| | d | ρ | Label | ID |
---|
C64 | Cyclic group | 64 | 1 | C64 | 64,1 |
C82 | Abelian group of type [8,8] | 64 | | C8^2 | 64,2 |
C43 | Abelian group of type [4,4,4] | 64 | | C4^3 | 64,55 |
C26 | Elementary abelian group of type [2,2,2,2,2,2] | 64 | | C2^6 | 64,267 |
C4×C16 | Abelian group of type [4,16] | 64 | | C4xC16 | 64,26 |
C2×C32 | Abelian group of type [2,32] | 64 | | C2xC32 | 64,50 |
C23×C8 | Abelian group of type [2,2,2,8] | 64 | | C2^3xC8 | 64,246 |
C24×C4 | Abelian group of type [2,2,2,2,4] | 64 | | C2^4xC4 | 64,260 |
C22×C16 | Abelian group of type [2,2,16] | 64 | | C2^2xC16 | 64,183 |
C22×C42 | Abelian group of type [2,2,4,4] | 64 | | C2^2xC4^2 | 64,192 |
C2×C4×C8 | Abelian group of type [2,4,8] | 64 | | C2xC4xC8 | 64,83 |
| | d | ρ | Label | ID |
---|
C72 | Cyclic group | 72 | 1 | C72 | 72,2 |
F9 | Frobenius group; = C32⋊C8 = AGL1(𝔽9) | 9 | 8+ | F9 | 72,39 |
C32⋊2C8 | The semidirect product of C32 and C8 acting via C8/C2=C4 | 24 | 4- | C3^2:2C8 | 72,19 |
C9⋊C8 | The semidirect product of C9 and C8 acting via C8/C4=C2 | 72 | 2 | C9:C8 | 72,1 |
C32⋊4C8 | 2nd semidirect product of C32 and C8 acting via C8/C4=C2 | 72 | | C3^2:4C8 | 72,13 |
C6.D6 | 2nd non-split extension by C6 of D6 acting via D6/S3=C2 | 12 | 4+ | C6.D6 | 72,21 |
C2×C36 | Abelian group of type [2,36] | 72 | | C2xC36 | 72,9 |
C3×C24 | Abelian group of type [3,24] | 72 | | C3xC24 | 72,14 |
C6×C12 | Abelian group of type [6,12] | 72 | | C6xC12 | 72,36 |
C2×C62 | Abelian group of type [2,6,6] | 72 | | C2xC6^2 | 72,50 |
C22×C18 | Abelian group of type [2,2,18] | 72 | | C2^2xC18 | 72,18 |
S3×A4 | Direct product of S3 and A4 | 12 | 6+ | S3xA4 | 72,44 |
C6×A4 | Direct product of C6 and A4 | 18 | 3 | C6xA4 | 72,47 |
S3×C12 | Direct product of C12 and S3 | 24 | 2 | S3xC12 | 72,27 |
S3×Dic3 | Direct product of S3 and Dic3 | 24 | 4- | S3xDic3 | 72,20 |
C6×Dic3 | Direct product of C6 and Dic3 | 24 | | C6xDic3 | 72,29 |
C4×D9 | Direct product of C4 and D9 | 36 | 2 | C4xD9 | 72,5 |
C22×D9 | Direct product of C22 and D9 | 36 | | C2^2xD9 | 72,17 |
C2×Dic9 | Direct product of C2 and Dic9 | 72 | | C2xDic9 | 72,7 |
C2×S32 | Direct product of C2, S3 and S3 | 12 | 4+ | C2xS3^2 | 72,46 |
C2×C32⋊C4 | Direct product of C2 and C32⋊C4 | 12 | 4+ | C2xC3^2:C4 | 72,45 |
C2×C3.A4 | Direct product of C2 and C3.A4 | 18 | 3 | C2xC3.A4 | 72,16 |
C3×C3⋊C8 | Direct product of C3 and C3⋊C8 | 24 | 2 | C3xC3:C8 | 72,12 |
S3×C2×C6 | Direct product of C2×C6 and S3 | 24 | | S3xC2xC6 | 72,48 |
C4×C3⋊S3 | Direct product of C4 and C3⋊S3 | 36 | | C4xC3:S3 | 72,32 |
C22×C3⋊S3 | Direct product of C22 and C3⋊S3 | 36 | | C2^2xC3:S3 | 72,49 |
C2×C3⋊Dic3 | Direct product of C2 and C3⋊Dic3 | 72 | | C2xC3:Dic3 | 72,34 |
| | d | ρ | Label | ID |
---|
C96 | Cyclic group | 96 | 1 | C96 | 96,2 |
C3⋊C32 | The semidirect product of C3 and C32 acting via C32/C16=C2 | 96 | 2 | C3:C32 | 96,1 |
C4×C24 | Abelian group of type [4,24] | 96 | | C4xC24 | 96,46 |
C2×C48 | Abelian group of type [2,48] | 96 | | C2xC48 | 96,59 |
C24×C6 | Abelian group of type [2,2,2,2,6] | 96 | | C2^4xC6 | 96,231 |
C22×C24 | Abelian group of type [2,2,24] | 96 | | C2^2xC24 | 96,176 |
C23×C12 | Abelian group of type [2,2,2,12] | 96 | | C2^3xC12 | 96,220 |
C2×C4×C12 | Abelian group of type [2,4,12] | 96 | | C2xC4xC12 | 96,161 |
C8×A4 | Direct product of C8 and A4 | 24 | 3 | C8xA4 | 96,73 |
C23×A4 | Direct product of C23 and A4 | 24 | | C2^3xA4 | 96,228 |
