21} | Direct product of C_{21} and Dic_{3} | 84 | 2 | Dic3xC21 | 252,21 |

C_{3}×Dic_{21} | Direct product of C_{3} and Dic_{21} | 84 | 2 | C3xDic21 | 252,22 |

S_{3}×C_{42} | Direct product of C_{42} and S_{3} | 84 | 2 | S3xC42 | 252,42 |

C_{6}×D_{21} | Direct product of C_{6} and D_{21} | 84 | 2 | C6xD21 | 252,43 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{43} | Direct product of C_{43} and S_{3} | 129 | 2 | S3xC43 | 258,3 |

C_{3}×D_{43} | Direct product of C_{3} and D_{43} | 129 | 2 | C3xD43 | 258,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}×Dic_{5} | Direct product of C_{13} and Dic_{5} | 260 | 2 | C13xDic5 | 260,1 |

C_{5}×Dic_{13} | Direct product of C_{5} and Dic_{13} | 260 | 2 | C5xDic13 | 260,2 |

C_{10}×D_{13} | Direct product of C_{10} and D_{13} | 130 | 2 | C10xD13 | 260,12 |

D_{5}×C_{26} | Direct product of C_{26} and D_{5} | 130 | 2 | D5xC26 | 260,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×C_{19} | Direct product of C_{19} and D_{7} | 133 | 2 | D7xC19 | 266,1 |

C_{7}×D_{19} | Direct product of C_{7} and D_{19} | 133 | 2 | C7xD19 | 266,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×D_{27} | Direct product of C_{5} and D_{27} | 135 | 2 | C5xD27 | 270,1 |

D_{5}×C_{27} | Direct product of C_{27} and D_{5} | 135 | 2 | D5xC27 | 270,2 |

C_{15}×D_{9} | Direct product of C_{15} and D_{9} | 90 | 2 | C15xD9 | 270,8 |

S_{3}×C_{45} | Direct product of C_{45} and S_{3} | 90 | 2 | S3xC45 | 270,9 |

C_{3}×D_{45} | Direct product of C_{3} and D_{45} | 90 | 2 | C3xD45 | 270,12 |

C_{9}×D_{15} | Direct product of C_{9} and D_{15} | 90 | 2 | C9xD15 | 270,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}⋊_{4}C_{16} | The semidirect product of C_{17} and C_{16} acting via C_{16}/C_{8}=C_{2} | 272 | 2 | C17:4C16 | 272,1 |

C_{8}×D_{17} | Direct product of C_{8} and D_{17} | 136 | 2 | C8xD17 | 272,4 |

C_{8}⋊D_{17} | 3^{rd} semidirect product of C_{8} and D_{17} acting via D_{17}/C_{17}=C_{2} | 136 | 2 | C8:D17 | 272,5 |

C_{136}⋊C_{2} | 2^{nd} semidirect product of C_{136} and C_{2} acting faithfully | 136 | 2 | C136:C2 | 272,6 |

C_{68}._{4}C_{4} | 1^{st} non-split extension by C_{68} of C_{4} acting via C_{4}/C_{2}=C_{2} | 136 | 2 | C68.4C4 | 272,10 |

M_{4}(2)×C_{17} | Direct product of C_{17} and M_{4}(2) | 136 | 2 | M4(2)xC17 | 272,24 |

D_{8}×C_{17} | Direct product of C_{17} and D_{8} | 136 | 2 | D8xC17 | 272,25 |

SD_{16}×C_{17} | Direct product of C_{17} and SD_{16} | 136 | 2 | SD16xC17 | 272,26 |

Q_{16}×C_{17} | Direct product of C_{17} and Q_{16} | 272 | 2 | Q16xC17 | 272,27 |

D_{68}⋊_{5}C_{2} | The semidirect product of D_{68} and C_{2} acting through Inn(D_{68}) | 136 | 2 | D68:5C2 | 272,39 |

C_{4}○D_{4}×C_{17} | Direct product of C_{17} and C_{4}○D_{4} | 136 | 2 | C4oD4xC17 | 272,49 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{23} | Direct product of C_{23} and Dic_{3} | 276 | 2 | Dic3xC23 | 276,1 |

C_{3}×Dic_{23} | Direct product of C_{3} and Dic_{23} | 276 | 2 | C3xDic23 | 276,2 |

C_{6}×D_{23} | Direct product of C_{6} and D_{23} | 138 | 2 | C6xD23 | 276,7 |

S_{3}×C_{46} | Direct product of C_{46} and S_{3} | 138 | 2 | S3xC46 | 276,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{47} | Direct product of C_{47} and S_{3} | 141 | 2 | S3xC47 | 282,1 |

C_{3}×D_{47} | Direct product of C_{3} and D_{47} | 141 | 2 | C3xD47 | 282,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}×D_{11} | Direct product of C_{13} and D_{11} | 143 | 2 | C13xD11 | 286,1 |

C_{11}×D_{13} | Direct product of C_{11} and D_{13} | 143 | 2 | C11xD13 | 286,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{29} | Direct product of C_{29} and D_{5} | 145 | 2 | D5xC29 | 290,1 |

C_{5}×D_{29} | Direct product of C_{5} and D_{29} | 145 | 2 | C5xD29 | 290,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{49} | Direct product of C_{49} and S_{3} | 147 | 2 | S3xC49 | 294,3 |

C_{3}×D_{49} | Direct product of C_{3} and D_{49} | 147 | 2 | C3xD49 | 294,4 |

D_{7}×C_{21} | Direct product of C_{21} and D_{7} | 42 | 2 | D7xC21 | 294,18 |

C_{7}×D_{21} | Direct product of C_{7} and D_{21} | 42 | 2 | C7xD21 | 294,21 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{37}⋊_{2}C_{8} | The semidirect product of C_{37} and C_{8} acting via C_{8}/C_{4}=C_{2} | 296 | 2 | C37:2C8 | 296,1 |

C_{4}×D_{37} | Direct product of C_{4} and D_{37} | 148 | 2 | C4xD37 | 296,5 |

C_{37}⋊D_{4} | The semidirect product of C_{37} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 148 | 2 | C37:D4 | 296,8 |

D_{4}×C_{37} | Direct product of C_{37} and D_{4} | 148 | 2 | D4xC37 | 296,10 |

Q_{8}×C_{37} | Direct product of C_{37} and Q_{8} | 296 | 2 | Q8xC37 | 296,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{25} | Direct product of C_{25} and Dic_{3} | 300 | 2 | Dic3xC25 | 300,1 |

C_{3}×Dic_{25} | Direct product of C_{3} and Dic_{25} | 300 | 2 | C3xDic25 | 300,2 |

C_{6}×D_{25} | Direct product of C_{6} and D_{25} | 150 | 2 | C6xD25 | 300,9 |

S_{3}×C_{50} | Direct product of C_{50} and S_{3} | 150 | 2 | S3xC50 | 300,10 |

C_{15}×Dic_{5} | Direct product of C_{15} and Dic_{5} | 60 | 2 | C15xDic5 | 300,16 |

C_{5}×Dic_{15} | Direct product of C_{5} and Dic_{15} | 60 | 2 | C5xDic15 | 300,19 |

D_{5}×C_{30} | Direct product of C_{30} and D_{5} | 60 | 2 | D5xC30 | 300,44 |

C_{10}×D_{15} | Direct product of C_{10} and D_{15} | 60 | 2 | C10xD15 | 300,47 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{19}⋊C_{16} | The semidirect product of C_{19} and C_{16} acting via C_{16}/C_{8}=C_{2} | 304 | 2 | C19:C16 | 304,1 |

C_{8}×D_{19} | Direct product of C_{8} and D_{19} | 152 | 2 | C8xD19 | 304,3 |

C_{8}⋊D_{19} | 3^{rd} semidirect product of C_{8} and D_{19} acting via D_{19}/C_{19}=C_{2} | 152 | 2 | C8:D19 | 304,4 |

C_{152}⋊C_{2} | 2^{nd} semidirect product of C_{152} and C_{2} acting faithfully | 152 | 2 | C152:C2 | 304,5 |

C_{76}.C_{4} | 1^{st} non-split extension by C_{76} of C_{4} acting via C_{4}/C_{2}=C_{2} | 152 | 2 | C76.C4 | 304,9 |

M_{4}(2)×C_{19} | Direct product of C_{19} and M_{4}(2) | 152 | 2 | M4(2)xC19 | 304,23 |

D_{8}×C_{19} | Direct product of C_{19} and D_{8} | 152 | 2 | D8xC19 | 304,24 |

SD_{16}×C_{19} | Direct product of C_{19} and SD_{16} | 152 | 2 | SD16xC19 | 304,25 |

Q_{16}×C_{19} | Direct product of C_{19} and Q_{16} | 304 | 2 | Q16xC19 | 304,26 |

D_{76}⋊_{5}C_{2} | The semidirect product of D_{76} and C_{2} acting through Inn(D_{76}) | 152 | 2 | D76:5C2 | 304,30 |

C_{4}○D_{4}×C_{19} | Direct product of C_{19} and C_{4}○D_{4} | 152 | 2 | C4oD4xC19 | 304,40 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}×D_{9} | Direct product of C_{17} and D_{9} | 153 | 2 | C17xD9 | 306,1 |

C_{9}×D_{17} | Direct product of C_{9} and D_{17} | 153 | 2 | C9xD17 | 306,2 |

S_{3}×C_{51} | Direct product of C_{51} and S_{3} | 102 | 2 | S3xC51 | 306,6 |

C_{3}×D_{51} | Direct product of C_{3} and D_{51} | 102 | 2 | C3xD51 | 306,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×Dic_{7} | Direct product of C_{11} and Dic_{7} | 308 | 2 | C11xDic7 | 308,1 |

C_{7}×Dic_{11} | Direct product of C_{7} and Dic_{11} | 308 | 2 | C7xDic11 | 308,2 |

C_{14}×D_{11} | Direct product of C_{14} and D_{11} | 154 | 2 | C14xD11 | 308,6 |

D_{7}×C_{22} | Direct product of C_{22} and D_{7} | 154 | 2 | D7xC22 | 308,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{31} | Direct product of C_{31} and D_{5} | 155 | 2 | D5xC31 | 310,3 |

C_{5}×D_{31} | Direct product of C_{5} and D_{31} | 155 | 2 | C5xD31 | 310,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{53} | Direct product of C_{53} and S_{3} | 159 | 2 | S3xC53 | 318,1 |

C_{3}×D_{53} | Direct product of C_{3} and D_{53} | 159 | 2 | C3xD53 | 318,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×C_{23} | Direct product of C_{23} and D_{7} | 161 | 2 | D7xC23 | 322,1 |

C_{7}×D_{23} | Direct product of C_{7} and D_{23} | 161 | 2 | C7xD23 | 322,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{9}×Dic_{9} | Direct product of C_{9} and Dic_{9} | 36 | 2 | C9xDic9 | 324,6 |

C_{3}×Dic_{27} | Direct product of C_{3} and Dic_{27} | 108 | 2 | C3xDic27 | 324,10 |

Dic_{3}×C_{27} | Direct product of C_{27} and Dic_{3} | 108 | 2 | Dic3xC27 | 324,11 |

D_{9}×C_{18} | Direct product of C_{18} and D_{9} | 36 | 2 | D9xC18 | 324,61 |

C_{6}×D_{27} | Direct product of C_{6} and D_{27} | 108 | 2 | C6xD27 | 324,65 |

S_{3}×C_{54} | Direct product of C_{54} and S_{3} | 108 | 2 | S3xC54 | 324,66 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{41}⋊_{3}C_{8} | The semidirect product of C_{41} and C_{8} acting via C_{8}/C_{4}=C_{2} | 328 | 2 | C41:3C8 | 328,1 |

C_{4}×D_{41} | Direct product of C_{4} and D_{41} | 164 | 2 | C4xD41 | 328,5 |

C_{41}⋊D_{4} | The semidirect product of C_{41} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 164 | 2 | C41:D4 | 328,8 |

D_{4}×C_{41} | Direct product of C_{41} and D_{4} | 164 | 2 | D4xC41 | 328,10 |

Q_{8}×C_{41} | Direct product of C_{41} and Q_{8} | 328 | 2 | Q8xC41 | 328,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{15}×D_{11} | Direct product of C_{15} and D_{11} | 165 | 2 | C15xD11 | 330,5 |

D_{5}×C_{33} | Direct product of C_{33} and D_{5} | 165 | 2 | D5xC33 | 330,6 |

C_{3}×D_{55} | Direct product of C_{3} and D_{55} | 165 | 2 | C3xD55 | 330,7 |

S_{3}×C_{55} | Direct product of C_{55} and S_{3} | 165 | 2 | S3xC55 | 330,8 |

C_{5}×D_{33} | Direct product of C_{5} and D_{33} | 165 | 2 | C5xD33 | 330,9 |

C_{11}×D_{15} | Direct product of C_{11} and D_{15} | 165 | 2 | C11xD15 | 330,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}×D_{13} | Direct product of C_{13} and D_{13}; = AΣL_{1}(𝔽_{169}) | 26 | 2 | C13xD13 | 338,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}×Dic_{5} | Direct product of C_{17} and Dic_{5} | 340 | 2 | C17xDic5 | 340,1 |

C_{5}×Dic_{17} | Direct product of C_{5} and Dic_{17} | 340 | 2 | C5xDic17 | 340,2 |

C_{10}×D_{17} | Direct product of C_{10} and D_{17} | 170 | 2 | C10xD17 | 340,12 |

D_{5}×C_{34} | Direct product of C_{34} and D_{5} | 170 | 2 | D5xC34 | 340,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{9}×C_{19} | Direct product of C_{19} and D_{9} | 171 | 2 | D9xC19 | 342,3 |

C_{9}×D_{19} | Direct product of C_{9} and D_{19} | 171 | 2 | C9xD19 | 342,4 |

S_{3}×C_{57} | Direct product of C_{57} and S_{3} | 114 | 2 | S3xC57 | 342,14 |

C_{3}×D_{57} | Direct product of C_{3} and D_{57} | 114 | 2 | C3xD57 | 342,15 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{43}⋊C_{8} | The semidirect product of C_{43} and C_{8} acting via C_{8}/C_{4}=C_{2} | 344 | 2 | C43:C8 | 344,1 |

C_{4}×D_{43} | Direct product of C_{4} and D_{43} | 172 | 2 | C4xD43 | 344,4 |

C_{43}⋊D_{4} | The semidirect product of C_{43} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 172 | 2 | C43:D4 | 344,7 |

D_{4}×C_{43} | Direct product of C_{43} and D_{4} | 172 | 2 | D4xC43 | 344,9 |

Q_{8}×C_{43} | Direct product of C_{43} and Q_{8} | 344 | 2 | Q8xC43 | 344,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{29} | Direct product of C_{29} and Dic_{3} | 348 | 2 | Dic3xC29 | 348,1 |

C_{3}×Dic_{29} | Direct product of C_{3} and Dic_{29} | 348 | 2 | C3xDic29 | 348,2 |

C_{6}×D_{29} | Direct product of C_{6} and D_{29} | 174 | 2 | C6xD29 | 348,9 |

S_{3}×C_{58} | Direct product of C_{58} and S_{3} | 174 | 2 | S3xC58 | 348,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×D_{25} | Direct product of C_{7} and D_{25} | 175 | 2 | C7xD25 | 350,1 |

D_{7}×C_{25} | Direct product of C_{25} and D_{7} | 175 | 2 | D7xC25 | 350,2 |

D_{5}×C_{35} | Direct product of C_{35} and D_{5} | 70 | 2 | D5xC35 | 350,6 |

C_{5}×D_{35} | Direct product of C_{5} and D_{35} | 70 | 2 | C5xD35 | 350,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{59} | Direct product of C_{59} and S_{3} | 177 | 2 | S3xC59 | 354,1 |

C_{3}×D_{59} | Direct product of C_{3} and D_{59} | 177 | 2 | C3xD59 | 354,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}×Dic_{7} | Direct product of C_{13} and Dic_{7} | 364 | 2 | C13xDic7 | 364,1 |

C_{7}×Dic_{13} | Direct product of C_{7} and Dic_{13} | 364 | 2 | C7xDic13 | 364,2 |

C_{14}×D_{13} | Direct product of C_{14} and D_{13} | 182 | 2 | C14xD13 | 364,8 |

D_{7}×C_{26} | Direct product of C_{26} and D_{7} | 182 | 2 | D7xC26 | 364,9 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{61} | Direct product of C_{61} and S_{3} | 183 | 2 | S3xC61 | 366,3 |

C_{3}×D_{61} | Direct product of C_{3} and D_{61} | 183 | 2 | C3xD61 | 366,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{23}⋊C_{16} | The semidirect product of C_{23} and C_{16} acting via C_{16}/C_{8}=C_{2} | 368 | 2 | C23:C16 | 368,1 |

C_{8}×D_{23} | Direct product of C_{8} and D_{23} | 184 | 2 | C8xD23 | 368,3 |

C_{8}⋊D_{23} | 3^{rd} semidirect product of C_{8} and D_{23} acting via D_{23}/C_{23}=C_{2} | 184 | 2 | C8:D23 | 368,4 |

C_{184}⋊C_{2} | 2^{nd} semidirect product of C_{184} and C_{2} acting faithfully | 184 | 2 | C184:C2 | 368,5 |

C_{92}.C_{4} | 1^{st} non-split extension by C_{92} of C_{4} acting via C_{4}/C_{2}=C_{2} | 184 | 2 | C92.C4 | 368,9 |

M_{4}(2)×C_{23} | Direct product of C_{23} and M_{4}(2) | 184 | 2 | M4(2)xC23 | 368,23 |

D_{8}×C_{23} | Direct product of C_{23} and D_{8} | 184 | 2 | D8xC23 | 368,24 |

SD_{16}×C_{23} | Direct product of C_{23} and SD_{16} | 184 | 2 | SD16xC23 | 368,25 |

Q_{16}×C_{23} | Direct product of C_{23} and Q_{16} | 368 | 2 | Q16xC23 | 368,26 |

D_{92}⋊_{5}C_{2} | The semidirect product of D_{92} and C_{2} acting through Inn(D_{92}) | 184 | 2 | D92:5C2 | 368,30 |

C_{4}○D_{4}×C_{23} | Direct product of C_{23} and C_{4}○D_{4} | 184 | 2 | C4oD4xC23 | 368,40 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{37} | Direct product of C_{37} and D_{5} | 185 | 2 | D5xC37 | 370,1 |

C_{5}×D_{37} | Direct product of C_{5} and D_{37} | 185 | 2 | C5xD37 | 370,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{31} | Direct product of C_{31} and Dic_{3} | 372 | 2 | Dic3xC31 | 372,3 |

C_{3}×Dic_{31} | Direct product of C_{3} and Dic_{31} | 372 | 2 | C3xDic31 | 372,4 |

C_{6}×D_{31} | Direct product of C_{6} and D_{31} | 186 | 2 | C6xD31 | 372,12 |

S_{3}×C_{62} | Direct product of C_{62} and S_{3} | 186 | 2 | S3xC62 | 372,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}×D_{11} | Direct product of C_{17} and D_{11} | 187 | 2 | C17xD11 | 374,1 |

C_{11}×D_{17} | Direct product of C_{11} and D_{17} | 187 | 2 | C11xD17 | 374,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{47}⋊C_{8} | The semidirect product of C_{47} and C_{8} acting via C_{8}/C_{4}=C_{2} | 376 | 2 | C47:C8 | 376,1 |

C_{4}×D_{47} | Direct product of C_{4} and D_{47} | 188 | 2 | C4xD47 | 376,4 |

C_{47}⋊D_{4} | The semidirect product of C_{47} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 188 | 2 | C47:D4 | 376,7 |

D_{4}×C_{47} | Direct product of C_{47} and D_{4} | 188 | 2 | D4xC47 | 376,9 |

Q_{8}×C_{47} | Direct product of C_{47} and Q_{8} | 376 | 2 | Q8xC47 | 376,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}×D_{27} | Direct product of C_{7} and D_{27} | 189 | 2 | C7xD27 | 378,3 |

D_{7}×C_{27} | Direct product of C_{27} and D_{7} | 189 | 2 | D7xC27 | 378,4 |

D_{9}×C_{21} | Direct product of C_{21} and D_{9} | 126 | 2 | D9xC21 | 378,32 |

S_{3}×C_{63} | Direct product of C_{63} and S_{3} | 126 | 2 | S3xC63 | 378,33 |

C_{3}×D_{63} | Direct product of C_{3} and D_{63} | 126 | 2 | C3xD63 | 378,36 |

C_{9}×D_{21} | Direct product of C_{9} and D_{21} | 126 | 2 | C9xD21 | 378,37 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{19}×Dic_{5} | Direct product of C_{19} and Dic_{5} | 380 | 2 | C19xDic5 | 380,1 |

C_{5}×Dic_{19} | Direct product of C_{5} and Dic_{19} | 380 | 2 | C5xDic19 | 380,2 |

C_{10}×D_{19} | Direct product of C_{10} and D_{19} | 190 | 2 | C10xD19 | 380,8 |

D_{5}×C_{38} | Direct product of C_{38} and D_{5} | 190 | 2 | D5xC38 | 380,9 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{15}×D_{13} | Direct product of C_{15} and D_{13} | 195 | 2 | C15xD13 | 390,5 |

D_{5}×C_{39} | Direct product of C_{39} and D_{5} | 195 | 2 | D5xC39 | 390,6 |

C_{3}×D_{65} | Direct product of C_{3} and D_{65} | 195 | 2 | C3xD65 | 390,7 |

S_{3}×C_{65} | Direct product of C_{65} and S_{3} | 195 | 2 | S3xC65 | 390,8 |

C_{5}×D_{39} | Direct product of C_{5} and D_{39} | 195 | 2 | C5xD39 | 390,9 |

C_{13}×D_{15} | Direct product of C_{13} and D_{15} | 195 | 2 | C13xD15 | 390,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{49}⋊C_{8} | The semidirect product of C_{49} and C_{8} acting via C_{8}/C_{4}=C_{2} | 392 | 2 | C49:C8 | 392,1 |

C_{4}×D_{49} | Direct product of C_{4} and D_{49} | 196 | 2 | C4xD49 | 392,4 |

C_{49}⋊D_{4} | The semidirect product of C_{49} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 196 | 2 | C49:D4 | 392,7 |

D_{4}×C_{49} | Direct product of C_{49} and D_{4} | 196 | 2 | D4xC49 | 392,9 |

Q_{8}×C_{49} | Direct product of C_{49} and Q_{8} | 392 | 2 | Q8xC49 | 392,10 |

C_{7}×C_{7}⋊C_{8} | Direct product of C_{7} and C_{7}⋊C_{8} | 56 | 2 | C7xC7:C8 | 392,14 |

C_{7}×Dic_{14} | Direct product of C_{7} and Dic_{14} | 56 | 2 | C7xDic14 | 392,23 |

D_{7}×C_{28} | Direct product of C_{28} and D_{7} | 56 | 2 | D7xC28 | 392,24 |

C_{7}×D_{28} | Direct product of C_{7} and D_{28} | 56 | 2 | C7xD28 | 392,25 |

C_{7}×C_{7}⋊D_{4} | Direct product of C_{7} and C_{7}⋊D_{4} | 28 | 2 | C7xC7:D4 | 392,27 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×Dic_{9} | Direct product of C_{11} and Dic_{9} | 396 | 2 | C11xDic9 | 396,1 |

C_{9}×Dic_{11} | Direct product of C_{9} and Dic_{11} | 396 | 2 | C9xDic11 | 396,2 |

C_{18}×D_{11} | Direct product of C_{18} and D_{11} | 198 | 2 | C18xD11 | 396,7 |

D_{9}×C_{22} | Direct product of C_{22} and D_{9} | 198 | 2 | D9xC22 | 396,8 |

Dic_{3}×C_{33} | Direct product of C_{33} and Dic_{3} | 132 | 2 | Dic3xC33 | 396,12 |

C_{3}×Dic_{33} | Direct product of C_{3} and Dic_{33} | 132 | 2 | C3xDic33 | 396,13 |

S_{3}×C_{66} | Direct product of C_{66} and S_{3} | 132 | 2 | S3xC66 | 396,26 |

C_{6}×D_{33} | Direct product of C_{6} and D_{33} | 132 | 2 | C6xD33 | 396,27 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{67} | Direct product of C_{67} and S_{3} | 201 | 2 | S3xC67 | 402,3 |

C_{3}×D_{67} | Direct product of C_{3} and D_{67} | 201 | 2 | C3xD67 | 402,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×C_{29} | Direct product of C_{29} and D_{7} | 203 | 2 | D7xC29 | 406,3 |

C_{7}×D_{29} | Direct product of C_{7} and D_{29} | 203 | 2 | C7xD29 | 406,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{41} | Direct product of C_{41} and D_{5} | 205 | 2 | D5xC41 | 410,3 |

C_{5}×D_{41} | Direct product of C_{5} and D_{41} | 205 | 2 | C5xD41 | 410,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{9}×C_{23} | Direct product of C_{23} and D_{9} | 207 | 2 | D9xC23 | 414,1 |

C_{9}×D_{23} | Direct product of C_{9} and D_{23} | 207 | 2 | C9xD23 | 414,2 |

S_{3}×C_{69} | Direct product of C_{69} and S_{3} | 138 | 2 | S3xC69 | 414,6 |

C_{3}×D_{69} | Direct product of C_{3} and D_{69} | 138 | 2 | C3xD69 | 414,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{19}×D_{11} | Direct product of C_{19} and D_{11} | 209 | 2 | C19xD11 | 418,1 |

C_{11}×D_{19} | Direct product of C_{11} and D_{19} | 209 | 2 | C11xD19 | 418,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{15}×Dic_{7} | Direct product of C_{15} and Dic_{7} | 420 | 2 | C15xDic7 | 420,5 |

Dic_{5}×C_{21} | Direct product of C_{21} and Dic_{5} | 420 | 2 | Dic5xC21 | 420,6 |

C_{3}×Dic_{35} | Direct product of C_{3} and Dic_{35} | 420 | 2 | C3xDic35 | 420,7 |

Dic_{3}×C_{35} | Direct product of C_{35} and Dic_{3} | 420 | 2 | Dic3xC35 | 420,8 |

C_{5}×Dic_{21} | Direct product of C_{5} and Dic_{21} | 420 | 2 | C5xDic21 | 420,9 |

C_{7}×Dic_{15} | Direct product of C_{7} and Dic_{15} | 420 | 2 | C7xDic15 | 420,10 |

D_{7}×C_{30} | Direct product of C_{30} and D_{7} | 210 | 2 | D7xC30 | 420,34 |

D_{5}×C_{42} | Direct product of C_{42} and D_{5} | 210 | 2 | D5xC42 | 420,35 |

C_{6}×D_{35} | Direct product of C_{6} and D_{35} | 210 | 2 | C6xD35 | 420,36 |

S_{3}×C_{70} | Direct product of C_{70} and S_{3} | 210 | 2 | S3xC70 | 420,37 |

C_{10}×D_{21} | Direct product of C_{10} and D_{21} | 210 | 2 | C10xD21 | 420,38 |

C_{14}×D_{15} | Direct product of C_{14} and D_{15} | 210 | 2 | C14xD15 | 420,39 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{53}⋊_{2}C_{8} | The semidirect product of C_{53} and C_{8} acting via C_{8}/C_{4}=C_{2} | 424 | 2 | C53:2C8 | 424,1 |

C_{4}×D_{53} | Direct product of C_{4} and D_{53} | 212 | 2 | C4xD53 | 424,5 |

C_{53}⋊D_{4} | The semidirect product of C_{53} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 212 | 2 | C53:D4 | 424,8 |

D_{4}×C_{53} | Direct product of C_{53} and D_{4} | 212 | 2 | D4xC53 | 424,10 |

Q_{8}×C_{53} | Direct product of C_{53} and Q_{8} | 424 | 2 | Q8xC53 | 424,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{71} | Direct product of C_{71} and S_{3} | 213 | 2 | S3xC71 | 426,1 |

C_{3}×D_{71} | Direct product of C_{3} and D_{71} | 213 | 2 | C3xD71 | 426,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{43} | Direct product of C_{43} and D_{5} | 215 | 2 | D5xC43 | 430,1 |

C_{5}×D_{43} | Direct product of C_{5} and D_{43} | 215 | 2 | C5xD43 | 430,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×C_{31} | Direct product of C_{31} and D_{7} | 217 | 2 | D7xC31 | 434,1 |

C_{7}×D_{31} | Direct product of C_{7} and D_{31} | 217 | 2 | C7xD31 | 434,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{73} | Direct product of C_{73} and S_{3} | 219 | 2 | S3xC73 | 438,3 |

C_{3}×D_{73} | Direct product of C_{3} and D_{73} | 219 | 2 | C3xD73 | 438,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}×D_{13} | Direct product of C_{17} and D_{13} | 221 | 2 | C17xD13 | 442,1 |

C_{13}×D_{17} | Direct product of C_{13} and D_{17} | 221 | 2 | C13xD17 | 442,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{37} | Direct product of C_{37} and Dic_{3} | 444 | 2 | Dic3xC37 | 444,3 |

C_{3}×Dic_{37} | Direct product of C_{3} and Dic_{37} | 444 | 2 | C3xDic37 | 444,4 |

C_{6}×D_{37} | Direct product of C_{6} and D_{37} | 222 | 2 | C6xD37 | 444,15 |

S_{3}×C_{74} | Direct product of C_{74} and S_{3} | 222 | 2 | S3xC74 | 444,16 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{9}×C_{25} | Direct product of C_{25} and D_{9} | 225 | 2 | D9xC25 | 450,1 |

C_{9}×D_{25} | Direct product of C_{9} and D_{25} | 225 | 2 | C9xD25 | 450,2 |

S_{3}×C_{75} | Direct product of C_{75} and S_{3} | 150 | 2 | S3xC75 | 450,6 |

C_{3}×D_{75} | Direct product of C_{3} and D_{75} | 150 | 2 | C3xD75 | 450,7 |

D_{5}×C_{45} | Direct product of C_{45} and D_{5} | 90 | 2 | D5xC45 | 450,14 |

C_{5}×D_{45} | Direct product of C_{5} and D_{45} | 90 | 2 | C5xD45 | 450,17 |

C_{15}×D_{15} | Direct product of C_{15} and D_{15} | 30 | 2 | C15xD15 | 450,29 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{5}×C_{23} | Direct product of C_{23} and Dic_{5} | 460 | 2 | Dic5xC23 | 460,1 |

C_{5}×Dic_{23} | Direct product of C_{5} and Dic_{23} | 460 | 2 | C5xDic23 | 460,2 |

C_{10}×D_{23} | Direct product of C_{10} and D_{23} | 230 | 2 | C10xD23 | 460,8 |

D_{5}×C_{46} | Direct product of C_{46} and D_{5} | 230 | 2 | D5xC46 | 460,9 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{21}×D_{11} | Direct product of C_{21} and D_{11} | 231 | 2 | C21xD11 | 462,5 |

D_{7}×C_{33} | Direct product of C_{33} and D_{7} | 231 | 2 | D7xC33 | 462,6 |

C_{3}×D_{77} | Direct product of C_{3} and D_{77} | 231 | 2 | C3xD77 | 462,7 |

S_{3}×C_{77} | Direct product of C_{77} and S_{3} | 231 | 2 | S3xC77 | 462,8 |

C_{7}×D_{33} | Direct product of C_{7} and D_{33} | 231 | 2 | C7xD33 | 462,9 |

C_{11}×D_{21} | Direct product of C_{11} and D_{21} | 231 | 2 | C11xD21 | 462,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{29}⋊_{2}C_{16} | The semidirect product of C_{29} and C_{16} acting via C_{16}/C_{8}=C_{2} | 464 | 2 | C29:2C16 | 464,1 |

C_{8}×D_{29} | Direct product of C_{8} and D_{29} | 232 | 2 | C8xD29 | 464,4 |

C_{8}⋊D_{29} | 3^{rd} semidirect product of C_{8} and D_{29} acting via D_{29}/C_{29}=C_{2} | 232 | 2 | C8:D29 | 464,5 |

C_{232}⋊C_{2} | 2^{nd} semidirect product of C_{232} and C_{2} acting faithfully | 232 | 2 | C232:C2 | 464,6 |

C_{4}.Dic_{29} | The non-split extension by C_{4} of Dic_{29} acting via Dic_{29}/C_{58}=C_{2} | 232 | 2 | C4.Dic29 | 464,10 |

M_{4}(2)×C_{29} | Direct product of C_{29} and M_{4}(2) | 232 | 2 | M4(2)xC29 | 464,24 |

D_{8}×C_{29} | Direct product of C_{29} and D_{8} | 232 | 2 | D8xC29 | 464,25 |

SD_{16}×C_{29} | Direct product of C_{29} and SD_{16} | 232 | 2 | SD16xC29 | 464,26 |

Q_{16}×C_{29} | Direct product of C_{29} and Q_{16} | 464 | 2 | Q16xC29 | 464,27 |

D_{116}⋊_{5}C_{2} | The semidirect product of D_{116} and C_{2} acting through Inn(D_{116}) | 232 | 2 | D116:5C2 | 464,38 |

C_{4}○D_{4}×C_{29} | Direct product of C_{29} and C_{4}○D_{4} | 232 | 2 | C4oD4xC29 | 464,48 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}×Dic_{9} | Direct product of C_{13} and Dic_{9} | 468 | 2 | C13xDic9 | 468,3 |

C_{9}×Dic_{13} | Direct product of C_{9} and Dic_{13} | 468 | 2 | C9xDic13 | 468,4 |

C_{18}×D_{13} | Direct product of C_{18} and D_{13} | 234 | 2 | C18xD13 | 468,15 |

D_{9}×C_{26} | Direct product of C_{26} and D_{9} | 234 | 2 | D9xC26 | 468,16 |

Dic_{3}×C_{39} | Direct product of C_{39} and Dic_{3} | 156 | 2 | Dic3xC39 | 468,24 |

C_{3}×Dic_{39} | Direct product of C_{3} and Dic_{39} | 156 | 2 | C3xDic39 | 468,25 |

S_{3}×C_{78} | Direct product of C_{78} and S_{3} | 156 | 2 | S3xC78 | 468,51 |

C_{6}×D_{39} | Direct product of C_{6} and D_{39} | 156 | 2 | C6xD39 | 468,52 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{47} | Direct product of C_{47} and D_{5} | 235 | 2 | D5xC47 | 470,1 |

C_{5}×D_{47} | Direct product of C_{5} and D_{47} | 235 | 2 | C5xD47 | 470,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{59}⋊C_{8} | The semidirect product of C_{59} and C_{8} acting via C_{8}/C_{4}=C_{2} | 472 | 2 | C59:C8 | 472,1 |

C_{4}×D_{59} | Direct product of C_{4} and D_{59} | 236 | 2 | C4xD59 | 472,4 |

C_{59}⋊D_{4} | The semidirect product of C_{59} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 236 | 2 | C59:D4 | 472,7 |

D_{4}×C_{59} | Direct product of C_{59} and D_{4} | 236 | 2 | D4xC59 | 472,9 |

Q_{8}×C_{59} | Direct product of C_{59} and Q_{8} | 472 | 2 | Q8xC59 | 472,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{79} | Direct product of C_{79} and S_{3} | 237 | 2 | S3xC79 | 474,3 |

C_{3}×D_{79} | Direct product of C_{3} and D_{79} | 237 | 2 | C3xD79 | 474,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}×Dic_{7} | Direct product of C_{17} and Dic_{7} | 476 | 2 | C17xDic7 | 476,1 |