S3×C16 | Direct product of C16 and S3 | 48 | 2 | S3xC16 | 96,4 |
S3×C42 | Direct product of C42 and S3 | 48 | | S3xC4^2 | 96,78 |
S3×C24 | Direct product of C24 and S3 | 48 | | S3xC2^4 | 96,230 |
C8×Dic3 | Direct product of C8 and Dic3 | 96 | | C8xDic3 | 96,20 |
C23×Dic3 | Direct product of C23 and Dic3 | 96 | | C2^3xDic3 | 96,218 |
C2×C42⋊C3 | Direct product of C2 and C42⋊C3 | 12 | 3 | C2xC4^2:C3 | 96,68 |
C2×C22⋊A4 | Direct product of C2 and C22⋊A4 | 12 | | C2xC2^2:A4 | 96,229 |
C2×C4×A4 | Direct product of C2×C4 and A4 | 24 | | C2xC4xA4 | 96,196 |
S3×C2×C8 | Direct product of C2×C8 and S3 | 48 | | S3xC2xC8 | 96,106 |
S3×C22×C4 | Direct product of C22×C4 and S3 | 48 | | S3xC2^2xC4 | 96,206 |
C4×C3⋊C8 | Direct product of C4 and C3⋊C8 | 96 | | C4xC3:C8 | 96,9 |
C2×C3⋊C16 | Direct product of C2 and C3⋊C16 | 96 | | C2xC3:C16 | 96,18 |
C22×C3⋊C8 | Direct product of C22 and C3⋊C8 | 96 | | C2^2xC3:C8 | 96,127 |
C2×C4×Dic3 | Direct product of C2×C4 and Dic3 | 96 | | C2xC4xDic3 | 96,129 |
| | d | ρ | Label | ID |
---|
C108 | Cyclic group | 108 | 1 | C108 | 108,2 |
D54 | Dihedral group; = C2×D27 | 54 | 2+ | D54 | 108,4 |
Dic27 | Dicyclic group; = C27⋊C4 | 108 | 2- | Dic27 | 108,1 |
C33⋊C4 | 2nd semidirect product of C33 and C4 acting faithfully | 12 | 4 | C3^3:C4 | 108,37 |
C32⋊4D6 | The semidirect product of C32 and D6 acting via D6/C3=C22 | 12 | 4 | C3^2:4D6 | 108,40 |
C9⋊Dic3 | The semidirect product of C9 and Dic3 acting via Dic3/C6=C2 | 108 | | C9:Dic3 | 108,10 |
C33⋊5C4 | 3rd semidirect product of C33 and C4 acting via C4/C2=C2 | 108 | | C3^3:5C4 | 108,34 |
C9.A4 | The central extension by C9 of A4 | 54 | 3 | C9.A4 | 108,3 |
C2×C54 | Abelian group of type [2,54] | 108 | | C2xC54 | 108,5 |
C3×C36 | Abelian group of type [3,36] | 108 | | C3xC36 | 108,12 |
C6×C18 | Abelian group of type [6,18] | 108 | | C6xC18 | 108,29 |
C3×C62 | Abelian group of type [3,6,6] | 108 | | C3xC6^2 | 108,45 |
C32×C12 | Abelian group of type [3,3,12] | 108 | | C3^2xC12 | 108,35 |
S3×D9 | Direct product of S3 and D9 | 18 | 4+ | S3xD9 | 108,16 |
C9×A4 | Direct product of C9 and A4 | 36 | 3 | C9xA4 | 108,18 |
C6×D9 | Direct product of C6 and D9 | 36 | 2 | C6xD9 | 108,23 |
S3×C18 | Direct product of C18 and S3 | 36 | 2 | S3xC18 | 108,24 |
C32×A4 | Direct product of C32 and A4 | 36 | | C3^2xA4 | 108,41 |
C3×Dic9 | Direct product of C3 and Dic9 | 36 | 2 | C3xDic9 | 108,6 |
C9×Dic3 | Direct product of C9 and Dic3 | 36 | 2 | C9xDic3 | 108,7 |
C32×Dic3 | Direct product of C32 and Dic3 | 36 | | C3^2xDic3 | 108,32 |
C3×S32 | Direct product of C3, S3 and S3 | 12 | 4 | C3xS3^2 | 108,38 |
C3×C32⋊C4 | Direct product of C3 and C32⋊C4 | 12 | 4 | C3xC3^2:C4 | 108,36 |
S3×C3⋊S3 | Direct product of S3 and C3⋊S3 | 18 | | S3xC3:S3 | 108,39 |
S3×C3×C6 | Direct product of C3×C6 and S3 | 36 | | S3xC3xC6 | 108,42 |
C6×C3⋊S3 | Direct product of C6 and C3⋊S3 | 36 | | C6xC3:S3 | 108,43 |
C3×C3⋊Dic3 | Direct product of C3 and C3⋊Dic3 | 36 | | C3xC3:Dic3 | 108,33 |
C2×C9⋊S3 | Direct product of C2 and C9⋊S3 | 54 | | C2xC9:S3 | 108,27 |
C3×C3.A4 | Direct product of C3 and C3.A4 | 54 | | C3xC3.A4 | 108,20 |
C2×C33⋊C2 | Direct product of C2 and C33⋊C2 | 54 | | C2xC3^3:C2 | 108,44 |
| | d | ρ | Label | ID |
---|
C120 | Cyclic group | 120 | 1 | C120 | 120,4 |
C15⋊3C8 | 1st semidirect product of C15 and C8 acting via C8/C4=C2 | 120 | 2 | C15:3C8 | 120,3 |
C15⋊C8 | 1st semidirect product of C15 and C8 acting via C8/C2=C4 | 120 | 4 | C15:C8 | 120,7 |