C_{7}×Dic_{17} | Direct product of C_{7} and Dic_{17} | 476 | 2 | C7xDic17 | 476,2 |

C_{14}×D_{17} | Direct product of C_{14} and D_{17} | 238 | 2 | C14xD17 | 476,8 |

D_{7}×C_{34} | Direct product of C_{34} and D_{7} | 238 | 2 | D7xC34 | 476,9 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×Dic_{11} | Direct product of C_{11} and Dic_{11} | 44 | 2 | C11xDic11 | 484,5 |

D_{11}×C_{22} | Direct product of C_{22} and D_{11} | 44 | 2 | D11xC22 | 484,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{9}×D_{27} | Direct product of C_{9} and D_{27} | 54 | 2 | C9xD27 | 486,13 |

D_{9}×C_{27} | Direct product of C_{27} and D_{9} | 54 | 2 | D9xC27 | 486,14 |

C_{3}×D_{81} | Direct product of C_{3} and D_{81} | 162 | 2 | C3xD81 | 486,32 |

S_{3}×C_{81} | Direct product of C_{81} and S_{3} | 162 | 2 | S3xC81 | 486,33 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{61}⋊_{2}C_{8} | The semidirect product of C_{61} and C_{8} acting via C_{8}/C_{4}=C_{2} | 488 | 2 | C61:2C8 | 488,1 |

C_{4}×D_{61} | Direct product of C_{4} and D_{61} | 244 | 2 | C4xD61 | 488,5 |

C_{61}⋊D_{4} | The semidirect product of C_{61} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 244 | 2 | C61:D4 | 488,8 |

D_{4}×C_{61} | Direct product of C_{61} and D_{4} | 244 | 2 | D4xC61 | 488,10 |

Q_{8}×C_{61} | Direct product of C_{61} and Q_{8} | 488 | 2 | Q8xC61 | 488,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×C_{49} | Direct product of C_{49} and D_{5} | 245 | 2 | D5xC49 | 490,1 |

C_{5}×D_{49} | Direct product of C_{5} and D_{49} | 245 | 2 | C5xD49 | 490,2 |

D_{7}×C_{35} | Direct product of C_{35} and D_{7} | 70 | 2 | D7xC35 | 490,5 |

C_{7}×D_{35} | Direct product of C_{7} and D_{35} | 70 | 2 | C7xD35 | 490,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×C_{41} | Direct product of C_{41} and Dic_{3} | 492 | 2 | Dic3xC41 | 492,1 |

C_{3}×Dic_{41} | Direct product of C_{3} and Dic_{41} | 492 | 2 | C3xDic41 | 492,2 |

C_{6}×D_{41} | Direct product of C_{6} and D_{41} | 246 | 2 | C6xD41 | 492,9 |

S_{3}×C_{82} | Direct product of C_{82} and S_{3} | 246 | 2 | S3xC82 | 492,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{19}×D_{13} | Direct product of C_{19} and D_{13} | 247 | 2 | C19xD13 | 494,1 |

C_{13}×D_{19} | Direct product of C_{13} and D_{19} | 247 | 2 | C13xD19 | 494,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{31}⋊C_{16} | The semidirect product of C_{31} and C_{16} acting via C_{16}/C_{8}=C_{2} | 496 | 2 | C31:C16 | 496,1 |

C_{8}×D_{31} | Direct product of C_{8} and D_{31} | 248 | 2 | C8xD31 | 496,3 |

C_{8}⋊D_{31} | 3^{rd} semidirect product of C_{8} and D_{31} acting via D_{31}/C_{31}=C_{2} | 248 | 2 | C8:D31 | 496,4 |

C_{248}⋊C_{2} | 2^{nd} semidirect product of C_{248} and C_{2} acting faithfully | 248 | 2 | C248:C2 | 496,5 |

C_{4}.Dic_{31} | The non-split extension by C_{4} of Dic_{31} acting via Dic_{31}/C_{62}=C_{2} | 248 | 2 | C4.Dic31 | 496,9 |

M_{4}(2)×C_{31} | Direct product of C_{31} and M_{4}(2) | 248 | 2 | M4(2)xC31 | 496,23 |

D_{8}×C_{31} | Direct product of C_{31} and D_{8} | 248 | 2 | D8xC31 | 496,24 |

SD_{16}×C_{31} | Direct product of C_{31} and SD_{16} | 248 | 2 | SD16xC31 | 496,25 |

Q_{16}×C_{31} | Direct product of C_{31} and Q_{16} | 496 | 2 | Q16xC31 | 496,26 |

D_{124}⋊_{5}C_{2} | The semidirect product of D_{124} and C_{2} acting through Inn(D_{124}) | 248 | 2 | D124:5C2 | 496,30 |

C_{4}○D_{4}×C_{31} | Direct product of C_{31} and C_{4}○D_{4} | 248 | 2 | C4oD4xC31 | 496,40 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×C_{83} | Direct product of C_{83} and S_{3} | 249 | 2 | S3xC83 | 498,1 |

C_{3}×D_{83} | Direct product of C_{3} and D_{83} | 249 | 2 | C3xD83 | 498,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×Dic_{25} | Direct product of C_{5} and Dic_{25} | 100 | 2 | C5xDic25 | 500,6 |

Dic_{5}×C_{25} | Direct product of C_{25} and Dic_{5} | 100 | 2 | Dic5xC25 | 500,7 |

C_{10}×D_{25} | Direct product of C_{10} and D_{25} | 100 | 2 | C10xD25 | 500,28 |

D_{5}×C_{50} | Direct product of C_{50} and D_{5} | 100 | 2 | D5xC50 | 500,29 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

A_{4} | Alternating group on 4 letters; = PSL_{2}(𝔽_{3}) = L_{2}(3) = tetrahedron rotations | 4 | 3+ | A4 | 12,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{4} | Symmetric group on 4 letters; = PGL_{2}(𝔽_{3}) = Aut(Q_{8}) = Hol(C_{2}^{2}) = tetrahedron symmetries = cube/octahedron rotations | 4 | 3+ | S4 | 24,12 |

C_{2}×A_{4} | Direct product of C_{2} and A_{4}; = AΣL_{1}(𝔽_{8}) | 6 | 3+ | C2xA4 | 24,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×S_{4} | Direct product of C_{2} and S_{4}; = O_{3}(𝔽_{3}) = cube/octahedron symmetries | 6 | 3+ | C2xS4 | 48,48 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

A_{5} | Alternating group on 5 letters; = SL_{2}(𝔽_{4}) = L_{2}(5) = L_{2}(4) = icosahedron/dodecahedron rotations; 1^{st} non-abelian simple | 5 | 3+ | A5 | 60,5 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×A_{5} | Direct product of C_{2} and A_{5}; = icosahedron/dodecahedron symmetries | 10 | 3+ | C2xA5 | 120,35 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}⋊C_{3} | The semidirect product of C_{7} and C_{3} acting faithfully | 7 | 3 | C7:C3 | 21,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

He_{3} | Heisenberg group; = C_{3}^{2}⋊C_{3} = 3_{+}^{ 1+2} | 9 | 3 | He3 | 27,3 |

3_{-}^{ 1+2} | Extraspecial group | 9 | 3 | ES-(3,1) | 27,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}.A_{4} | The central extension by C_{3} of A_{4} | 18 | 3 | C3.A4 | 36,3 |

C_{3}×A_{4} | Direct product of C_{3} and A_{4} | 12 | 3 | C3xA4 | 36,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}⋊C_{3} | The semidirect product of C_{13} and C_{3} acting faithfully | 13 | 3 | C13:C3 | 39,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{7}⋊C_{3} | Direct product of C_{2} and C_{7}⋊C_{3} | 14 | 3 | C2xC7:C3 | 42,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}^{2}⋊C_{3} | The semidirect product of C_{4}^{2} and C_{3} acting faithfully | 12 | 3 | C4^2:C3 | 48,3 |

A_{4}⋊C_{4} | The semidirect product of A_{4} and C_{4} acting via C_{4}/C_{2}=C_{2}; = SL_{2}(ℤ/4ℤ) | 12 | 3 | A4:C4 | 48,30 |

C_{4}×A_{4} | Direct product of C_{4} and A_{4} | 12 | 3 | C4xA4 | 48,31 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

He_{3}⋊C_{2} | 2^{nd} semidirect product of He_{3} and C_{2} acting faithfully; = Aut(3_{-}^{ 1+2}) | 9 | 3 | He3:C2 | 54,8 |

C_{2}×He_{3} | Direct product of C_{2} and He_{3} | 18 | 3 | C2xHe3 | 54,10 |

C_{2}×3_{-}^{ 1+2} | Direct product of C_{2} and 3_{-}^{ 1+2} | 18 | 3 | C2xES-(3,1) | 54,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{19}⋊C_{3} | The semidirect product of C_{19} and C_{3} acting faithfully | 19 | 3 | C19:C3 | 57,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×A_{4} | Direct product of C_{5} and A_{4} | 20 | 3 | C5xA4 | 60,9 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}⋊C_{9} | The semidirect product of C_{7} and C_{9} acting via C_{9}/C_{3}=C_{3} | 63 | 3 | C7:C9 | 63,1 |

C_{3}×C_{7}⋊C_{3} | Direct product of C_{3} and C_{7}⋊C_{3} | 21 | 3 | C3xC7:C3 | 63,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{3}.A_{4} | Direct product of C_{2} and C_{3}.A_{4} | 18 | 3 | C2xC3.A4 | 72,16 |

C_{3}×S_{4} | Direct product of C_{3} and S_{4} | 12 | 3 | C3xS4 | 72,42 |

C_{6}×A_{4} | Direct product of C_{6} and A_{4} | 18 | 3 | C6xA4 | 72,47 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}^{2}⋊C_{3} | The semidirect product of C_{5}^{2} and C_{3} acting faithfully | 15 | 3 | C5^2:C3 | 75,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{13}⋊C_{3} | Direct product of C_{2} and C_{13}⋊C_{3} | 26 | 3 | C2xC13:C3 | 78,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{27}⋊C_{3} | The semidirect product of C_{27} and C_{3} acting faithfully | 27 | 3 | C27:C3 | 81,6 |

C_{3}≀C_{3} | Wreath product of C_{3} by C_{3}; = AΣL_{1}(𝔽_{27}) | 9 | 3 | C3wrC3 | 81,7 |

He_{3}.C_{3} | The non-split extension by He_{3} of C_{3} acting faithfully | 27 | 3 | He3.C3 | 81,8 |

He_{3}⋊C_{3} | 2^{nd} semidirect product of He_{3} and C_{3} acting faithfully | 27 | 3 | He3:C3 | 81,9 |

C_{3}.He_{3} | 4^{th} central stem extension by C_{3} of He_{3} | 27 | 3 | C3.He3 | 81,10 |

C_{9}○He_{3} | Central product of C_{9} and He_{3} | 27 | 3 | C9oHe3 | 81,14 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}×C_{7}⋊C_{3} | Direct product of C_{4} and C_{7}⋊C_{3} | 28 | 3 | C4xC7:C3 | 84,2 |

C_{7}×A_{4} | Direct product of C_{7} and A_{4} | 28 | 3 | C7xA4 | 84,10 |

C_{7}⋊A_{4} | The semidirect product of C_{7} and A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 28 | 3 | C7:A4 | 84,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{31}⋊C_{3} | The semidirect product of C_{31} and C_{3} acting faithfully | 31 | 3 | C31:C3 | 93,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}^{2}⋊S_{3} | The semidirect product of C_{4}^{2} and S_{3} acting faithfully | 12 | 3 | C4^2:S3 | 96,64 |

A_{4}⋊C_{8} | The semidirect product of A_{4} and C_{8} acting via C_{8}/C_{4}=C_{2} | 24 | 3 | A4:C8 | 96,65 |

C_{2}×C_{4}^{2}⋊C_{3} | Direct product of C_{2} and C_{4}^{2}⋊C_{3} | 12 | 3 | C2xC4^2:C3 | 96,68 |

C_{8}×A_{4} | Direct product of C_{8} and A_{4} | 24 | 3 | C8xA4 | 96,73 |

C_{4}×S_{4} | Direct product of C_{4} and S_{4} | 12 | 3 | C4xS4 | 96,186 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{7}⋊C_{3} | Direct product of C_{5} and C_{7}⋊C_{3} | 35 | 3 | C5xC7:C3 | 105,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{9}.A_{4} | The central extension by C_{9} of A_{4} | 54 | 3 | C9.A4 | 108,3 |

He_{3}⋊_{3}C_{4} | 2^{nd} semidirect product of He_{3} and C_{4} acting via C_{4}/C_{2}=C_{2} | 36 | 3 | He3:3C4 | 108,11 |

C_{4}×He_{3} | Direct product of C_{4} and He_{3} | 36 | 3 | C4xHe3 | 108,13 |

C_{4}×3_{-}^{ 1+2} | Direct product of C_{4} and 3_{-}^{ 1+2} | 36 | 3 | C4xES-(3,1) | 108,14 |

He_{3}⋊C_{4} | The semidirect product of He_{3} and C_{4} acting faithfully | 18 | 3 | He3:C4 | 108,15 |

C_{9}×A_{4} | Direct product of C_{9} and A_{4} | 36 | 3 | C9xA4 | 108,18 |

C_{9}⋊A_{4} | The semidirect product of C_{9} and A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 36 | 3 | C9:A4 | 108,19 |

C_{3}^{2}.A_{4} | The non-split extension by C_{3}^{2} of A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 18 | 3 | C3^2.A4 | 108,21 |

C_{3}^{2}⋊A_{4} | The semidirect product of C_{3}^{2} and A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 18 | 3 | C3^2:A4 | 108,22 |

C_{2}×He_{3}⋊C_{2} | Direct product of C_{2} and He_{3}⋊C_{2} | 18 | 3 | C2xHe3:C2 | 108,28 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{37}⋊C_{3} | The semidirect product of C_{37} and C_{3} acting faithfully | 37 | 3 | C37:C3 | 111,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{19}⋊C_{3} | Direct product of C_{2} and C_{19}⋊C_{3} | 38 | 3 | C2xC19:C3 | 114,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}⋊C_{9} | The semidirect product of C_{13} and C_{9} acting via C_{9}/C_{3}=C_{3} | 117 | 3 | C13:C9 | 117,1 |

C_{3}×C_{13}⋊C_{3} | Direct product of C_{3} and C_{13}⋊C_{3} | 39 | 3 | C3xC13:C3 | 117,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×S_{4} | Direct product of C_{5} and S_{4} | 20 | 3 | C5xS4 | 120,37 |

C_{10}×A_{4} | Direct product of C_{10} and A_{4} | 30 | 3 | C10xA4 | 120,43 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{7}⋊C_{9} | Direct product of C_{2} and C_{7}⋊C_{9} | 126 | 3 | C2xC7:C9 | 126,2 |

C_{6}×C_{7}⋊C_{3} | Direct product of C_{6} and C_{7}⋊C_{3} | 42 | 3 | C6xC7:C3 | 126,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{43}⋊C_{3} | The semidirect product of C_{43} and C_{3} acting faithfully | 43 | 3 | C43:C3 | 129,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×A_{4} | Direct product of C_{11} and A_{4} | 44 | 3 | C11xA4 | 132,6 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×He_{3} | Direct product of C_{5} and He_{3} | 45 | 3 | C5xHe3 | 135,3 |

C_{5}×3_{-}^{ 1+2} | Direct product of C_{5} and 3_{-}^{ 1+2} | 45 | 3 | C5xES-(3,1) | 135,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}^{2}⋊C_{9} | The semidirect product of C_{4}^{2} and C_{9} acting via C_{9}/C_{3}=C_{3} | 36 | 3 | C4^2:C9 | 144,3 |

C_{4}×C_{3}.A_{4} | Direct product of C_{4} and C_{3}.A_{4} | 36 | 3 | C4xC3.A4 | 144,34 |

C_{3}×C_{4}^{2}⋊C_{3} | Direct product of C_{3} and C_{4}^{2}⋊C_{3} | 36 | 3 | C3xC4^2:C3 | 144,68 |

C_{3}×A_{4}⋊C_{4} | Direct product of C_{3} and A_{4}⋊C_{4} | 36 | 3 | C3xA4:C4 | 144,123 |

C_{12}×A_{4} | Direct product of C_{12} and A_{4} | 36 | 3 | C12xA4 | 144,155 |

C_{6}×S_{4} | Direct product of C_{6} and S_{4} | 18 | 3 | C6xS4 | 144,188 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{49}⋊C_{3} | The semidirect product of C_{49} and C_{3} acting faithfully | 49 | 3 | C49:C3 | 147,1 |

C_{7}×C_{7}⋊C_{3} | Direct product of C_{7} and C_{7}⋊C_{3} | 21 | 3 | C7xC7:C3 | 147,3 |

C_{7}^{2}⋊_{3}C_{3} | 3^{rd} semidirect product of C_{7}^{2} and C_{3} acting faithfully | 21 | 3 | C7^2:3C3 | 147,5 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}^{2}⋊S_{3} | The semidirect product of C_{5}^{2} and S_{3} acting faithfully | 15 | 3 | C5^2:S3 | 150,5 |

C_{2}×C_{5}^{2}⋊C_{3} | Direct product of C_{2} and C_{5}^{2}⋊C_{3} | 30 | 3 | C2xC5^2:C3 | 150,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}×C_{13}⋊C_{3} | Direct product of C_{4} and C_{13}⋊C_{3} | 52 | 3 | C4xC13:C3 | 156,2 |

A_{4}×C_{13} | Direct product of C_{13} and A_{4} | 52 | 3 | A4xC13 | 156,13 |

C_{13}⋊A_{4} | The semidirect product of C_{13} and A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 52 | 3 | C13:A4 | 156,14 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}≀S_{3} | Wreath product of C_{3} by S_{3} | 9 | 3 | C3wrS3 | 162,10 |

He_{3}.C_{6} | 1^{st} non-split extension by He_{3} of C_{6} acting faithfully | 27 | 3 | He3.C6 | 162,12 |