D30.C2 | The non-split extension by D30 of C2 acting faithfully | 60 | 4+ | D30.C2 | 120,10 |
C2×C60 | Abelian group of type [2,60] | 120 | | C2xC60 | 120,31 |
C22×C30 | Abelian group of type [2,2,30] | 120 | | C2^2xC30 | 120,47 |
C2×A5 | Direct product of C2 and A5; = icosahedron/dodecahedron symmetries | 10 | 3+ | C2xA5 | 120,35 |
S3×F5 | Direct product of S3 and F5; = Aut(D15) = Hol(C15) | 15 | 8+ | S3xF5 | 120,36 |
D5×A4 | Direct product of D5 and A4 | 20 | 6+ | D5xA4 | 120,39 |
C6×F5 | Direct product of C6 and F5 | 30 | 4 | C6xF5 | 120,40 |
C10×A4 | Direct product of C10 and A4 | 30 | 3 | C10xA4 | 120,43 |
S3×C20 | Direct product of C20 and S3 | 60 | 2 | S3xC20 | 120,22 |
D5×C12 | Direct product of C12 and D5 | 60 | 2 | D5xC12 | 120,17 |
C4×D15 | Direct product of C4 and D15 | 60 | 2 | C4xD15 | 120,27 |
D5×Dic3 | Direct product of D5 and Dic3 | 60 | 4- | D5xDic3 | 120,8 |
S3×Dic5 | Direct product of S3 and Dic5 | 60 | 4- | S3xDic5 | 120,9 |
C22×D15 | Direct product of C22 and D15 | 60 | | C2^2xD15 | 120,46 |
C6×Dic5 | Direct product of C6 and Dic5 | 120 | | C6xDic5 | 120,19 |
C10×Dic3 | Direct product of C10 and Dic3 | 120 | | C10xDic3 | 120,24 |
C2×Dic15 | Direct product of C2 and Dic15 | 120 | | C2xDic15 | 120,29 |
C2×S3×D5 | Direct product of C2, S3 and D5 | 30 | 4+ | C2xS3xD5 | 120,42 |
C2×C3⋊F5 | Direct product of C2 and C3⋊F5 | 30 | 4 | C2xC3:F5 | 120,41 |
D5×C2×C6 | Direct product of C2×C6 and D5 | 60 | | D5xC2xC6 | 120,44 |
S3×C2×C10 | Direct product of C2×C10 and S3 | 60 | | S3xC2xC10 | 120,45 |
C5×C3⋊C8 | Direct product of C5 and C3⋊C8 | 120 | 2 | C5xC3:C8 | 120,1 |
C3×C5⋊C8 | Direct product of C3 and C5⋊C8 | 120 | 4 | C3xC5:C8 | 120,6 |
C3×C5⋊2C8 | Direct product of C3 and C5⋊2C8 | 120 | 2 | C3xC5:2C8 | 120,2 |
| | d | ρ | Label | ID |
---|
C128 | Cyclic group | 128 | 1 | C128 | 128,1 |
C27 | Elementary abelian group of type [2,2,2,2,2,2,2] | 128 | | C2^7 | 128,2328 |
C8×C16 | Abelian group of type [8,16] | 128 | | C8xC16 | 128,42 |
C4×C32 | Abelian group of type [4,32] | 128 | | C4xC32 | 128,128 |
C2×C64 | Abelian group of type [2,64] | 128 | | C2xC64 | 128,159 |
C2×C82 | Abelian group of type [2,8,8] | 128 | | C2xC8^2 | 128,179 |
C42×C8 | Abelian group of type [4,4,8] | 128 | | C4^2xC8 | 128,456 |
C2×C43 | Abelian group of type [2,4,4,4] | 128 | | C2xC4^3 | 128,997 |
C24×C8 | Abelian group of type [2,2,2,2,8] | 128 | | C2^4xC8 | 128,2301 |
C25×C4 | Abelian group of type [2,2,2,2,2,4] | 128 | | C2^5xC4 | 128,2319 |
C22×C32 | Abelian group of type [2,2,32] | 128 | | C2^2xC32 | 128,988 |
C23×C16 | Abelian group of type [2,2,2,16] | 128 | | C2^3xC16 | 128,2136 |
C23×C42 | Abelian group of type [2,2,2,4,4] | 128 | | C2^3xC4^2 | 128,2150 |
C2×C4×C16 | Abelian group of type [2,4,16] | 128 | | C2xC4xC16 | 128,837 |
C22×C4×C8 | Abelian group of type [2,2,4,8] | 128 | | C2^2xC4xC8 | 128,1601 |
| | d | ρ | Label | ID |
---|
C144 | Cyclic group | 144 | 1 | C144 | 144,2 |
C42⋊C9 | The semidirect product of C42 and C9 acting via C9/C3=C3 | 36 | 3 | C4^2:C9 | 144,3 |
C24⋊C9 | 2nd semidirect product of C24 and C9 acting via C9/C3=C3 | 36 | | C2^4:C9 | 144,111 |
C32⋊2C16 | The semidirect product of C32 and C16 acting via C16/C4=C4 | 48 | 4 | C3^2:2C16 | 144,51 |
C9⋊C16 | The semidirect product of C9 and C16 acting via C16/C8=C2 | 144 | 2 | C9:C16 | 144,1 |
C3⋊S3⋊3C8 | 2nd semidirect product of C3⋊S3 and C8 acting via C8/C4=C2 | 24 | 4 | C3:S3:3C8 | 144,130 |
C12.29D6 | 3rd non-split extension by C12 of D6 acting via D6/S3=C2 | 24 | 4 | C12.29D6 | 144,53 |
C2.F9 | The central extension by C2 of F9 | 48 | 8- | C2.F9 | 144,114 |
C24.S3 | 9th non-split extension by C24 of S3 acting via S3/C3=C2 | 144 | | C24.S3 | 144,29 |
C122 | Abelian group of type [12,12] | 144 | | C12^2 | 144,101 |
C4×C36 | Abelian group of type [4,36] | 144 | | C4xC36 | 144,20 |
C2×C72 | Abelian group of type [2,72] | 144 | | C2xC72 | 144,23 |
C3×C48 | Abelian group of type [3,48] | 144 | | C3xC48 | 144,30 |
C6×C24 | Abelian group of type [6,24] | 144 | | C6xC24 | 144,104 |
C22×C36 | Abelian group of type [2,2,36] | 144 | | C2^2xC36 | 144,47 |
C23×C18 | Abelian group of type [2,2,2,18] | 144 | | C2^3xC18 | 144,113 |
C22×C62 | Abelian group of type [2,2,6,6] | 144 | | C2^2xC6^2 | 144,197 |
C2×C6×C12 | Abelian group of type [2,6,12] | 144 | | C2xC6xC12 | 144,178 |
A42 | Direct product of A4 and A4; = PΩ+4(𝔽3) | 12 | 9+ | A4^2 | 144,184 |
C2×F9 | Direct product of C2 and F9 | 18 | 8+ | C2xF9 | 144,185 |
C12×A4 | Direct product of C12 and A4 | 36 | 3 | C12xA4 | 144,155 |
Dic3×A4 | Direct product of Dic3 and A4 | 36 | 6- | Dic3xA4 | 144,129 |
S3×C24 | Direct product of C24 and S3 | 48 | 2 | S3xC24 | 144,69 |
Dic32 | Direct product of Dic3 and Dic3 | 48 | | Dic3^2 | 144,63 |
Dic3×C12 | Direct product of C12 and Dic3 | 48 | | Dic3xC12 | 144,76 |
C8×D9 | Direct product of C8 and D9 | 72 | 2 | C8xD9 | 144,5 |
C23×D9 | Direct product of C23 and D9 | 72 | | C2^3xD9 | 144,112 |
C4×Dic9 | Direct product of C4 and Dic9 | 144 | | C4xDic9 | 144,11 |
C22×Dic9 | Direct product of C22 and Dic9 | 144 | | C2^2xDic9 | 144,45 |
C2×S3×A4 | Direct product of C2, S3 and A4 | 18 | 6+ | C2xS3xA4 | 144,190 |
C4×S32 | Direct product of C4, S3 and S3 | 24 | 4 | C4xS3^2 | 144,143 |
C22×S32 | Direct product of C22, S3 and S3 | 24 | | C2^2xS3^2 | 144,192 |
C4×C32⋊C4 | Direct product of C4 and C32⋊C4 | 24 | 4 | C4xC3^2:C4 | 144,132 |
C2×C6.D6 | Direct product of C2 and C6.D6 | 24 | | C2xC6.D6 | 144,149 |
C22×C32⋊C4 | Direct product of C22 and C32⋊C4 | 24 | | C2^2xC3^2:C4 | 144,191 |
A4×C2×C6 | Direct product of C2×C6 and A4 | 36 | | A4xC2xC6 | 144,193 |
C4×C3.A4 | Direct product of C4 and C3.A4 | 36 | 3 | C4xC3.A4 | 144,34 |
C3×C42⋊C3 | Direct product of C3 and C42⋊C3 | 36 | 3 | C3xC4^2:C3 | 144,68 |
C3×C22⋊A4 | Direct product of C3 and C22⋊A4 | 36 | | C3xC2^2:A4 | 144,194 |
C22×C3.A4 | Direct product of C22 and C3.A4 | 36 | | C2^2xC3.A4 | 144,110 |
C6×C3⋊C8 | Direct product of C6 and C3⋊C8 | 48 | | C6xC3:C8 | 144,74 |
S3×C3⋊C8 | Direct product of S3 and C3⋊C8 | 48 | 4 | S3xC3:C8 | 144,52 |
C3×C3⋊C16 | Direct product of C3 and C3⋊C16 | 48 | 2 | C3xC3:C16 | 144,28 |
S3×C2×C12 | Direct product of C2×C12 and S3 | 48 | | S3xC2xC12 | 144,159 |
S3×C22×C6 | Direct product of C22×C6 and S3 | 48 | | S3xC2^2xC6 | 144,195 |
C2×S3×Dic3 | Direct product of C2, S3 and Dic3 | 48 | | C2xS3xDic3 | 144,146 |
Dic3×C2×C6 | Direct product of C2×C6 and Dic3 | 48 | | Dic3xC2xC6 | 144,166 |
C2×C32⋊2C8 | Direct product of C2 and C32⋊2C8 | 48 | | C2xC3^2:2C8 | 144,134 |
C2×C4×D9 | Direct product of C2×C4 and D9 | 72 | | C2xC4xD9 | 144,38 |
C8×C3⋊S3 | Direct product of C8 and C3⋊S3 | 72 | | C8xC3:S3 | 144,85 |
C23×C3⋊S3 | Direct product of C23 and C3⋊S3 | 72 | | C2^3xC3:S3 | 144,196 |
C2×C9⋊C8 | Direct product of C2 and C9⋊C8 | 144 | | C2xC9:C8 | 144,9 |
C4×C3⋊Dic3 | Direct product of C4 and C3⋊Dic3 | 144 | | C4xC3:Dic3 | 144,92 |