He_{3}._{2}C_{6} | 2^{nd} non-split extension by He_{3} of C_{6} acting faithfully | 27 | 3 | He3.2C6 | 162,14 |

C_{2}×C_{27}⋊C_{3} | Direct product of C_{2} and C_{27}⋊C_{3} | 54 | 3 | C2xC27:C3 | 162,27 |

C_{2}×C_{3}≀C_{3} | Direct product of C_{2} and C_{3}≀C_{3} | 18 | 3 | C2xC3wrC3 | 162,28 |

C_{2}×He_{3}.C_{3} | Direct product of C_{2} and He_{3}.C_{3} | 54 | 3 | C2xHe3.C3 | 162,29 |

C_{2}×He_{3}⋊C_{3} | Direct product of C_{2} and He_{3}⋊C_{3} | 54 | 3 | C2xHe3:C3 | 162,30 |

C_{2}×C_{3}.He_{3} | Direct product of C_{2} and C_{3}.He_{3} | 54 | 3 | C2xC3.He3 | 162,31 |

He_{3}._{4}C_{6} | The non-split extension by He_{3} of C_{6} acting via C_{6}/C_{3}=C_{2} | 27 | 3 | He3.4C6 | 162,44 |

C_{2}×C_{9}○He_{3} | Direct product of C_{2} and C_{9}○He_{3} | 54 | 3 | C2xC9oHe3 | 162,50 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{8}×C_{7}⋊C_{3} | Direct product of C_{8} and C_{7}⋊C_{3} | 56 | 3 | C8xC7:C3 | 168,2 |

GL_{3}(𝔽_{2}) | General linear group on 𝔽_{2}^{3}; = Aut(C_{2}^{3}) = L_{3}(2) = L_{2}(7); 2^{nd} non-abelian simple | 7 | 3 | GL(3,2) | 168,42 |

C_{7}×S_{4} | Direct product of C_{7} and S_{4} | 28 | 3 | C7xS4 | 168,45 |

A_{4}×C_{14} | Direct product of C_{14} and A_{4} | 42 | 3 | A4xC14 | 168,52 |

C_{2}×C_{7}⋊A_{4} | Direct product of C_{2} and C_{7}⋊A_{4} | 42 | 3 | C2xC7:A4 | 168,53 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{19}⋊_{2}C_{9} | The semidirect product of C_{19} and C_{9} acting via C_{9}/C_{3}=C_{3} | 171 | 3 | C19:2C9 | 171,1 |

C_{3}×C_{19}⋊C_{3} | Direct product of C_{3} and C_{19}⋊C_{3} | 57 | 3 | C3xC19:C3 | 171,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{3}.A_{4} | Direct product of C_{5} and C_{3}.A_{4} | 90 | 3 | C5xC3.A4 | 180,8 |

C_{3}×A_{5} | Direct product of C_{3} and A_{5}; = GL_{2}(𝔽_{4}) | 15 | 3 | C3xA5 | 180,19 |

A_{4}×C_{15} | Direct product of C_{15} and A_{4} | 60 | 3 | A4xC15 | 180,31 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{61}⋊C_{3} | The semidirect product of C_{61} and C_{3} acting faithfully | 61 | 3 | C61:C3 | 183,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{31}⋊C_{3} | Direct product of C_{2} and C_{31}⋊C_{3} | 62 | 3 | C2xC31:C3 | 186,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}⋊C_{27} | The semidirect product of C_{7} and C_{27} acting via C_{27}/C_{9}=C_{3} | 189 | 3 | C7:C27 | 189,1 |

C_{9}×C_{7}⋊C_{3} | Direct product of C_{9} and C_{7}⋊C_{3} | 63 | 3 | C9xC7:C3 | 189,3 |

C_{63}⋊C_{3} | 2^{nd} semidirect product of C_{63} and C_{3} acting faithfully | 63 | 3 | C63:C3 | 189,4 |

C_{63}⋊_{3}C_{3} | 3^{rd} semidirect product of C_{63} and C_{3} acting faithfully | 63 | 3 | C63:3C3 | 189,5 |

C_{21}.C_{3}^{2} | 5^{th} non-split extension by C_{21} of C_{3}^{2} acting via C_{3}^{2}/C_{3}=C_{3} | 63 | 3 | C21.C3^2 | 189,7 |

C_{7}⋊He_{3} | The semidirect product of C_{7} and He_{3} acting via He_{3}/C_{3}^{2}=C_{3} | 63 | 3 | C7:He3 | 189,8 |

C_{7}×He_{3} | Direct product of C_{7} and He_{3} | 63 | 3 | C7xHe3 | 189,10 |

C_{7}×3_{-}^{ 1+2} | Direct product of C_{7} and 3_{-}^{ 1+2} | 63 | 3 | C7xES-(3,1) | 189,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{8}^{2}⋊C_{3} | The semidirect product of C_{8}^{2} and C_{3} acting faithfully | 24 | 3 | C8^2:C3 | 192,3 |

C_{2}^{3}._{9}S_{4} | 3^{rd} non-split extension by C_{2}^{3} of S_{4} acting via S_{4}/C_{2}^{2}=S_{3} | 12 | 3 | C2^3.9S4 | 192,182 |

A_{4}⋊C_{16} | The semidirect product of A_{4} and C_{16} acting via C_{16}/C_{8}=C_{2} | 48 | 3 | A4:C16 | 192,186 |

C_{4}×C_{4}^{2}⋊C_{3} | Direct product of C_{4} and C_{4}^{2}⋊C_{3} | 12 | 3 | C4xC4^2:C3 | 192,188 |

A_{4}×C_{16} | Direct product of C_{16} and A_{4} | 48 | 3 | A4xC16 | 192,203 |

C_{2}×C_{4}^{2}⋊S_{3} | Direct product of C_{2} and C_{4}^{2}⋊S_{3} | 12 | 3 | C2xC4^2:S3 | 192,944 |

C_{8}×S_{4} | Direct product of C_{8} and S_{4} | 24 | 3 | C8xS4 | 192,958 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{13}⋊C_{3} | Direct product of C_{5} and C_{13}⋊C_{3} | 65 | 3 | C5xC13:C3 | 195,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{67}⋊C_{3} | The semidirect product of C_{67} and C_{3} acting faithfully | 67 | 3 | C67:C3 | 201,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

A_{4}×C_{17} | Direct product of C_{17} and A_{4} | 68 | 3 | A4xC17 | 204,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{10}×C_{7}⋊C_{3} | Direct product of C_{10} and C_{7}⋊C_{3} | 70 | 3 | C10xC7:C3 | 210,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{73}⋊C_{3} | The semidirect product of C_{73} and C_{3} acting faithfully | 73 | 3 | C73:C3 | 219,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{37}⋊C_{3} | Direct product of C_{2} and C_{37}⋊C_{3} | 74 | 3 | C2xC37:C3 | 222,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}^{2}⋊C_{9} | The semidirect product of C_{5}^{2} and C_{9} acting via C_{9}/C_{3}=C_{3} | 45 | 3 | C5^2:C9 | 225,3 |

C_{3}×C_{5}^{2}⋊C_{3} | Direct product of C_{3} and C_{5}^{2}⋊C_{3} | 45 | 3 | C3xC5^2:C3 | 225,5 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}×C_{19}⋊C_{3} | Direct product of C_{4} and C_{19}⋊C_{3} | 76 | 3 | C4xC19:C3 | 228,2 |

A_{4}×C_{19} | Direct product of C_{19} and A_{4} | 76 | 3 | A4xC19 | 228,10 |

C_{19}⋊A_{4} | The semidirect product of C_{19} and A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 76 | 3 | C19:A4 | 228,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×C_{7}⋊C_{3} | Direct product of C_{11} and C_{7}⋊C_{3} | 77 | 3 | C11xC7:C3 | 231,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{13}⋊C_{9} | Direct product of C_{2} and C_{13}⋊C_{9} | 234 | 3 | C2xC13:C9 | 234,2 |

C_{6}×C_{13}⋊C_{3} | Direct product of C_{6} and C_{13}⋊C_{3} | 78 | 3 | C6xC13:C3 | 234,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{79}⋊C_{3} | The semidirect product of C_{79} and C_{3} acting faithfully | 79 | 3 | C79:C3 | 237,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{4}^{2}⋊C_{3} | Direct product of C_{5} and C_{4}^{2}⋊C_{3} | 60 | 3 | C5xC4^2:C3 | 240,32 |

C_{4}×A_{5} | Direct product of C_{4} and A_{5} | 20 | 3 | C4xA5 | 240,92 |

C_{5}×A_{4}⋊C_{4} | Direct product of C_{5} and A_{4}⋊C_{4} | 60 | 3 | C5xA4:C4 | 240,104 |

A_{4}×C_{20} | Direct product of C_{20} and A_{4} | 60 | 3 | A4xC20 | 240,152 |

C_{10}×S_{4} | Direct product of C_{10} and S_{4} | 30 | 3 | C10xS4 | 240,196 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{9}._{4}He_{3} | 2^{nd} central extension by C_{9} of He_{3} | 27 | 3 | C9.4He3 | 243,16 |

C_{9}._{5}He_{3} | 3^{rd} central extension by C_{9} of He_{3} | 81 | 3 | C9.5He3 | 243,19 |

C_{9}._{6}He_{3} | 4^{th} central extension by C_{9} of He_{3} | 81 | 3 | C9.6He3 | 243,20 |

C_{81}⋊C_{3} | The semidirect product of C_{81} and C_{3} acting faithfully | 81 | 3 | C81:C3 | 243,24 |

C_{9}^{2}⋊C_{3} | 1^{st} semidirect product of C_{9}^{2} and C_{3} acting faithfully | 27 | 3 | C9^2:C3 | 243,25 |

C_{9}^{2}⋊_{2}C_{3} | 2^{nd} semidirect product of C_{9}^{2} and C_{3} acting faithfully | 27 | 3 | C9^2:2C3 | 243,26 |

C_{9}^{2}.C_{3} | 2^{nd} non-split extension by C_{9}^{2} of C_{3} acting faithfully | 27 | 3 | C9^2.C3 | 243,27 |

C_{27}○He_{3} | Central product of C_{27} and He_{3} | 81 | 3 | C27oHe3 | 243,50 |

C_{9}.He_{3} | 1^{st} non-split extension by C_{9} of He_{3} acting via He_{3}/C_{3}^{2}=C_{3} | 27 | 3 | C9.He3 | 243,55 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}×C_{7}⋊C_{9} | Direct product of C_{4} and C_{7}⋊C_{9} | 252 | 3 | C4xC7:C9 | 252,2 |

C_{7}×C_{3}.A_{4} | Direct product of C_{7} and C_{3}.A_{4} | 126 | 3 | C7xC3.A4 | 252,10 |

C_{21}.A_{4} | The non-split extension by C_{21} of A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 126 | 3 | C21.A4 | 252,11 |

C_{12}×C_{7}⋊C_{3} | Direct product of C_{12} and C_{7}⋊C_{3} | 84 | 3 | C12xC7:C3 | 252,19 |

A_{4}×C_{21} | Direct product of C_{21} and A_{4} | 84 | 3 | A4xC21 | 252,39 |

C_{3}×C_{7}⋊A_{4} | Direct product of C_{3} and C_{7}⋊A_{4} | 84 | 3 | C3xC7:A4 | 252,40 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{43}⋊C_{3} | Direct product of C_{2} and C_{43}⋊C_{3} | 86 | 3 | C2xC43:C3 | 258,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×S_{4} | Direct product of C_{11} and S_{4} | 44 | 3 | C11xS4 | 264,31 |

A_{4}×C_{22} | Direct product of C_{22} and A_{4} | 66 | 3 | A4xC22 | 264,35 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×He_{3}⋊C_{2} | Direct product of C_{5} and He_{3}⋊C_{2} | 45 | 3 | C5xHe3:C2 | 270,17 |

C_{10}×He_{3} | Direct product of C_{10} and He_{3} | 90 | 3 | C10xHe3 | 270,21 |

C_{10}×3_{-}^{ 1+2} | Direct product of C_{10} and 3_{-}^{ 1+2} | 90 | 3 | C10xES-(3,1) | 270,22 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}×C_{7}⋊C_{3} | Direct product of C_{13} and C_{7}⋊C_{3} | 91 | 3 | C13xC7:C3 | 273,1 |

C_{7}×C_{13}⋊C_{3} | Direct product of C_{7} and C_{13}⋊C_{3} | 91 | 3 | C7xC13:C3 | 273,2 |

C_{91}⋊C_{3} | 3^{rd} semidirect product of C_{91} and C_{3} acting faithfully | 91 | 3 | C91:C3 | 273,3 |

C_{91}⋊_{4}C_{3} | 4^{th} semidirect product of C_{91} and C_{3} acting faithfully | 91 | 3 | C91:4C3 | 273,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

A_{4}×C_{23} | Direct product of C_{23} and A_{4} | 92 | 3 | A4xC23 | 276,6 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{31}⋊C_{9} | The semidirect product of C_{31} and C_{9} acting via C_{9}/C_{3}=C_{3} | 279 | 3 | C31:C9 | 279,1 |

C_{3}×C_{31}⋊C_{3} | Direct product of C_{3} and C_{31}⋊C_{3} | 93 | 3 | C3xC31:C3 | 279,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{19}⋊C_{3} | Direct product of C_{5} and C_{19}⋊C_{3} | 95 | 3 | C5xC19:C3 | 285,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{4}^{2}⋊C_{9} | Direct product of C_{2} and C_{4}^{2}⋊C_{9} | 36 | 3 | C2xC4^2:C9 | 288,71 |

C_{8}×C_{3}.A_{4} | Direct product of C_{8} and C_{3}.A_{4} | 72 | 3 | C8xC3.A4 | 288,76 |

C_{3}×C_{4}^{2}⋊S_{3} | Direct product of C_{3} and C_{4}^{2}⋊S_{3} | 36 | 3 | C3xC4^2:S3 | 288,397 |

C_{3}×A_{4}⋊C_{8} | Direct product of C_{3} and A_{4}⋊C_{8} | 72 | 3 | C3xA4:C8 | 288,398 |

C_{6}×C_{4}^{2}⋊C_{3} | Direct product of C_{6} and C_{4}^{2}⋊C_{3} | 36 | 3 | C6xC4^2:C3 | 288,632 |

A_{4}×C_{24} | Direct product of C_{24} and A_{4} | 72 | 3 | A4xC24 | 288,637 |

C_{12}×S_{4} | Direct product of C_{12} and S_{4} | 36 | 3 | C12xS4 | 288,897 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{97}⋊C_{3} | The semidirect product of C_{97} and C_{3} acting faithfully | 97 | 3 | C97:C3 | 291,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{49}⋊C_{3} | Direct product of C_{2} and C_{49}⋊C_{3} | 98 | 3 | C2xC49:C3 | 294,2 |

C_{7}^{2}⋊S_{3} | The semidirect product of C_{7}^{2} and S_{3} acting faithfully | 14 | 3 | C7^2:S3 | 294,7 |

C_{14}×C_{7}⋊C_{3} | Direct product of C_{14} and C_{7}⋊C_{3} | 42 | 3 | C14xC7:C3 | 294,15 |

C_{2}×C_{7}^{2}⋊_{3}C_{3} | Direct product of C_{2} and C_{7}^{2}⋊_{3}C_{3} | 42 | 3 | C2xC7^2:3C3 | 294,17 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×He_{3} | Direct product of C_{11} and He_{3} | 99 | 3 | C11xHe3 | 297,3 |

C_{11}×3_{-}^{ 1+2} | Direct product of C_{11} and 3_{-}^{ 1+2} | 99 | 3 | C11xES-(3,1) | 297,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

A_{4}×C_{25} | Direct product of C_{25} and A_{4} | 100 | 3 | A4xC25 | 300,8 |

C_{5}^{2}⋊_{2}Dic_{3} | The semidirect product of C_{5}^{2} and Dic_{3} acting via Dic_{3}/C_{2}=S_{3} | 60 | 3 | C5^2:2Dic3 | 300,13 |

C_{4}×C_{5}^{2}⋊C_{3} | Direct product of C_{4} and C_{5}^{2}⋊C_{3} | 60 | 3 | C4xC5^2:C3 | 300,15 |

C_{5}×A_{5} | Direct product of C_{5} and A_{5}; = U_{2}(𝔽_{4}) | 25 | 3 | C5xA5 | 300,22 |

C_{2}×C_{5}^{2}⋊S_{3} | Direct product of C_{2} and C_{5}^{2}⋊S_{3} | 30 | 3 | C2xC5^2:S3 | 300,26 |

C_{5}^{2}⋊A_{4} | The semidirect product of C_{5}^{2} and A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 30 | 3 | C5^2:A4 | 300,43 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{103}⋊C_{3} | The semidirect product of C_{103} and C_{3} acting faithfully | 103 | 3 | C103:C3 | 309,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{8}×C_{13}⋊C_{3} | Direct product of C_{8} and C_{13}⋊C_{3} | 104 | 3 | C8xC13:C3 | 312,2 |

C_{13}×S_{4} | Direct product of C_{13} and S_{4} | 52 | 3 | C13xS4 | 312,47 |

A_{4}×C_{26} | Direct product of C_{26} and A_{4} | 78 | 3 | A4xC26 | 312,56 |

C_{2}×C_{13}⋊A_{4} | Direct product of C_{2} and C_{13}⋊A_{4} | 78 | 3 | C2xC13:A4 | 312,57 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{7}⋊C_{9} | Direct product of C_{5} and C_{7}⋊C_{9} | 315 | 3 | C5xC7:C9 | 315,1 |

C_{15}×C_{7}⋊C_{3} | Direct product of C_{15} and C_{7}⋊C_{3} | 105 | 3 | C15xC7:C3 | 315,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{109}⋊C_{3} | The semidirect product of C_{109} and C_{3} acting faithfully | 109 | 3 | C109:C3 | 327,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{37}⋊_{2}C_{9} | The semidirect product of C_{37} and C_{9} acting via C_{9}/C_{3}=C_{3} | 333 | 3 | C37:2C9 | 333,1 |

C_{3}×C_{37}⋊C_{3} | Direct product of C_{3} and C_{37}⋊C_{3} | 111 | 3 | C3xC37:C3 | 333,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{16}×C_{7}⋊C_{3} | Direct product of C_{16} and C_{7}⋊C_{3} | 112 | 3 | C16xC7:C3 | 336,2 |

C_{7}×C_{4}^{2}⋊C_{3} | Direct product of C_{7} and C_{4}^{2}⋊C_{3} | 84 | 3 | C7xC4^2:C3 | 336,56 |

C_{4}^{2}⋊(C_{7}⋊C_{3}) | The semidirect product of C_{4}^{2} and C_{7}⋊C_{3} acting via C_{7}⋊C_{3}/C_{7}=C_{3} | 84 | 3 | C4^2:(C7:C3) | 336,57 |

C_{7}×A_{4}⋊C_{4} | Direct product of C_{7} and A_{4}⋊C_{4} | 84 | 3 | C7xA4:C4 | 336,117 |

A_{4}×C_{28} | Direct product of C_{28} and A_{4} | 84 | 3 | A4xC28 | 336,168 |

C_{4}×C_{7}⋊A_{4} | Direct product of C_{4} and C_{7}⋊A_{4} | 84 | 3 | C4xC7:A4 | 336,171 |

C_{2}×GL_{3}(𝔽_{2}) | Direct product of C_{2} and GL_{3}(𝔽_{2}) | 14 | 3 | C2xGL(3,2) | 336,209 |

C_{14}×S_{4} | Direct product of C_{14} and S_{4} | 42 | 3 | C14xS4 | 336,214 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{19}⋊_{2}C_{9} | Direct product of C_{2} and C_{19}⋊_{2}C_{9} | 342 | 3 | C2xC19:2C9 | 342,2 |

C_{6}×C_{19}⋊C_{3} | Direct product of C_{6} and C_{19}⋊C_{3} | 114 | 3 | C6xC19:C3 | 342,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

A_{4}×C_{29} | Direct product of C_{29} and A_{4} | 116 | 3 | A4xC29 | 348,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}⋊C_{27} | The semidirect product of C_{13} and C_{27} acting via C_{27}/C_{9}=C_{3} | 351 | 3 | C13:C27 | 351,1 |

C_{9}×C_{13}⋊C_{3} | Direct product of C_{9} and C_{13}⋊C_{3} | 117 | 3 | C9xC13:C3 | 351,3 |

C_{117}⋊C_{3} | 2^{nd} semidirect product of C_{117} and C_{3} acting faithfully | 117 | 3 | C117:C3 | 351,4 |

C_{117}⋊_{3}C_{3} | 3^{rd} semidirect product of C_{117} and C_{3} acting faithfully | 117 | 3 | C117:3C3 | 351,5 |

C_{39}.C_{3}^{2} | 5^{th} non-split extension by C_{39} of C_{3}^{2} acting via C_{3}^{2}/C_{3}=C_{3} | 117 | 3 | C39.C3^2 | 351,7 |

C_{13}⋊He_{3} | The semidirect product of C_{13} and He_{3} acting via He_{3}/C_{3}^{2}=C_{3} | 117 | 3 | C13:He3 | 351,8 |

C_{13}×He_{3} | Direct product of C_{13} and He_{3} | 117 | 3 | C13xHe3 | 351,10 |

C_{13}×3_{-}^{ 1+2} | Direct product of C_{13} and 3_{-}^{ 1+2} | 117 | 3 | C13xES-(3,1) | 351,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}×C_{7}⋊C_{3} | Direct product of C_{17} and C_{7}⋊C_{3} | 119 | 3 | C17xC7:C3 | 357,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{10}×C_{3}.A_{4} | Direct product of C_{10} and C_{3}.A_{4} | 90 | 3 | C10xC3.A4 | 360,46 |

C_{6}×A_{5} | Direct product of C_{6} and A_{5} | 30 | 3 | C6xA5 | 360,122 |

C_{15}×S_{4} | Direct product of C_{15} and S_{4} | 60 | 3 | C15xS4 | 360,138 |

A_{4}×C_{30} | Direct product of C_{30} and A_{4} | 90 | 3 | A4xC30 | 360,156 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}^{2}⋊C_{3} | The semidirect product of C_{11}^{2} and C_{3} acting faithfully | 33 | 3 | C11^2:C3 | 363,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{61}⋊C_{3} | Direct product of C_{2} and C_{61}⋊C_{3} | 122 | 3 | C2xC61:C3 | 366,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}×C_{31}⋊C_{3} | Direct product of C_{4} and C_{31}⋊C_{3} | 124 | 3 | C4xC31:C3 | 372,2 |

A_{4}×C_{31} | Direct product of C_{31} and A_{4} | 124 | 3 | A4xC31 | 372,10 |

C_{31}⋊A_{4} | The semidirect product of C_{31} and A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 124 | 3 | C31:A4 | 372,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{5}^{2}⋊C_{3} | Direct product of C_{5} and C_{5}^{2}⋊C_{3}; = AΣL_{1}(𝔽_{125}) | 15 | 3 | C5xC5^2:C3 | 375,6 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{7}⋊C_{27} | Direct product of C_{2} and C_{7}⋊C_{27} | 378 | 3 | C2xC7:C27 | 378,2 |

C_{18}×C_{7}⋊C_{3} | Direct product of C_{18} and C_{7}⋊C_{3} | 126 | 3 | C18xC7:C3 | 378,23 |

C_{2}×C_{63}⋊C_{3} | Direct product of C_{2} and C_{63}⋊C_{3} | 126 | 3 | C2xC63:C3 | 378,24 |

C_{2}×C_{63}⋊_{3}C_{3} | Direct product of C_{2} and C_{63}⋊_{3}C_{3} | 126 | 3 | C2xC63:3C3 | 378,25 |

C_{2}×C_{21}.C_{3}^{2} | Direct product of C_{2} and C_{21}.C_{3}^{2} | 126 | 3 | C2xC21.C3^2 | 378,27 |

C_{2}×C_{7}⋊He_{3} | Direct product of C_{2} and C_{7}⋊He_{3} | 126 | 3 | C2xC7:He3 | 378,28 |

C_{7}×He_{3}⋊C_{2} | Direct product of C_{7} and He_{3}⋊C_{2} | 63 | 3 | C7xHe3:C2 | 378,41 |

C_{14}×He_{3} | Direct product of C_{14} and He_{3} | 126 | 3 | C14xHe3 | 378,45 |

C_{14}×3_{-}^{ 1+2} | Direct product of C_{14} and 3_{-}^{ 1+2} | 126 | 3 | C14xES-(3,1) | 378,46 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{127}⋊C_{3} | The semidirect product of C_{127} and C_{3} acting faithfully | 127 | 3 | C127:C3 | 381,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{43}⋊C_{9} | The semidirect product of C_{43} and C_{9} acting via C_{9}/C_{3}=C_{3} | 387 | 3 | C43:C9 | 387,1 |

C_{3}×C_{43}⋊C_{3} | Direct product of C_{3} and C_{43}⋊C_{3} | 129 | 3 | C3xC43:C3 | 387,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{10}×C_{13}⋊C_{3} | Direct product of C_{10} and C_{13}⋊C_{3} | 130 | 3 | C10xC13:C3 | 390,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×C_{3}.A_{4} | Direct product of C_{11} and C_{3}.A_{4} | 198 | 3 | C11xC3.A4 | 396,6 |

A_{4}×C_{33} | Direct product of C_{33} and A_{4} | 132 | 3 | A4xC33 | 396,24 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{19}×C_{7}⋊C_{3} | Direct product of C_{19} and C_{7}⋊C_{3} | 133 | 3 | C19xC7:C3 | 399,1 |

C_{7}×C_{19}⋊C_{3} | Direct product of C_{7} and C_{19}⋊C_{3} | 133 | 3 | C7xC19:C3 | 399,2 |

C_{133}⋊C_{3} | 3^{rd} semidirect product of C_{133} and C_{3} acting faithfully | 133 | 3 | C133:C3 | 399,3 |

C_{133}⋊_{4}C_{3} | 4^{th} semidirect product of C_{133} and C_{3} acting faithfully | 133 | 3 | C133:4C3 | 399,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{67}⋊C_{3} | Direct product of C_{2} and C_{67}⋊C_{3} | 134 | 3 | C2xC67:C3 | 402,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{27}⋊C_{3} | Direct product of C_{5} and C_{27}⋊C_{3} | 135 | 3 | C5xC27:C3 | 405,6 |

C_{5}×C_{3}≀C_{3} | Direct product of C_{5} and C_{3}≀C_{3} | 45 | 3 | C5xC3wrC3 | 405,7 |

C_{5}×He_{3}.C_{3} | Direct product of C_{5} and He_{3}.C_{3} | 135 | 3 | C5xHe3.C3 | 405,8 |

C_{5}×He_{3}⋊C_{3} | Direct product of C_{5} and He_{3}⋊C_{3} | 135 | 3 | C5xHe3:C3 | 405,9 |

C_{5}×C_{3}.He_{3} | Direct product of C_{5} and C_{3}.He_{3} | 135 | 3 | C5xC3.He3 | 405,10 |

C_{5}×C_{9}○He_{3} | Direct product of C_{5} and C_{9}○He_{3} | 135 | 3 | C5xC9oHe3 | 405,14 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}×S_{4} | Direct product of C_{17} and S_{4} | 68 | 3 | C17xS4 | 408,36 |

A_{4}×C_{34} | Direct product of C_{34} and A_{4} | 102 | 3 | A4xC34 | 408,42 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{139}⋊C_{3} | The semidirect product of C_{139} and C_{3} acting faithfully | 139 | 3 | C139:C3 | 417,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{20}×C_{7}⋊C_{3} | Direct product of C_{20} and C_{7}⋊C_{3} | 140 | 3 | C20xC7:C3 | 420,4 |

C_{7}×A_{5} | Direct product of C_{7} and A_{5} | 35 | 3 | C7xA5 | 420,13 |

A_{4}×C_{35} | Direct product of C_{35} and A_{4} | 140 | 3 | A4xC35 | 420,32 |

C_{5}×C_{7}⋊A_{4} | Direct product of C_{5} and C_{7}⋊A_{4} | 140 | 3 | C5xC7:A4 | 420,33 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}×C_{13}⋊C_{3} | Direct product of C_{11} and C_{13}⋊C_{3} | 143 | 3 | C11xC13:C3 | 429,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{73}⋊C_{3} | Direct product of C_{2} and C_{73}⋊C_{3} | 146 | 3 | C2xC73:C3 | 438,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{49}⋊C_{9} | The semidirect product of C_{49} and C_{9} acting via C_{9}/C_{3}=C_{3} | 441 | 3 | C49:C9 | 441,1 |

C_{3}×C_{49}⋊C_{3} | Direct product of C_{3} and C_{49}⋊C_{3} | 147 | 3 | C3xC49:C3 | 441,3 |

C_{7}×C_{7}⋊C_{9} | Direct product of C_{7} and C_{7}⋊C_{9} | 63 | 3 | C7xC7:C9 | 441,5 |

C_{7}^{2}⋊_{3}C_{9} | 3^{rd} semidirect product of C_{7}^{2} and C_{9} acting via C_{9}/C_{3}=C_{3} | 63 | 3 | C7^2:3C9 | 441,7 |

C_{7}⋊C_{3}×C_{21} | Direct product of C_{21} and C_{7}⋊C_{3} | 63 | 3 | C7:C3xC21 | 441,10 |

C_{3}×C_{7}^{2}⋊_{3}C_{3} | Direct product of C_{3} and C_{7}^{2}⋊_{3}C_{3} | 63 | 3 | C3xC7^2:3C3 | 441,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}×C_{37}⋊C_{3} | Direct product of C_{4} and C_{37}⋊C_{3} | 148 | 3 | C4xC37:C3 | 444,2 |

A_{4}×C_{37} | Direct product of C_{37} and A_{4} | 148 | 3 | A4xC37 | 444,13 |

C_{37}⋊A_{4} | The semidirect product of C_{37} and A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 148 | 3 | C37:A4 | 444,14 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{5}^{2}⋊C_{9} | Direct product of C_{2} and C_{5}^{2}⋊C_{9} | 90 | 3 | C2xC5^2:C9 | 450,13 |

C_{3}×C_{5}^{2}⋊S_{3} | Direct product of C_{3} and C_{5}^{2}⋊S_{3} | 45 | 3 | C3xC5^2:S3 | 450,20 |

C_{6}×C_{5}^{2}⋊C_{3} | Direct product of C_{6} and C_{5}^{2}⋊C_{3} | 90 | 3 | C6xC5^2:C3 | 450,25 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{151}⋊C_{3} | The semidirect product of C_{151} and C_{3} acting faithfully | 151 | 3 | C151:C3 | 453,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{8}×C_{19}⋊C_{3} | Direct product of C_{8} and C_{19}⋊C_{3} | 152 | 3 | C8xC19:C3 | 456,2 |

C_{19}×S_{4} | Direct product of C_{19} and S_{4} | 76 | 3 | C19xS4 | 456,42 |

A_{4}×C_{38} | Direct product of C_{38} and A_{4} | 114 | 3 | A4xC38 | 456,49 |

C_{2}×C_{19}⋊A_{4} | Direct product of C_{2} and C_{19}⋊A_{4} | 114 | 3 | C2xC19:A4 | 456,50 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}×He_{3} | Direct product of C_{17} and He_{3} | 153 | 3 | C17xHe3 | 459,3 |

C_{17}×3_{-}^{ 1+2} | Direct product of C_{17} and 3_{-}^{ 1+2} | 153 | 3 | C17xES-(3,1) | 459,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}⋊C_{3}×C_{22} | Direct product of C_{22} and C_{7}⋊C_{3} | 154 | 3 | C7:C3xC22 | 462,4 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}×C_{31}⋊C_{3} | Direct product of C_{5} and C_{31}⋊C_{3} | 155 | 3 | C5xC31:C3 | 465,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}×C_{13}⋊C_{9} | Direct product of C_{4} and C_{13}⋊C_{9} | 468 | 3 | C4xC13:C9 | 468,2 |

C_{13}×C_{3}.A_{4} | Direct product of C_{13} and C_{3}.A_{4} | 234 | 3 | C13xC3.A4 | 468,13 |

C_{39}.A_{4} | The non-split extension by C_{39} of A_{4} acting via A_{4}/C_{2}^{2}=C_{3} | 234 | 3 | C39.A4 | 468,14 |

C_{12}×C_{13}⋊C_{3} | Direct product of C_{12} and C_{13}⋊C_{3} | 156 | 3 | C12xC13:C3 | 468,22 |

A_{4}×C_{39} | Direct product of C_{39} and A_{4} | 156 | 3 | A4xC39 | 468,48 |

C_{3}×C_{13}⋊A_{4} | Direct product of C_{3} and C_{13}⋊A_{4} | 156 | 3 | C3xC13:A4 | 468,49 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{157}⋊C_{3} | The semidirect product of C_{157} and C_{3} acting faithfully | 157 | 3 | C157:C3 | 471,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{79}⋊C_{3} | Direct product of C_{2} and C_{79}⋊C_{3} | 158 | 3 | C2xC79:C3 | 474,2 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{8}×A_{5} | Direct product of C_{8} and A_{5} | 40 | 3 | C8xA5 | 480,220 |

C_{5}×C_{4}^{2}⋊S_{3} | Direct product of C_{5} and C_{4}^{2}⋊S_{3} | 60 | 3 | C5xC4^2:S3 | 480,254 |

C_{5}×A_{4}⋊C_{8} | Direct product of C_{5} and A_{4}⋊C_{8} | 120 | 3 | C5xA4:C8 | 480,255 |

C_{10}×C_{4}^{2}⋊C_{3} | Direct product of C_{10} and C_{4}^{2}⋊C_{3} | 60 | 3 | C10xC4^2:C3 | 480,654 |

A_{4}×C_{40} | Direct product of C_{40} and A_{4} | 120 | 3 | A4xC40 | 480,659 |

C_{20}×S_{4} | Direct product of C_{20} and S_{4} | 60 | 3 | C20xS4 | 480,1014 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}⋊C_{3}×C_{23} | Direct product of C_{23} and C_{7}⋊C_{3} | 161 | 3 | C7:C3xC23 | 483,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{163}⋊C_{3} | The semidirect product of C_{163} and C_{3} acting faithfully | 163 | 3 | C163:C3 | 489,1 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

A_{4}×C_{41} | Direct product of C_{41} and A_{4} | 164 | 3 | A4xC41 | 492,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

F_{5} | Frobenius group; = C_{5}⋊C_{4} = AGL_{1}(𝔽_{5}) = Aut(D_{5}) = Hol(C_{5}) = Sz(2) | 5 | 4+ | F5 | 20,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}^{3}⋊C_{4} | The semidirect product of C_{2}^{3} and C_{4} acting faithfully | 8 | 4+ | C2^3:C4 | 32,6 |

C_{4}.D_{4} | 1^{st} non-split extension by C_{4} of D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 8 | 4+ | C4.D4 | 32,7 |

C_{8}⋊C_{2}^{2} | The semidirect product of C_{8} and C_{2}^{2} acting faithfully; = Aut(D_{8}) = Hol(C_{8}) | 8 | 4+ | C8:C2^2 | 32,43 |

2_{+}^{ 1+4} | Extraspecial group; = D_{4}○D_{4} | 8 | 4+ | ES+(2,2) | 32,49 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}^{2}⋊C_{4} | The semidirect product of C_{3}^{2} and C_{4} acting faithfully | 6 | 4+ | C3^2:C4 | 36,9 |