C2×C32⋊4C8 | Direct product of C2 and C32⋊4C8 | 144 | | C2xC3^2:4C8 | 144,90 |
C22×C3⋊Dic3 | Direct product of C22 and C3⋊Dic3 | 144 | | C2^2xC3:Dic3 | 144,176 |
C2×C4×C3⋊S3 | Direct product of C2×C4 and C3⋊S3 | 72 | | C2xC4xC3:S3 | 144,169 |
| | d | ρ | Label | ID |
---|
C160 | Cyclic group | 160 | 1 | C160 | 160,2 |
D5⋊C16 | The semidirect product of D5 and C16 acting via C16/C8=C2 | 80 | 4 | D5:C16 | 160,64 |
C5⋊C32 | The semidirect product of C5 and C32 acting via C32/C8=C4 | 160 | 4 | C5:C32 | 160,3 |
C5⋊2C32 | The semidirect product of C5 and C32 acting via C32/C16=C2 | 160 | 2 | C5:2C32 | 160,1 |
C4×C40 | Abelian group of type [4,40] | 160 | | C4xC40 | 160,46 |
C2×C80 | Abelian group of type [2,80] | 160 | | C2xC80 | 160,59 |
C22×C40 | Abelian group of type [2,2,40] | 160 | | C2^2xC40 | 160,190 |
C23×C20 | Abelian group of type [2,2,2,20] | 160 | | C2^3xC20 | 160,228 |
C24×C10 | Abelian group of type [2,2,2,2,10] | 160 | | C2^4xC10 | 160,238 |
C2×C4×C20 | Abelian group of type [2,4,20] | 160 | | C2xC4xC20 | 160,175 |
C8×F5 | Direct product of C8 and F5 | 40 | 4 | C8xF5 | 160,66 |
C23×F5 | Direct product of C23 and F5 | 40 | | C2^3xF5 | 160,236 |
D5×C16 | Direct product of C16 and D5 | 80 | 2 | D5xC16 | 160,4 |
D5×C42 | Direct product of C42 and D5 | 80 | | D5xC4^2 | 160,92 |
D5×C24 | Direct product of C24 and D5 | 80 | | D5xC2^4 | 160,237 |
C8×Dic5 | Direct product of C8 and Dic5 | 160 | | C8xDic5 | 160,20 |
C23×Dic5 | Direct product of C23 and Dic5 | 160 | | C2^3xDic5 | 160,226 |
C2×C24⋊C5 | Direct product of C2 and C24⋊C5; = AΣL1(𝔽32) | 10 | 5+ | C2xC2^4:C5 | 160,235 |
C2×C4×F5 | Direct product of C2×C4 and F5 | 40 | | C2xC4xF5 | 160,203 |
D5×C2×C8 | Direct product of C2×C8 and D5 | 80 | | D5xC2xC8 | 160,120 |
C2×D5⋊C8 | Direct product of C2 and D5⋊C8 | 80 | | C2xD5:C8 | 160,200 |
D5×C22×C4 | Direct product of C22×C4 and D5 | 80 | | D5xC2^2xC4 | 160,214 |
C4×C5⋊C8 | Direct product of C4 and C5⋊C8 | 160 | | C4xC5:C8 | 160,75 |
C2×C5⋊C16 | Direct product of C2 and C5⋊C16 | 160 | | C2xC5:C16 | 160,72 |
C4×C5⋊2C8 | Direct product of C4 and C5⋊2C8 | 160 | | C4xC5:2C8 | 160,9 |
C22×C5⋊C8 | Direct product of C22 and C5⋊C8 | 160 | | C2^2xC5:C8 | 160,210 |
C2×C4×Dic5 | Direct product of C2×C4 and Dic5 | 160 | | C2xC4xDic5 | 160,143 |
C2×C5⋊2C16 | Direct product of C2 and C5⋊2C16 | 160 | | C2xC5:2C16 | 160,18 |
C22×C5⋊2C8 | Direct product of C22 and C5⋊2C8 | 160 | | C2^2xC5:2C8 | 160,141 |
| | d | ρ | Label | ID |
---|
C162 | Cyclic group | 162 | 1 | C162 | 162,2 |
D81 | Dihedral group | 81 | 2+ | D81 | 162,1 |
C9⋊D9 | The semidirect product of C9 and D9 acting via D9/C9=C2 | 81 | | C9:D9 | 162,16 |
C27⋊S3 | The semidirect product of C27 and S3 acting via S3/C3=C2 | 81 | | C27:S3 | 162,18 |
C34⋊C2 | 4th semidirect product of C34 and C2 acting faithfully | 81 | | C3^4:C2 | 162,54 |
C32⋊4D9 | 2nd semidirect product of C32 and D9 acting via D9/C9=C2 | 81 | | C3^2:4D9 | 162,45 |
C9×C18 | Abelian group of type [9,18] | 162 | | C9xC18 | 162,23 |
C3×C54 | Abelian group of type [3,54] | 162 | | C3xC54 | 162,26 |
C33×C6 | Abelian group of type [3,3,3,6] | 162 | | C3^3xC6 | 162,55 |
C32×C18 | Abelian group of type [3,3,18] | 162 | | C3^2xC18 | 162,47 |
C9×D9 | Direct product of C9 and D9 | 18 | 2 | C9xD9 | 162,3 |
S3×C27 | Direct product of C27 and S3 | 54 | 2 | S3xC27 | 162,8 |
C3×D27 | Direct product of C3 and D27 | 54 | 2 | C3xD27 | 162,7 |