S_{3}^{2} | Direct product of S_{3} and S_{3}; = Spin+_{4}(𝔽_{2}) = Hol(S_{3}) | 6 | 4+ | S3^2 | 36,10 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×F_{5} | Direct product of C_{2} and F_{5}; = Aut(D_{10}) = Hol(C_{10}) | 10 | 4+ | C2xF5 | 40,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊S_{3} | The semidirect product of D_{4} and S_{3} acting via S_{3}/C_{3}=C_{2} | 24 | 4+ | D4:S3 | 48,15 |

Q_{8}⋊_{2}S_{3} | The semidirect product of Q_{8} and S_{3} acting via S_{3}/C_{3}=C_{2} | 24 | 4+ | Q8:2S3 | 48,17 |

S_{3}×D_{4} | Direct product of S_{3} and D_{4}; = Aut(D_{12}) = Hol(C_{12}) | 12 | 4+ | S3xD4 | 48,38 |

Q_{8}⋊_{3}S_{3} | The semidirect product of Q_{8} and S_{3} acting through Inn(Q_{8}) | 24 | 4+ | Q8:3S3 | 48,41 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}⋊C_{4} | The semidirect product of C_{13} and C_{4} acting faithfully | 13 | 4+ | C13:C4 | 52,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{5} | Direct product of S_{3} and D_{5} | 15 | 4+ | S3xD5 | 60,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}≀C_{4} | Wreath product of C_{2} by C_{4}; = AΣL_{1}(𝔽_{16}) | 8 | 4+ | C2wrC4 | 64,32 |

C_{4}^{2}⋊C_{4} | 2^{nd} semidirect product of C_{4}^{2} and C_{4} acting faithfully | 8 | 4+ | C4^2:C4 | 64,34 |

M_{5}(2)⋊C_{2} | 6^{th} semidirect product of M_{5}(2) and C_{2} acting faithfully | 16 | 4+ | M5(2):C2 | 64,42 |

D_{4}⋊_{4}D_{4} | 3^{rd} semidirect product of D_{4} and D_{4} acting via D_{4}/C_{2}^{2}=C_{2}; = Hol(D_{4}) | 8 | 4+ | D4:4D4 | 64,134 |

C_{2}≀C_{2}^{2} | Wreath product of C_{2} by C_{2}^{2}; = Hol(C_{2}×C_{4}) | 8 | 4+ | C2wrC2^2 | 64,138 |

D_{4}._{4}D_{4} | 4^{th} non-split extension by D_{4} of D_{4} acting via D_{4}/C_{4}=C_{2} | 16 | 4+ | D4.4D4 | 64,153 |

C_{16}⋊C_{2}^{2} | The semidirect product of C_{16} and C_{2}^{2} acting faithfully | 16 | 4+ | C16:C2^2 | 64,190 |

D_{4}○D_{8} | Central product of D_{4} and D_{8} | 16 | 4+ | D4oD8 | 64,257 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}⋊C_{4} | The semidirect product of C_{17} and C_{4} acting faithfully | 17 | 4+ | C17:C4 | 68,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{6}.D_{6} | 2^{nd} non-split extension by C_{6} of D_{6} acting via D_{6}/S_{3}=C_{2} | 12 | 4+ | C6.D6 | 72,21 |

C_{3}⋊D_{12} | The semidirect product of C_{3} and D_{12} acting via D_{12}/D_{6}=C_{2} | 12 | 4+ | C3:D12 | 72,23 |

S_{3}≀C_{2} | Wreath product of S_{3} by C_{2}; = SO+_{4}(𝔽_{2}) | 6 | 4+ | S3wrC2 | 72,40 |

C_{2}×C_{3}^{2}⋊C_{4} | Direct product of C_{2} and C_{3}^{2}⋊C_{4} | 12 | 4+ | C2xC3^2:C4 | 72,45 |

C_{2}×S_{3}^{2} | Direct product of C_{2}, S_{3} and S_{3} | 12 | 4+ | C2xS3^2 | 72,46 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{5} | The semidirect product of D_{4} and D_{5} acting via D_{5}/C_{5}=C_{2} | 40 | 4+ | D4:D5 | 80,15 |

Q_{8}⋊D_{5} | The semidirect product of Q_{8} and D_{5} acting via D_{5}/C_{5}=C_{2} | 40 | 4+ | Q8:D5 | 80,17 |

C_{2}^{2}⋊F_{5} | The semidirect product of C_{2}^{2} and F_{5} acting via F_{5}/D_{5}=C_{2} | 20 | 4+ | C2^2:F5 | 80,34 |

D_{4}×D_{5} | Direct product of D_{4} and D_{5} | 20 | 4+ | D4xD5 | 80,39 |

Q_{8}⋊_{2}D_{5} | The semidirect product of Q_{8} and D_{5} acting through Inn(Q_{8}) | 40 | 4+ | Q8:2D5 | 80,42 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{7} | Direct product of S_{3} and D_{7} | 21 | 4+ | S3xD7 | 84,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{25}⋊C_{4} | The semidirect product of C_{25} and C_{4} acting faithfully | 25 | 4+ | C25:C4 | 100,3 |

C_{5}^{2}⋊C_{4} | 4^{th} semidirect product of C_{5}^{2} and C_{4} acting faithfully | 10 | 4+ | C5^2:C4 | 100,12 |

D_{5}^{2} | Direct product of D_{5} and D_{5} | 10 | 4+ | D5^2 | 100,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{13}⋊C_{4} | Direct product of C_{2} and C_{13}⋊C_{4} | 26 | 4+ | C2xC13:C4 | 104,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{9} | Direct product of S_{3} and D_{9} | 18 | 4+ | S3xD9 | 108,16 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{7} | The semidirect product of D_{4} and D_{7} acting via D_{7}/C_{7}=C_{2} | 56 | 4+ | D4:D7 | 112,14 |

Q_{8}⋊D_{7} | The semidirect product of Q_{8} and D_{7} acting via D_{7}/C_{7}=C_{2} | 56 | 4+ | Q8:D7 | 112,16 |

D_{4}×D_{7} | Direct product of D_{4} and D_{7} | 28 | 4+ | D4xD7 | 112,31 |

Q_{8}⋊_{2}D_{7} | The semidirect product of Q_{8} and D_{7} acting through Inn(Q_{8}) | 56 | 4+ | Q8:2D7 | 112,34 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{29}⋊C_{4} | The semidirect product of C_{29} and C_{4} acting faithfully | 29 | 4+ | C29:C4 | 116,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{30}.C_{2} | The non-split extension by D_{30} of C_{2} acting faithfully | 60 | 4+ | D30.C2 | 120,10 |

C_{3}⋊D_{20} | The semidirect product of C_{3} and D_{20} acting via D_{20}/D_{10}=C_{2} | 60 | 4+ | C3:D20 | 120,12 |

C_{5}⋊D_{12} | The semidirect product of C_{5} and D_{12} acting via D_{12}/D_{6}=C_{2} | 60 | 4+ | C5:D12 | 120,13 |

S_{5} | Symmetric group on 5 letters; = PGL_{2}(𝔽_{5}) = Aut(A_{5}) = 5-cell symmetries; almost simple | 5 | 4+ | S5 | 120,34 |

C_{2}×S_{3}×D_{5} | Direct product of C_{2}, S_{3} and D_{5} | 30 | 4+ | C2xS3xD5 | 120,42 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{11} | Direct product of S_{3} and D_{11} | 33 | 4+ | S3xD11 | 132,5 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{17}⋊C_{4} | Direct product of C_{2} and C_{17}⋊C_{4} | 34 | 4+ | C2xC17:C4 | 136,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×D_{7} | Direct product of D_{5} and D_{7} | 35 | 4+ | D5xD7 | 140,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{37}⋊C_{4} | The semidirect product of C_{37} and C_{4} acting faithfully | 37 | 4+ | C37:C4 | 148,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{13} | Direct product of S_{3} and D_{13} | 39 | 4+ | S3xD13 | 156,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{41}⋊C_{4} | The semidirect product of C_{41} and C_{4} acting faithfully | 41 | 4+ | C41:C4 | 164,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{21}⋊C_{4} | The semidirect product of D_{21} and C_{4} acting via C_{4}/C_{2}=C_{2} | 84 | 4+ | D21:C4 | 168,14 |

C_{3}⋊D_{28} | The semidirect product of C_{3} and D_{28} acting via D_{28}/D_{14}=C_{2} | 84 | 4+ | C3:D28 | 168,16 |

C_{7}⋊D_{12} | The semidirect product of C_{7} and D_{12} acting via D_{12}/D_{6}=C_{2} | 84 | 4+ | C7:D12 | 168,17 |

C_{2}×S_{3}×D_{7} | Direct product of C_{2}, S_{3} and D_{7} | 42 | 4+ | C2xS3xD7 | 168,50 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{11} | The semidirect product of D_{4} and D_{11} acting via D_{11}/C_{11}=C_{2} | 88 | 4+ | D4:D11 | 176,14 |

Q_{8}⋊D_{11} | The semidirect product of Q_{8} and D_{11} acting via D_{11}/C_{11}=C_{2} | 88 | 4+ | Q8:D11 | 176,16 |

D_{4}×D_{11} | Direct product of D_{4} and D_{11} | 44 | 4+ | D4xD11 | 176,31 |

D_{44}⋊C_{2} | 4^{th} semidirect product of D_{44} and C_{2} acting faithfully | 88 | 4+ | D44:C2 | 176,34 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×D_{9} | Direct product of D_{5} and D_{9} | 45 | 4+ | D5xD9 | 180,7 |

C_{3}^{2}⋊F_{5} | The semidirect product of C_{3}^{2} and F_{5} acting via F_{5}/C_{5}=C_{4} | 30 | 4+ | C3^2:F5 | 180,25 |

S_{3}×D_{15} | Direct product of S_{3} and D_{15} | 30 | 4+ | S3xD15 | 180,29 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}^{2}⋊C_{4} | The semidirect product of C_{7}^{2} and C_{4} acting faithfully | 14 | 4+ | C7^2:C4 | 196,8 |

D_{7}^{2} | Direct product of D_{7} and D_{7} | 14 | 4+ | D7^2 | 196,9 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{25}⋊C_{4} | Direct product of C_{2} and C_{25}⋊C_{4} | 50 | 4+ | C2xC25:C4 | 200,12 |

Dic_{5}⋊_{2}D_{5} | The semidirect product of Dic_{5} and D_{5} acting through Inn(Dic_{5}) | 20 | 4+ | Dic5:2D5 | 200,23 |

C_{5}⋊D_{20} | The semidirect product of C_{5} and D_{20} acting via D_{20}/D_{10}=C_{2} | 20 | 4+ | C5:D20 | 200,25 |

D_{5}≀C_{2} | Wreath product of D_{5} by C_{2} | 10 | 4+ | D5wrC2 | 200,43 |

C_{2}×C_{5}^{2}⋊C_{4} | Direct product of C_{2} and C_{5}^{2}⋊C_{4} | 20 | 4+ | C2xC5^2:C4 | 200,48 |

C_{2}×D_{5}^{2} | Direct product of C_{2}, D_{5} and D_{5} | 20 | 4+ | C2xD5^2 | 200,49 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{17} | Direct product of S_{3} and D_{17} | 51 | 4+ | S3xD17 | 204,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{13} | The semidirect product of D_{4} and D_{13} acting via D_{13}/C_{13}=C_{2} | 104 | 4+ | D4:D13 | 208,15 |

Q_{8}⋊D_{13} | The semidirect product of Q_{8} and D_{13} acting via D_{13}/C_{13}=C_{2} | 104 | 4+ | Q8:D13 | 208,17 |

D_{13}.D_{4} | The non-split extension by D_{13} of D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 52 | 4+ | D13.D4 | 208,34 |

D_{4}×D_{13} | Direct product of D_{4} and D_{13} | 52 | 4+ | D4xD13 | 208,39 |

D_{52}⋊C_{2} | 4^{th} semidirect product of D_{52} and C_{2} acting faithfully | 104 | 4+ | D52:C2 | 208,42 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{53}⋊C_{4} | The semidirect product of C_{53} and C_{4} acting faithfully | 53 | 4+ | C53:C4 | 212,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{18}.D_{6} | 3^{rd} non-split extension by C_{18} of D_{6} acting via D_{6}/S_{3}=C_{2} | 36 | 4+ | C18.D6 | 216,28 |

C_{3}⋊D_{36} | The semidirect product of C_{3} and D_{36} acting via D_{36}/D_{18}=C_{2} | 36 | 4+ | C3:D36 | 216,29 |

C_{9}⋊D_{12} | The semidirect product of C_{9} and D_{12} acting via D_{12}/D_{6}=C_{2} | 36 | 4+ | C9:D12 | 216,32 |

C_{2}×S_{3}×D_{9} | Direct product of C_{2}, S_{3} and D_{9} | 36 | 4+ | C2xS3xD9 | 216,101 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×D_{11} | Direct product of D_{5} and D_{11} | 55 | 4+ | D5xD11 | 220,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

M_{4}(2)⋊D_{7} | 3^{rd} semidirect product of M_{4}(2) and D_{7} acting via D_{7}/C_{7}=C_{2} | 56 | 4+ | M4(2):D7 | 224,29 |

C_{7}⋊D_{16} | The semidirect product of C_{7} and D_{16} acting via D_{16}/D_{8}=C_{2} | 112 | 4+ | C7:D16 | 224,32 |

C_{7}⋊SD_{32} | The semidirect product of C_{7} and SD_{32} acting via SD_{32}/Q_{16}=C_{2} | 112 | 4+ | C7:SD32 | 224,34 |

C_{8}⋊D_{14} | 1^{st} semidirect product of C_{8} and D_{14} acting via D_{14}/C_{7}=C_{2}^{2} | 56 | 4+ | C8:D14 | 224,103 |

D_{7}×D_{8} | Direct product of D_{7} and D_{8} | 56 | 4+ | D7xD8 | 224,105 |

D_{56}⋊C_{2} | 6^{th} semidirect product of D_{56} and C_{2} acting faithfully | 56 | 4+ | D56:C2 | 224,109 |

Q_{8}.D_{14} | 5^{th} non-split extension by Q_{8} of D_{14} acting via D_{14}/D_{7}=C_{2} | 112 | 4+ | Q8.D14 | 224,114 |

D_{4}⋊D_{14} | 2^{nd} semidirect product of D_{4} and D_{14} acting via D_{14}/C_{14}=C_{2} | 56 | 4+ | D4:D14 | 224,144 |

D_{4}⋊_{8}D_{14} | 4^{th} semidirect product of D_{4} and D_{14} acting through Inn(D_{4}) | 56 | 4+ | D4:8D14 | 224,185 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{19} | Direct product of S_{3} and D_{19} | 57 | 4+ | S3xD19 | 228,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{29}⋊C_{4} | Direct product of C_{2} and C_{29}⋊C_{4} | 58 | 4+ | C2xC29:C4 | 232,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{61}⋊C_{4} | The semidirect product of C_{61} and C_{4} acting faithfully | 61 | 4+ | C61:C4 | 244,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×D_{9} | Direct product of D_{7} and D_{9} | 63 | 4+ | D7xD9 | 252,8 |

S_{3}×D_{21} | Direct product of S_{3} and D_{21} | 42 | 4+ | S3xD21 | 252,36 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}⋊F_{5} | 1^{st} semidirect product of C_{13} and F_{5} acting via F_{5}/C_{5}=C_{4} | 65 | 4+ | C13:F5 | 260,9 |

C_{65}⋊_{2}C_{4} | 2^{nd} semidirect product of C_{65} and C_{4} acting faithfully | 65 | 4+ | C65:2C4 | 260,10 |

D_{5}×D_{13} | Direct product of D_{5} and D_{13} | 65 | 4+ | D5xD13 | 260,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{33}⋊C_{4} | The semidirect product of D_{33} and C_{4} acting via C_{4}/C_{2}=C_{2} | 132 | 4+ | D33:C4 | 264,7 |

C_{3}⋊D_{44} | The semidirect product of C_{3} and D_{44} acting via D_{44}/D_{22}=C_{2} | 132 | 4+ | C3:D44 | 264,9 |

C_{11}⋊D_{12} | The semidirect product of C_{11} and D_{12} acting via D_{12}/D_{6}=C_{2} | 132 | 4+ | C11:D12 | 264,10 |

C_{2}×S_{3}×D_{11} | Direct product of C_{2}, S_{3} and D_{11} | 66 | 4+ | C2xS3xD11 | 264,34 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{17} | The semidirect product of D_{4} and D_{17} acting via D_{17}/C_{17}=C_{2} | 136 | 4+ | D4:D17 | 272,15 |

Q_{8}⋊D_{17} | The semidirect product of Q_{8} and D_{17} acting via D_{17}/C_{17}=C_{2} | 136 | 4+ | Q8:D17 | 272,17 |

D_{17}.D_{4} | The non-split extension by D_{17} of D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 68 | 4+ | D17.D4 | 272,35 |

D_{4}×D_{17} | Direct product of D_{4} and D_{17} | 68 | 4+ | D4xD17 | 272,40 |

D_{68}⋊C_{2} | 4^{th} semidirect product of D_{68} and C_{2} acting faithfully | 136 | 4+ | D68:C2 | 272,43 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{23} | Direct product of S_{3} and D_{23} | 69 | 4+ | S3xD23 | 276,5 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{70}.C_{2} | The non-split extension by D_{70} of C_{2} acting faithfully | 140 | 4+ | D70.C2 | 280,9 |

C_{5}⋊D_{28} | The semidirect product of C_{5} and D_{28} acting via D_{28}/D_{14}=C_{2} | 140 | 4+ | C5:D28 | 280,11 |

C_{7}⋊D_{20} | The semidirect product of C_{7} and D_{20} acting via D_{20}/D_{10}=C_{2} | 140 | 4+ | C7:D20 | 280,12 |

C_{2}×D_{5}×D_{7} | Direct product of C_{2}, D_{5} and D_{7} | 70 | 4+ | C2xD5xD7 | 280,36 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{73}⋊C_{4} | The semidirect product of C_{73} and C_{4} acting faithfully | 73 | 4+ | C73:C4 | 292,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{37}⋊C_{4} | Direct product of C_{2} and C_{37}⋊C_{4} | 74 | 4+ | C2xC37:C4 | 296,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{25} | Direct product of S_{3} and D_{25} | 75 | 4+ | S3xD25 | 300,7 |

D_{5}×D_{15} | Direct product of D_{5} and D_{15} | 30 | 4+ | D5xD15 | 300,39 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{19} | The semidirect product of D_{4} and D_{19} acting via D_{19}/C_{19}=C_{2} | 152 | 4+ | D4:D19 | 304,14 |

Q_{8}⋊D_{19} | The semidirect product of Q_{8} and D_{19} acting via D_{19}/C_{19}=C_{2} | 152 | 4+ | Q8:D19 | 304,16 |

D_{4}×D_{19} | Direct product of D_{4} and D_{19} | 76 | 4+ | D4xD19 | 304,31 |

D_{76}⋊C_{2} | 4^{th} semidirect product of D_{76} and C_{2} acting faithfully | 152 | 4+ | D76:C2 | 304,34 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×D_{11} | Direct product of D_{7} and D_{11} | 77 | 4+ | D7xD11 | 308,5 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{78}.C_{2} | The non-split extension by D_{78} of C_{2} acting faithfully | 156 | 4+ | D78.C2 | 312,17 |

C_{3}⋊D_{52} | The semidirect product of C_{3} and D_{52} acting via D_{52}/D_{26}=C_{2} | 156 | 4+ | C3:D52 | 312,19 |

C_{13}⋊D_{12} | The semidirect product of C_{13} and D_{12} acting via D_{12}/D_{6}=C_{2} | 156 | 4+ | C13:D12 | 312,20 |

C_{2}×S_{3}×D_{13} | Direct product of C_{2}, S_{3} and D_{13} | 78 | 4+ | C2xS3xD13 | 312,54 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{9}^{2}⋊C_{4} | The semidirect product of C_{9}^{2} and C_{4} acting faithfully | 18 | 4+ | C9^2:C4 | 324,35 |

D_{9}^{2} | Direct product of D_{9} and D_{9} | 18 | 4+ | D9^2 | 324,36 |

S_{3}×D_{27} | Direct product of S_{3} and D_{27} | 54 | 4+ | S3xD27 | 324,38 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{41}⋊C_{4} | Direct product of C_{2} and C_{41}⋊C_{4} | 82 | 4+ | C2xC41:C4 | 328,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}⋊F_{5} | 1^{st} semidirect product of C_{17} and F_{5} acting via F_{5}/C_{5}=C_{4} | 85 | 4+ | C17:F5 | 340,9 |

C_{85}⋊_{2}C_{4} | 2^{nd} semidirect product of C_{85} and C_{4} acting faithfully | 85 | 4+ | C85:2C4 | 340,10 |

D_{5}×D_{17} | Direct product of D_{5} and D_{17} | 85 | 4+ | D5xD17 | 340,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{29} | Direct product of S_{3} and D_{29} | 87 | 4+ | S3xD29 | 348,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

M_{4}(2)⋊D_{11} | 3^{rd} semidirect product of M_{4}(2) and D_{11} acting via D_{11}/C_{11}=C_{2} | 88 | 4+ | M4(2):D11 | 352,29 |

C_{11}⋊D_{16} | The semidirect product of C_{11} and D_{16} acting via D_{16}/D_{8}=C_{2} | 176 | 4+ | C11:D16 | 352,32 |

C_{8}._{6}D_{22} | 3^{rd} non-split extension by C_{8} of D_{22} acting via D_{22}/D_{11}=C_{2} | 176 | 4+ | C8.6D22 | 352,34 |

C_{8}⋊D_{22} | 1^{st} semidirect product of C_{8} and D_{22} acting via D_{22}/C_{11}=C_{2}^{2} | 88 | 4+ | C8:D22 | 352,103 |

D_{8}×D_{11} | Direct product of D_{8} and D_{11} | 88 | 4+ | D8xD11 | 352,105 |

D_{88}⋊C_{2} | 6^{th} semidirect product of D_{88} and C_{2} acting faithfully | 88 | 4+ | D88:C2 | 352,109 |

D_{88}⋊_{5}C_{2} | 5^{th} semidirect product of D_{88} and C_{2} acting faithfully | 176 | 4+ | D88:5C2 | 352,114 |

D_{4}⋊D_{22} | 2^{nd} semidirect product of D_{4} and D_{22} acting via D_{22}/C_{22}=C_{2} | 88 | 4+ | D4:D22 | 352,144 |

D_{4}⋊_{8}D_{22} | 4^{th} semidirect product of D_{4} and D_{22} acting through Inn(D_{4}) | 88 | 4+ | D4:8D22 | 352,184 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{89}⋊C_{4} | The semidirect product of C_{89} and C_{4} acting faithfully | 89 | 4+ | C89:C4 | 356,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{90}.C_{2} | The non-split extension by D_{90} of C_{2} acting faithfully | 180 | 4+ | D90.C2 | 360,9 |

C_{45}⋊D_{4} | 1^{st} semidirect product of C_{45} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 180 | 4+ | C45:D4 | 360,10 |

C_{9}⋊D_{20} | The semidirect product of C_{9} and D_{20} acting via D_{20}/D_{10}=C_{2} | 180 | 4+ | C9:D20 | 360,13 |

C_{2}×D_{5}×D_{9} | Direct product of C_{2}, D_{5} and D_{9} | 90 | 4+ | C2xD5xD9 | 360,45 |

C_{6}.D_{30} | 3^{rd} non-split extension by C_{6} of D_{30} acting via D_{30}/D_{15}=C_{2} | 60 | 4+ | C6.D30 | 360,79 |

C_{3}⋊D_{60} | The semidirect product of C_{3} and D_{60} acting via D_{60}/D_{30}=C_{2} | 60 | 4+ | C3:D60 | 360,81 |

D_{6}⋊_{2}D_{15} | 2^{nd} semidirect product of D_{6} and D_{15} acting via D_{15}/C_{15}=C_{2} | 60 | 4+ | D6:2D15 | 360,82 |

C_{2}×C_{3}^{2}⋊F_{5} | Direct product of C_{2} and C_{3}^{2}⋊F_{5} | 60 | 4+ | C2xC3^2:F5 | 360,150 |

C_{2}×S_{3}×D_{15} | Direct product of C_{2}, S_{3} and D_{15} | 60 | 4+ | C2xS3xD15 | 360,154 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×D_{13} | Direct product of D_{7} and D_{13} | 91 | 4+ | D7xD13 | 364,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{23} | The semidirect product of D_{4} and D_{23} acting via D_{23}/C_{23}=C_{2} | 184 | 4+ | D4:D23 | 368,14 |

Q_{8}⋊D_{23} | The semidirect product of Q_{8} and D_{23} acting via D_{23}/C_{23}=C_{2} | 184 | 4+ | Q8:D23 | 368,16 |

D_{4}×D_{23} | Direct product of D_{4} and D_{23} | 92 | 4+ | D4xD23 | 368,31 |

D_{92}⋊C_{2} | 4^{th} semidirect product of D_{92} and C_{2} acting faithfully | 184 | 4+ | D92:C2 | 368,34 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{31} | Direct product of S_{3} and D_{31} | 93 | 4+ | S3xD31 | 372,8 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×D_{19} | Direct product of D_{5} and D_{19} | 95 | 4+ | D5xD19 | 380,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{97}⋊C_{4} | The semidirect product of C_{97} and C_{4} acting faithfully | 97 | 4+ | C97:C4 | 388,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{7}⋊_{2}D_{7} | The semidirect product of Dic_{7} and D_{7} acting through Inn(Dic_{7}) | 28 | 4+ | Dic7:2D7 | 392,19 |

C_{7}⋊D_{28} | The semidirect product of C_{7} and D_{28} acting via D_{28}/D_{14}=C_{2} | 28 | 4+ | C7:D28 | 392,21 |

D_{7}≀C_{2} | Wreath product of D_{7} by C_{2} | 14 | 4+ | D7wrC2 | 392,37 |

C_{2}×C_{7}^{2}⋊C_{4} | Direct product of C_{2} and C_{7}^{2}⋊C_{4} | 28 | 4+ | C2xC7^2:C4 | 392,40 |

C_{2}×D_{7}^{2} | Direct product of C_{2}, D_{7} and D_{7} | 28 | 4+ | C2xD7^2 | 392,41 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{9}×D_{11} | Direct product of D_{9} and D_{11} | 99 | 4+ | D9xD11 | 396,5 |

S_{3}×D_{33} | Direct product of S_{3} and D_{33} | 66 | 4+ | S3xD33 | 396,22 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{101}⋊C_{4} | The semidirect product of C_{101} and C_{4} acting faithfully | 101 | 4+ | C101:C4 | 404,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{51}⋊_{2}C_{4} | The semidirect product of D_{51} and C_{4} acting via C_{4}/C_{2}=C_{2} | 204 | 4+ | D51:2C4 | 408,9 |

C_{3}⋊D_{68} | The semidirect product of C_{3} and D_{68} acting via D_{68}/D_{34}=C_{2} | 204 | 4+ | C3:D68 | 408,11 |

C_{17}⋊D_{12} | The semidirect product of C_{17} and D_{12} acting via D_{12}/D_{6}=C_{2} | 204 | 4+ | C17:D12 | 408,12 |

C_{2}×S_{3}×D_{17} | Direct product of C_{2}, S_{3} and D_{17} | 102 | 4+ | C2xS3xD17 | 408,41 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×D_{15} | Direct product of D_{7} and D_{15} | 105 | 4+ | D7xD15 | 420,26 |

D_{5}×D_{21} | Direct product of D_{5} and D_{21} | 105 | 4+ | D5xD21 | 420,28 |

S_{3}×D_{35} | Direct product of S_{3} and D_{35} | 105 | 4+ | S3xD35 | 420,29 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{53}⋊C_{4} | Direct product of C_{2} and C_{53}⋊C_{4} | 106 | 4+ | C2xC53:C4 | 424,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{109}⋊C_{4} | The semidirect product of C_{109} and C_{4} acting faithfully | 109 | 4+ | C109:C4 | 436,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{55}⋊_{2}C_{4} | The semidirect product of D_{55} and C_{4} acting via C_{4}/C_{2}=C_{2} | 220 | 4+ | D55:2C4 | 440,19 |

C_{5}⋊D_{44} | The semidirect product of C_{5} and D_{44} acting via D_{44}/D_{22}=C_{2} | 220 | 4+ | C5:D44 | 440,21 |

C_{11}⋊D_{20} | The semidirect product of C_{11} and D_{20} acting via D_{20}/D_{10}=C_{2} | 220 | 4+ | C11:D20 | 440,22 |

C_{2}×D_{5}×D_{11} | Direct product of C_{2}, D_{5} and D_{11} | 110 | 4+ | C2xD5xD11 | 440,47 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{37} | Direct product of S_{3} and D_{37} | 111 | 4+ | S3xD37 | 444,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{113}⋊C_{4} | The semidirect product of C_{113} and C_{4} acting faithfully | 113 | 4+ | C113:C4 | 452,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{57}⋊C_{4} | The semidirect product of D_{57} and C_{4} acting via C_{4}/C_{2}=C_{2} | 228 | 4+ | D57:C4 | 456,14 |

C_{3}⋊D_{76} | The semidirect product of C_{3} and D_{76} acting via D_{76}/D_{38}=C_{2} | 228 | 4+ | C3:D76 | 456,16 |

C_{19}⋊D_{12} | The semidirect product of C_{19} and D_{12} acting via D_{12}/D_{6}=C_{2} | 228 | 4+ | C19:D12 | 456,17 |

C_{2}×S_{3}×D_{19} | Direct product of C_{2}, S_{3} and D_{19} | 114 | 4+ | C2xS3xD19 | 456,47 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×D_{23} | Direct product of D_{5} and D_{23} | 115 | 4+ | D5xD23 | 460,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{29} | The semidirect product of D_{4} and D_{29} acting via D_{29}/C_{29}=C_{2} | 232 | 4+ | D4:D29 | 464,15 |

Q_{8}⋊D_{29} | The semidirect product of Q_{8} and D_{29} acting via D_{29}/C_{29}=C_{2} | 232 | 4+ | Q8:D29 | 464,17 |

D_{29}.D_{4} | The non-split extension by D_{29} of D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 116 | 4+ | D29.D4 | 464,34 |

D_{4}×D_{29} | Direct product of D_{4} and D_{29} | 116 | 4+ | D4xD29 | 464,39 |

Q_{8}⋊_{2}D_{29} | The semidirect product of Q_{8} and D_{29} acting through Inn(Q_{8}) | 232 | 4+ | Q8:2D29 | 464,42 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{9}×D_{13} | Direct product of D_{9} and D_{13} | 117 | 4+ | D9xD13 | 468,11 |

(C_{3}×C_{39})⋊C_{4} | 1^{st} semidirect product of C_{3}×C_{39} and C_{4} acting faithfully | 78 | 4+ | (C3xC39):C4 | 468,41 |

S_{3}×D_{39} | Direct product of S_{3} and D_{39} | 78 | 4+ | S3xD39 | 468,45 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×D_{17} | Direct product of D_{7} and D_{17} | 119 | 4+ | D7xD17 | 476,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{11}^{2}⋊C_{4} | The semidirect product of C_{11}^{2} and C_{4} acting faithfully | 22 | 4+ | C11^2:C4 | 484,8 |

D_{11}^{2} | Direct product of D_{11} and D_{11} | 22 | 4+ | D11^2 | 484,9 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{2}×C_{61}⋊C_{4} | Direct product of C_{2} and C_{61}⋊C_{4} | 122 | 4+ | C2xC61:C4 | 488,12 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

S_{3}×D_{41} | Direct product of S_{3} and D_{41} | 123 | 4+ | S3xD41 | 492,7 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}⋊D_{31} | The semidirect product of D_{4} and D_{31} acting via D_{31}/C_{31}=C_{2} | 248 | 4+ | D4:D31 | 496,14 |

Q_{8}⋊D_{31} | The semidirect product of Q_{8} and D_{31} acting via D_{31}/C_{31}=C_{2} | 248 | 4+ | Q8:D31 | 496,16 |

D_{4}×D_{31} | Direct product of D_{4} and D_{31} | 124 | 4+ | D4xD31 | 496,31 |

Q_{8}⋊_{2}D_{31} | The semidirect product of Q_{8} and D_{31} acting through Inn(Q_{8}) | 248 | 4+ | Q8:2D31 | 496,34 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{125}⋊C_{4} | The semidirect product of C_{125} and C_{4} acting faithfully | 125 | 4+ | C125:C4 | 500,3 |

C_{25}⋊_{2}F_{5} | 2^{nd} semidirect product of C_{25} and F_{5} acting via F_{5}/C_{5}=C_{4} | 50 | 4+ | C25:2F5 | 500,24 |

D_{5}×D_{25} | Direct product of D_{5} and D_{25} | 50 | 4+ | D5xD25 | 500,26 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}._{10}D_{4} | 2^{nd} non-split extension by C_{4} of D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 16 | 4- | C4.10D4 | 32,8 |

C_{8}.C_{2}^{2} | The non-split extension by C_{8} of C_{2}^{2} acting faithfully | 16 | 4- | C8.C2^2 | 32,44 |

2_{-}^{ 1+4} | Gamma matrices = Extraspecial group; = D_{4}○Q_{8} | 16 | 4- | ES-(2,2) | 32,50 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{5}⋊C_{8} | The semidirect product of C_{5} and C_{8} acting via C_{8}/C_{2}=C_{4} | 40 | 4- | C5:C8 | 40,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.S_{3} | The non-split extension by D_{4} of S_{3} acting via S_{3}/C_{3}=C_{2} | 24 | 4- | D4.S3 | 48,16 |

C_{3}⋊Q_{16} | The semidirect product of C_{3} and Q_{16} acting via Q_{16}/Q_{8}=C_{2} | 48 | 4- | C3:Q16 | 48,18 |

D_{4}⋊_{2}S_{3} | The semidirect product of D_{4} and S_{3} acting through Inn(D_{4}) | 24 | 4- | D4:2S3 | 48,39 |

S_{3}×Q_{8} | Direct product of S_{3} and Q_{8} | 24 | 4- | S3xQ8 | 48,40 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}^{2}._{3}C_{4} | 3^{rd} non-split extension by C_{4}^{2} of C_{4} acting faithfully | 16 | 4- | C4^2.3C4 | 64,37 |

C_{8}._{17}D_{4} | 4^{th} non-split extension by C_{8} of D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 32 | 4- | C8.17D4 | 64,43 |

D_{4}._{10}D_{4} | 5^{th} non-split extension by D_{4} of D_{4} acting via D_{4}/C_{2}^{2}=C_{2} | 16 | 4- | D4.10D4 | 64,137 |

D_{4}._{5}D_{4} | 5^{th} non-split extension by D_{4} of D_{4} acting via D_{4}/C_{4}=C_{2} | 32 | 4- | D4.5D4 | 64,154 |

Q_{32}⋊C_{2} | 2^{nd} semidirect product of Q_{32} and C_{2} acting faithfully | 32 | 4- | Q32:C2 | 64,191 |

Q_{8}○D_{8} | Central product of Q_{8} and D_{8} | 32 | 4- | Q8oD8 | 64,259 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{3}^{2}⋊_{2}C_{8} | The semidirect product of C_{3}^{2} and C_{8} acting via C_{8}/C_{2}=C_{4} | 24 | 4- | C3^2:2C8 | 72,19 |

S_{3}×Dic_{3} | Direct product of S_{3} and Dic_{3} | 24 | 4- | S3xDic3 | 72,20 |

D_{6}⋊S_{3} | 1^{st} semidirect product of D_{6} and S_{3} acting via S_{3}/C_{3}=C_{2} | 24 | 4- | D6:S3 | 72,22 |