S3×C33 | Direct product of C33 and S3 | 54 | | S3xC3^3 | 162,51 |
C32×D9 | Direct product of C32 and D9 | 54 | | C3^2xD9 | 162,32 |
C32×C3⋊S3 | Direct product of C32 and C3⋊S3 | 18 | | C3^2xC3:S3 | 162,52 |
S3×C3×C9 | Direct product of C3×C9 and S3 | 54 | | S3xC3xC9 | 162,33 |
C3×C9⋊S3 | Direct product of C3 and C9⋊S3 | 54 | | C3xC9:S3 | 162,38 |
C9×C3⋊S3 | Direct product of C9 and C3⋊S3 | 54 | | C9xC3:S3 | 162,39 |
C3×C33⋊C2 | Direct product of C3 and C33⋊C2 | 54 | | C3xC3^3:C2 | 162,53 |
| | d | ρ | Label | ID |
---|
C168 | Cyclic group | 168 | 1 | C168 | 168,6 |
AΓL1(𝔽8) | Affine semilinear group on 𝔽81; = F8⋊C3 = Aut(F8) | 8 | 7+ | AGammaL(1,8) | 168,43 |
D7⋊A4 | The semidirect product of D7 and A4 acting via A4/C22=C3 | 28 | 6+ | D7:A4 | 168,49 |
C7⋊C24 | The semidirect product of C7 and C24 acting via C24/C4=C6 | 56 | 6 | C7:C24 | 168,1 |
D21⋊C4 | The semidirect product of D21 and C4 acting via C4/C2=C2 | 84 | 4+ | D21:C4 | 168,14 |
C21⋊C8 | 1st semidirect product of C21 and C8 acting via C8/C4=C2 | 168 | 2 | C21:C8 | 168,5 |
C2×C84 | Abelian group of type [2,84] | 168 | | C2xC84 | 168,39 |
C22×C42 | Abelian group of type [2,2,42] | 168 | | C2^2xC42 | 168,57 |
C3×F8 | Direct product of C3 and F8 | 24 | 7 | C3xF8 | 168,44 |
A4×D7 | Direct product of A4 and D7 | 28 | 6+ | A4xD7 | 168,48 |
C4×F7 | Direct product of C4 and F7 | 28 | 6 | C4xF7 | 168,8 |
C22×F7 | Direct product of C22 and F7 | 28 | | C2^2xF7 | 168,47 |
A4×C14 | Direct product of C14 and A4 | 42 | 3 | A4xC14 | 168,52 |
S3×C28 | Direct product of C28 and S3 | 84 | 2 | S3xC28 | 168,30 |
C12×D7 | Direct product of C12 and D7 | 84 | 2 | C12xD7 | 168,25 |
C4×D21 | Direct product of C4 and D21 | 84 | 2 | C4xD21 | 168,35 |
Dic3×D7 | Direct product of Dic3 and D7 | 84 | 4- | Dic3xD7 | 168,12 |
S3×Dic7 | Direct product of S3 and Dic7 | 84 | 4- | S3xDic7 | 168,13 |
C22×D21 | Direct product of C22 and D21 | 84 | | C2^2xD21 | 168,56 |
C6×Dic7 | Direct product of C6 and Dic7 | 168 | | C6xDic7 | 168,27 |
Dic3×C14 | Direct product of C14 and Dic3 | 168 | | Dic3xC14 | 168,32 |
C2×Dic21 | Direct product of C2 and Dic21 | 168 | | C2xDic21 | 168,37 |
C2×C7⋊A4 | Direct product of C2 and C7⋊A4 | 42 | 3 | C2xC7:A4 | 168,53 |
C2×S3×D7 | Direct product of C2, S3 and D7 | 42 | 4+ | C2xS3xD7 | 168,50 |
C8×C7⋊C3 | Direct product of C8 and C7⋊C3 | 56 | 3 | C8xC7:C3 | 168,2 |
C2×C7⋊C12 | Direct product of C2 and C7⋊C12 | 56 | | C2xC7:C12 | 168,10 |
C23×C7⋊C3 | Direct product of C23 and C7⋊C3 | 56 | | C2^3xC7:C3 | 168,51 |
C2×C6×D7 | Direct product of C2×C6 and D7 | 84 | | C2xC6xD7 | 168,54 |
S3×C2×C14 | Direct product of C2×C14 and S3 | 84 | | S3xC2xC14 | 168,55 |
C7×C3⋊C8 | Direct product of C7 and C3⋊C8 | 168 | 2 | C7xC3:C8 | 168,3 |
C3×C7⋊C8 | Direct product of C3 and C7⋊C8 | 168 | 2 | C3xC7:C8 | 168,4 |
C2×C4×C7⋊C3 | Direct product of C2×C4 and C7⋊C3 | 56 | | C2xC4xC7:C3 | 168,19 |
| | d | ρ | Label | ID |
---|
C180 | Cyclic group | 180 | 1 | C180 | 180,4 |
D90 | Dihedral group; = C2×D45 | 90 | 2+ | D90 | 180,11 |
Dic45 | Dicyclic group; = C9⋊Dic5 | 180 | 2- | Dic45 | 180,3 |
C32⋊F5 | The semidirect product of C32 and F5 acting via F5/C5=C4 | 30 | 4+ | C3^2:F5 | 180,25 |
D15⋊S3 | The semidirect product of D15 and S3 acting via S3/C3=C2 | 30 | 4 | D15:S3 | 180,30 |
C32⋊Dic5 | The semidirect product of C32 and Dic5 acting via Dic5/C5=C4 | 30 | 4 | C3^2:Dic5 | 180,24 |
C9⋊F5 | The semidirect product of C9 and F5 acting via F5/D5=C2 | 45 | 4 | C9:F5 | 180,6 |