C_{3}^{2}⋊_{2}Q_{8} | The semidirect product of C_{3}^{2} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 24 | 4- | C3^2:2Q8 | 72,24 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.D_{5} | The non-split extension by D_{4} of D_{5} acting via D_{5}/C_{5}=C_{2} | 40 | 4- | D4.D5 | 80,16 |

C_{5}⋊Q_{16} | The semidirect product of C_{5} and Q_{16} acting via Q_{16}/Q_{8}=C_{2} | 80 | 4- | C5:Q16 | 80,18 |

C_{2}^{2}.F_{5} | The non-split extension by C_{2}^{2} of F_{5} acting via F_{5}/D_{5}=C_{2} | 40 | 4- | C2^2.F5 | 80,33 |

D_{4}⋊_{2}D_{5} | The semidirect product of D_{4} and D_{5} acting through Inn(D_{4}) | 40 | 4- | D4:2D5 | 80,40 |

Q_{8}×D_{5} | Direct product of Q_{8} and D_{5} | 40 | 4- | Q8xD5 | 80,41 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{13}⋊C_{8} | The semidirect product of C_{13} and C_{8} acting via C_{8}/C_{2}=C_{4} | 104 | 4- | C13:C8 | 104,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.D_{7} | The non-split extension by D_{4} of D_{7} acting via D_{7}/C_{7}=C_{2} | 56 | 4- | D4.D7 | 112,15 |

C_{7}⋊Q_{16} | The semidirect product of C_{7} and Q_{16} acting via Q_{16}/Q_{8}=C_{2} | 112 | 4- | C7:Q16 | 112,17 |

D_{4}⋊_{2}D_{7} | The semidirect product of D_{4} and D_{7} acting through Inn(D_{4}) | 56 | 4- | D4:2D7 | 112,32 |

Q_{8}×D_{7} | Direct product of Q_{8} and D_{7} | 56 | 4- | Q8xD7 | 112,33 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{5}×Dic_{3} | Direct product of D_{5} and Dic_{3} | 60 | 4- | D5xDic3 | 120,8 |

S_{3}×Dic_{5} | Direct product of S_{3} and Dic_{5} | 60 | 4- | S3xDic5 | 120,9 |

C_{15}⋊D_{4} | 1^{st} semidirect product of C_{15} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 60 | 4- | C15:D4 | 120,11 |

C_{15}⋊Q_{8} | The semidirect product of C_{15} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 120 | 4- | C15:Q8 | 120,14 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{17}⋊_{2}C_{8} | The semidirect product of C_{17} and C_{8} acting via C_{8}/C_{2}=C_{4} | 136 | 4- | C17:2C8 | 136,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×D_{7} | Direct product of Dic_{3} and D_{7} | 84 | 4- | Dic3xD7 | 168,12 |

S_{3}×Dic_{7} | Direct product of S_{3} and Dic_{7} | 84 | 4- | S3xDic7 | 168,13 |

C_{21}⋊D_{4} | 1^{st} semidirect product of C_{21} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 84 | 4- | C21:D4 | 168,15 |

C_{21}⋊Q_{8} | The semidirect product of C_{21} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 168 | 4- | C21:Q8 | 168,18 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.D_{11} | The non-split extension by D_{4} of D_{11} acting via D_{11}/C_{11}=C_{2} | 88 | 4- | D4.D11 | 176,15 |

C_{11}⋊Q_{16} | The semidirect product of C_{11} and Q_{16} acting via Q_{16}/Q_{8}=C_{2} | 176 | 4- | C11:Q16 | 176,17 |

D_{4}⋊_{2}D_{11} | The semidirect product of D_{4} and D_{11} acting through Inn(D_{4}) | 88 | 4- | D4:2D11 | 176,32 |

Q_{8}×D_{11} | Direct product of Q_{8} and D_{11} | 88 | 4- | Q8xD11 | 176,33 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{25}⋊C_{8} | The semidirect product of C_{25} and C_{8} acting via C_{8}/C_{2}=C_{4} | 200 | 4- | C25:C8 | 200,3 |

C_{5}^{2}⋊_{5}C_{8} | 4^{th} semidirect product of C_{5}^{2} and C_{8} acting via C_{8}/C_{2}=C_{4} | 40 | 4- | C5^2:5C8 | 200,21 |

D_{5}×Dic_{5} | Direct product of D_{5} and Dic_{5} | 40 | 4- | D5xDic5 | 200,22 |

C_{5}^{2}⋊_{2}D_{4} | 1^{st} semidirect product of C_{5}^{2} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 40 | 4- | C5^2:2D4 | 200,24 |

C_{5}^{2}⋊_{2}Q_{8} | The semidirect product of C_{5}^{2} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 40 | 4- | C5^2:2Q8 | 200,26 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.D_{13} | The non-split extension by D_{4} of D_{13} acting via D_{13}/C_{13}=C_{2} | 104 | 4- | D4.D13 | 208,16 |

C_{13}⋊Q_{16} | The semidirect product of C_{13} and Q_{16} acting via Q_{16}/Q_{8}=C_{2} | 208 | 4- | C13:Q16 | 208,18 |

C_{13}⋊M_{4}(2) | The semidirect product of C_{13} and M_{4}(2) acting via M_{4}(2)/C_{2}^{2}=C_{4} | 104 | 4- | C13:M4(2) | 208,33 |

D_{4}⋊_{2}D_{13} | The semidirect product of D_{4} and D_{13} acting through Inn(D_{4}) | 104 | 4- | D4:2D13 | 208,40 |

Q_{8}×D_{13} | Direct product of Q_{8} and D_{13} | 104 | 4- | Q8xD13 | 208,41 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{9}⋊Dic_{6} | The semidirect product of C_{9} and Dic_{6} acting via Dic_{6}/Dic_{3}=C_{2} | 72 | 4- | C9:Dic6 | 216,26 |

Dic_{3}×D_{9} | Direct product of Dic_{3} and D_{9} | 72 | 4- | Dic3xD9 | 216,27 |

S_{3}×Dic_{9} | Direct product of S_{3} and Dic_{9} | 72 | 4- | S3xDic9 | 216,30 |

D_{6}⋊D_{9} | 1^{st} semidirect product of D_{6} and D_{9} acting via D_{9}/C_{9}=C_{2} | 72 | 4- | D6:D9 | 216,31 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}._{12}D_{28} | 4^{th} non-split extension by C_{4} of D_{28} acting via D_{28}/D_{14}=C_{2} | 112 | 4- | C4.12D28 | 224,30 |

D_{8}.D_{7} | The non-split extension by D_{8} of D_{7} acting via D_{7}/C_{7}=C_{2} | 112 | 4- | D8.D7 | 224,33 |

C_{7}⋊Q_{32} | The semidirect product of C_{7} and Q_{32} acting via Q_{32}/Q_{16}=C_{2} | 224 | 4- | C7:Q32 | 224,35 |

C_{8}.D_{14} | 1^{st} non-split extension by C_{8} of D_{14} acting via D_{14}/C_{7}=C_{2}^{2} | 112 | 4- | C8.D14 | 224,104 |

D_{8}⋊_{3}D_{7} | The semidirect product of D_{8} and D_{7} acting through Inn(D_{8}) | 112 | 4- | D8:3D7 | 224,107 |

SD_{16}⋊D_{7} | 2^{nd} semidirect product of SD_{16} and D_{7} acting via D_{7}/C_{7}=C_{2} | 112 | 4- | SD16:D7 | 224,110 |

D_{7}×Q_{16} | Direct product of D_{7} and Q_{16} | 112 | 4- | D7xQ16 | 224,112 |

D_{4}._{9}D_{14} | 4^{th} non-split extension by D_{4} of D_{14} acting via D_{14}/C_{14}=C_{2} | 112 | 4- | D4.9D14 | 224,146 |

D_{4}._{10}D_{14} | The non-split extension by D_{4} of D_{14} acting through Inn(D_{4}) | 112 | 4- | D4.10D14 | 224,186 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{29}⋊C_{8} | The semidirect product of C_{29} and C_{8} acting via C_{8}/C_{2}=C_{4} | 232 | 4- | C29:C8 | 232,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×D_{11} | Direct product of Dic_{3} and D_{11} | 132 | 4- | Dic3xD11 | 264,5 |

S_{3}×Dic_{11} | Direct product of S_{3} and Dic_{11} | 132 | 4- | S3xDic11 | 264,6 |

C_{33}⋊D_{4} | 1^{st} semidirect product of C_{33} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 132 | 4- | C33:D4 | 264,8 |

C_{33}⋊Q_{8} | The semidirect product of C_{33} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 264 | 4- | C33:Q8 | 264,11 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.D_{17} | The non-split extension by D_{4} of D_{17} acting via D_{17}/C_{17}=C_{2} | 136 | 4- | D4.D17 | 272,16 |

C_{17}⋊Q_{16} | The semidirect product of C_{17} and Q_{16} acting via Q_{16}/Q_{8}=C_{2} | 272 | 4- | C17:Q16 | 272,18 |

C_{17}⋊M_{4}(2) | The semidirect product of C_{17} and M_{4}(2) acting via M_{4}(2)/C_{2}^{2}=C_{4} | 136 | 4- | C17:M4(2) | 272,34 |

D_{4}⋊_{2}D_{17} | The semidirect product of D_{4} and D_{17} acting through Inn(D_{4}) | 136 | 4- | D4:2D17 | 272,41 |

Q_{8}×D_{17} | Direct product of Q_{8} and D_{17} | 136 | 4- | Q8xD17 | 272,42 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{7}×Dic_{5} | Direct product of D_{7} and Dic_{5} | 140 | 4- | D7xDic5 | 280,7 |

D_{5}×Dic_{7} | Direct product of D_{5} and Dic_{7} | 140 | 4- | D5xDic7 | 280,8 |

C_{35}⋊D_{4} | 1^{st} semidirect product of C_{35} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 140 | 4- | C35:D4 | 280,10 |

C_{35}⋊Q_{8} | The semidirect product of C_{35} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 280 | 4- | C35:Q8 | 280,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{37}⋊C_{8} | The semidirect product of C_{37} and C_{8} acting via C_{8}/C_{2}=C_{4} | 296 | 4- | C37:C8 | 296,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.D_{19} | The non-split extension by D_{4} of D_{19} acting via D_{19}/C_{19}=C_{2} | 152 | 4- | D4.D19 | 304,15 |

C_{19}⋊Q_{16} | The semidirect product of C_{19} and Q_{16} acting via Q_{16}/Q_{8}=C_{2} | 304 | 4- | C19:Q16 | 304,17 |

D_{4}⋊_{2}D_{19} | The semidirect product of D_{4} and D_{19} acting through Inn(D_{4}) | 152 | 4- | D4:2D19 | 304,32 |

Q_{8}×D_{19} | Direct product of Q_{8} and D_{19} | 152 | 4- | Q8xD19 | 304,33 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×D_{13} | Direct product of Dic_{3} and D_{13} | 156 | 4- | Dic3xD13 | 312,15 |

S_{3}×Dic_{13} | Direct product of S_{3} and Dic_{13} | 156 | 4- | S3xDic13 | 312,16 |

C_{39}⋊D_{4} | 1^{st} semidirect product of C_{39} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 156 | 4- | C39:D4 | 312,18 |

C_{39}⋊Q_{8} | The semidirect product of C_{39} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 312 | 4- | C39:Q8 | 312,21 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{41}⋊_{2}C_{8} | The semidirect product of C_{41} and C_{8} acting via C_{8}/C_{2}=C_{4} | 328 | 4- | C41:2C8 | 328,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{4}._{12}D_{44} | 4^{th} non-split extension by C_{4} of D_{44} acting via D_{44}/D_{22}=C_{2} | 176 | 4- | C4.12D44 | 352,30 |

D_{8}.D_{11} | The non-split extension by D_{8} of D_{11} acting via D_{11}/C_{11}=C_{2} | 176 | 4- | D8.D11 | 352,33 |

C_{11}⋊Q_{32} | The semidirect product of C_{11} and Q_{32} acting via Q_{32}/Q_{16}=C_{2} | 352 | 4- | C11:Q32 | 352,35 |

C_{8}.D_{22} | 1^{st} non-split extension by C_{8} of D_{22} acting via D_{22}/C_{11}=C_{2}^{2} | 176 | 4- | C8.D22 | 352,104 |

D_{8}⋊_{3}D_{11} | The semidirect product of D_{8} and D_{11} acting through Inn(D_{8}) | 176 | 4- | D8:3D11 | 352,107 |

D_{4}.D_{22} | 4^{th} non-split extension by D_{4} of D_{22} acting via D_{22}/D_{11}=C_{2} | 176 | 4- | D4.D22 | 352,110 |

Q_{16}×D_{11} | Direct product of Q_{16} and D_{11} | 176 | 4- | Q16xD11 | 352,112 |

D_{4}._{9}D_{22} | 4^{th} non-split extension by D_{4} of D_{22} acting via D_{22}/C_{22}=C_{2} | 176 | 4- | D4.9D22 | 352,146 |

D_{4}._{10}D_{22} | The non-split extension by D_{4} of D_{22} acting through Inn(D_{4}) | 176 | 4- | D4.10D22 | 352,185 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{45}⋊Q_{8} | The semidirect product of C_{45} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 360 | 4- | C45:Q8 | 360,7 |

D_{9}×Dic_{5} | Direct product of D_{9} and Dic_{5} | 180 | 4- | D9xDic5 | 360,8 |

D_{5}×Dic_{9} | Direct product of D_{5} and Dic_{9} | 180 | 4- | D5xDic9 | 360,11 |

D_{10}⋊D_{9} | 1^{st} semidirect product of D_{10} and D_{9} acting via D_{9}/C_{9}=C_{2} | 180 | 4- | D10:D9 | 360,12 |

(C_{3}×C_{6}).F_{5} | The non-split extension by C_{3}×C_{6} of F_{5} acting via F_{5}/C_{5}=C_{4} | 120 | 4- | (C3xC6).F5 | 360,57 |

Dic_{3}×D_{15} | Direct product of Dic_{3} and D_{15} | 120 | 4- | Dic3xD15 | 360,77 |

S_{3}×Dic_{15} | Direct product of S_{3} and Dic_{15} | 120 | 4- | S3xDic15 | 360,78 |

D_{6}⋊D_{15} | 1^{st} semidirect product of D_{6} and D_{15} acting via D_{15}/C_{15}=C_{2} | 120 | 4- | D6:D15 | 360,80 |

C_{3}⋊Dic_{30} | The semidirect product of C_{3} and Dic_{30} acting via Dic_{30}/Dic_{15}=C_{2} | 120 | 4- | C3:Dic30 | 360,83 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

D_{4}.D_{23} | The non-split extension by D_{4} of D_{23} acting via D_{23}/C_{23}=C_{2} | 184 | 4- | D4.D23 | 368,15 |

C_{23}⋊Q_{16} | The semidirect product of C_{23} and Q_{16} acting via Q_{16}/Q_{8}=C_{2} | 368 | 4- | C23:Q16 | 368,17 |

D_{4}⋊_{2}D_{23} | The semidirect product of D_{4} and D_{23} acting through Inn(D_{4}) | 184 | 4- | D4:2D23 | 368,32 |

Q_{8}×D_{23} | Direct product of Q_{8} and D_{23} | 184 | 4- | Q8xD23 | 368,33 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{7}^{2}⋊_{2}C_{8} | The semidirect product of C_{7}^{2} and C_{8} acting via C_{8}/C_{2}=C_{4} | 56 | 4- | C7^2:2C8 | 392,17 |

D_{7}×Dic_{7} | Direct product of D_{7} and Dic_{7} | 56 | 4- | D7xDic7 | 392,18 |

C_{7}^{2}⋊_{2}D_{4} | 1^{st} semidirect product of C_{7}^{2} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 56 | 4- | C7^2:2D4 | 392,20 |

C_{7}^{2}⋊_{2}Q_{8} | The semidirect product of C_{7}^{2} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 56 | 4- | C7^2:2Q8 | 392,22 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{3}×D_{17} | Direct product of Dic_{3} and D_{17} | 204 | 4- | Dic3xD17 | 408,7 |

S_{3}×Dic_{17} | Direct product of S_{3} and Dic_{17} | 204 | 4- | S3xDic17 | 408,8 |

C_{51}⋊D_{4} | 1^{st} semidirect product of C_{51} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 204 | 4- | C51:D4 | 408,10 |

C_{51}⋊Q_{8} | The semidirect product of C_{51} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 408 | 4- | C51:Q8 | 408,13 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{53}⋊C_{8} | The semidirect product of C_{53} and C_{8} acting via C_{8}/C_{2}=C_{4} | 424 | 4- | C53:C8 | 424,3 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

Dic_{5}×D_{11} | Direct product of Dic_{5} and D_{11} | 220 | 4- | Dic5xD11 | 440,17 |

D_{5}×Dic_{11} | Direct product of D_{5} and Dic_{11} | 220 | 4- | D5xDic11 | 440,18 |

C_{55}⋊D_{4} | 1^{st} semidirect product of C_{55} and D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 220 | 4- | C55:D4 | 440,20 |

C_{55}⋊Q_{8} | The semidirect product of C_{55} and Q_{8} acting via Q_{8}/C_{2}=C_{2}^{2} | 440 | 4- | C55:Q8 | 440,23 |

d | ρ | Label | ID | ||
---|---|---|---|---|---|

C_{56}._{8}D_{4} | 8^{th} non-split extension by C_{56} of D_{4} acting via D_{4}/C_{2}=C_{2}^{2} | 224 | 4- | C56.8D4 | 448,53 |

C_{28}._{4}D_{8} | 4^{th} non-split extension by C_{28} of D_{8} acting via D_{8}/C_{4}=C_{2}^{2} | 224 | 4- | C28.4D8 | 448,74 |

D_{16}.D_{7} | The non-split extension by D_{16} of D_{7} acting via D_{7}</ |