C32⋊3F5 | 2nd semidirect product of C32 and F5 acting via F5/D5=C2 | 45 | | C3^2:3F5 | 180,22 |
C3⋊Dic15 | The semidirect product of C3 and Dic15 acting via Dic15/C30=C2 | 180 | | C3:Dic15 | 180,17 |
C2×C90 | Abelian group of type [2,90] | 180 | | C2xC90 | 180,12 |
C3×C60 | Abelian group of type [3,60] | 180 | | C3xC60 | 180,18 |
C6×C30 | Abelian group of type [6,30] | 180 | | C6xC30 | 180,37 |
C3×A5 | Direct product of C3 and A5; = GL2(𝔽4) | 15 | 3 | C3xA5 | 180,19 |
S3×D15 | Direct product of S3 and D15 | 30 | 4+ | S3xD15 | 180,29 |
D5×D9 | Direct product of D5 and D9 | 45 | 4+ | D5xD9 | 180,7 |
C9×F5 | Direct product of C9 and F5 | 45 | 4 | C9xF5 | 180,5 |
C32×F5 | Direct product of C32 and F5 | 45 | | C3^2xF5 | 180,20 |
S3×C30 | Direct product of C30 and S3 | 60 | 2 | S3xC30 | 180,33 |
A4×C15 | Direct product of C15 and A4 | 60 | 3 | A4xC15 | 180,31 |
C6×D15 | Direct product of C6 and D15 | 60 | 2 | C6xD15 | 180,34 |
Dic3×C15 | Direct product of C15 and Dic3 | 60 | 2 | Dic3xC15 | 180,14 |
C3×Dic15 | Direct product of C3 and Dic15 | 60 | 2 | C3xDic15 | 180,15 |
D5×C18 | Direct product of C18 and D5 | 90 | 2 | D5xC18 | 180,9 |
C10×D9 | Direct product of C10 and D9 | 90 | 2 | C10xD9 | 180,10 |
C5×Dic9 | Direct product of C5 and Dic9 | 180 | 2 | C5xDic9 | 180,1 |
C9×Dic5 | Direct product of C9 and Dic5 | 180 | 2 | C9xDic5 | 180,2 |
C32×Dic5 | Direct product of C32 and Dic5 | 180 | | C3^2xDic5 | 180,13 |
C5×S32 | Direct product of C5, S3 and S3 | 30 | 4 | C5xS3^2 | 180,28 |
C3×S3×D5 | Direct product of C3, S3 and D5 | 30 | 4 | C3xS3xD5 | 180,26 |
C3×C3⋊F5 | Direct product of C3 and C3⋊F5 | 30 | 4 | C3xC3:F5 | 180,21 |
C5×C32⋊C4 | Direct product of C5 and C32⋊C4 | 30 | 4 | C5xC3^2:C4 | 180,23 |
D5×C3⋊S3 | Direct product of D5 and C3⋊S3 | 45 | | D5xC3:S3 | 180,27 |
D5×C3×C6 | Direct product of C3×C6 and D5 | 90 | | D5xC3xC6 | 180,32 |
C10×C3⋊S3 | Direct product of C10 and C3⋊S3 | 90 | | C10xC3:S3 | 180,35 |
C2×C3⋊D15 | Direct product of C2 and C3⋊D15 | 90 | | C2xC3:D15 | 180,36 |
C5×C3.A4 | Direct product of C5 and C3.A4 | 90 | 3 | C5xC3.A4 | 180,8 |
C5×C3⋊Dic3 | Direct product of C5 and C3⋊Dic3 | 180 | | C5xC3:Dic3 | 180,16 |
| | d | ρ | Label | ID |
---|
C192 | Cyclic group | 192 | 1 | C192 | 192,2 |
C82⋊C3 | The semidirect product of C82 and C3 acting faithfully | 24 | 3 | C8^2:C3 | 192,3 |
C26⋊C3 | 3rd semidirect product of C26 and C3 acting faithfully | 24 | | C2^6:C3 | 192,1541 |
C42⋊2A4 | The semidirect product of C42 and A4 acting via A4/C22=C3 | 24 | | C4^2:2A4 | 192,1020 |
C3⋊C64 | The semidirect product of C3 and C64 acting via C64/C32=C2 | 192 | 2 | C3:C64 | 192,1 |
C8×C24 | Abelian group of type [8,24] | 192 | | C8xC24 | 192,127 |
C4×C48 | Abelian group of type [4,48] | 192 | | C4xC48 | 192,151 |
C2×C96 | Abelian group of type [2,96] | 192 | | C2xC96 | 192,175 |
C25×C6 | Abelian group of type [2,2,2,2,2,6] | 192 | | C2^5xC6 | 192,1543 |
C42×C12 | Abelian group of type [4,4,12] | 192 | | C4^2xC12 | 192,807 |
C22×C48 | Abelian group of type [2,2,48] | 192 | | C2^2xC48 | 192,935 |
C23×C24 | Abelian group of type [2,2,2,24] | 192 | | C2^3xC24 | 192,1454 |
C24×C12 | Abelian group of type [2,2,2,2,12] | 192 | | C2^4xC12 | 192,1530 |
C2×C4×C24 | Abelian group of type [2,4,24] | 192 | | C2xC4xC24 | 192,835 |
C22×C4×C12 | Abelian group of type [2,2,4,12] | 192 | | C2^2xC4xC12 | 192,1400 |
A4×C16 | Direct product of C16 and A4 | 48 | 3 | A4xC16 | 192,203 |
A4×C42 | Direct product of C42 and A4 | 48 | | A4xC4^2 | 192,993 |
A4×C24 | Direct product of C24 and A4 | 48 | | A4xC2^4 | 192,1539 |
S3×C32 | Direct product of C32 and S3 | 96 | 2 | S3xC32 | 192,5 |
S3×C25 | Direct product of C25 and S3 | 96 | | S3xC2^5 | 192,1542 |
Dic3×C16 | Direct product of C16 and Dic3 | 192 | | Dic3xC16 | 192,59 |
Dic3×C42 | Direct product of C42 and Dic3 | 192 | | Dic3xC4^2 | 192,489 |
Dic3×C24 | Direct product of C24 and Dic3 | 192 | | Dic3xC2^4 | 192,1528 |
C4×C42⋊C3 | Direct product of C4 and C42⋊C3 | 12 | 3 | C4xC4^2:C3 | 192,188 |
C22×C22⋊A4 | Direct product of C22 and C22⋊A4 | 12 | | C2^2xC2^2:A4 | 192,1540 |
C4×C22⋊A4 | Direct product of C4 and C22⋊A4 | 24 | | C4xC2^2:A4 | 192,1505 |
C22×C42⋊C3 | Direct product of C22 and C42⋊C3 | 24 | | C2^2xC4^2:C3 | 192,992 |
A4×C2×C8 | Direct product of C2×C8 and A4 | 48 | | A4xC2xC8 | 192,1010 |
A4×C22×C4 | Direct product of C22×C4 and A4 | 48 | | A4xC2^2xC4 | 192,1496 |
S3×C4×C8 | Direct product of C4×C8 and S3 | 96 | | S3xC4xC8 | 192,243 |
S3×C2×C16 | Direct product of C2×C16 and S3 | 96 | | S3xC2xC16 | 192,458 |
S3×C2×C42 | Direct product of C2×C42 and S3 | 96 | | S3xC2xC4^2 | 192,1030 |
S3×C22×C8 | Direct product of C22×C8 and S3 | 96 | | S3xC2^2xC8 | 192,1295 |
S3×C23×C4 | Direct product of C23×C4 and S3 | 96 | | S3xC2^3xC4 | 192,1511 |
C8×C3⋊C8 | Direct product of C8 and C3⋊C8 | 192 | | C8xC3:C8 | 192,12 |
C4×C3⋊C16 | Direct product of C4 and C3⋊C16 | 192 | | C4xC3:C16 | 192,19 |
C2×C3⋊C32 | Direct product of C2 and C3⋊C32 | 192 | | C2xC3:C32 | 192,57 |
C23×C3⋊C8 | Direct product of C23 and C3⋊C8 | 192 | | C2^3xC3:C8 | 192,1339 |
Dic3×C2×C8 | Direct product of C2×C8 and Dic3 | 192 | | Dic3xC2xC8 | 192,657 |
C22×C3⋊C16 | Direct product of C22 and C3⋊C16 | 192 | | C2^2xC3:C16 | 192,655 |
Dic3×C22×C4 | Direct product of C22×C4 and Dic3 | 192 | | Dic3xC2^2xC4 | 192,1341 |
C2×C4×C3⋊C8 | Direct product of C2×C4 and C3⋊C8 | 192 | | C2xC4xC3:C8 | 192,479 |
| | d | ρ | Label | ID |
---|
C200 | Cyclic group | 200 | 1 | C200 | 200,2 |
D5⋊F5 | The semidirect product of D5 and F5 acting via F5/D5=C2; = Hol(D5) | 10 | 8+ | D5:F5 | 200,42 |
C52⋊C8 | The semidirect product of C52 and C8 acting faithfully | 10 | 8+ | C5^2:C8 | 200,40 |
Dic5⋊2D5 | The semidirect product of Dic5 and D5 acting through Inn(Dic5) | 20 | 4+ | Dic5:2D5 | 200,23 |
C52⋊3C8 | 2nd semidirect product of C52 and C8 acting via C8/C2=C4 | 40 | 4 | C5^2:3C8 | 200,19 |
C52⋊5C8 | 4th semidirect product of C52 and C8 acting via C8/C2=C4 | 40 | 4- | C5^2:5C8 | 200,21 |
C25⋊C8 | The semidirect product of C25 and C8 acting via C8/C2=C4 | 200 | 4- | C25:C8 | 200,3 |
C25⋊2C8 | The semidirect product of C25 and C8 acting via C8/C4=C2 | 200 | 2 | C25:2C8 | 200,1 |
C52⋊7C8 | 2nd semidirect product of C52 and C8 acting via C8/C4=C2 | 200 | | C5^2:7C8 | 200,16 |
C52⋊4C8 | 3rd semidirect product of C52 and C8 acting via C8/C2=C4 | 200 | | C5^2:4C8 | 200,20 |
C5×C40 | Abelian group of type [5,40] | 200 | | C5xC40 | 200,17 |
C2×C100 | Abelian group of type [2,100] | 200 | | C2xC100 | 200,9 |
C10×C20 | Abelian group of type [10,20] | 200 | | C10xC20 | 200,37 |
C22×C50 | Abelian group of type [2,2,50] | 200 | | C2^2xC50 | 200,14 |
C2×C102 | Abelian group of type [2,10,10] | 200 | | C2xC10^2 | 200,52 |
D5×F5 | Direct product of D5 and F5 | 20 | 8+ | D5xF5 | 200,41 |
D5×C20 | Direct product of C20 and D5 | 40 | 2 | D5xC20 | 200,28 |
C10×F5 | Direct product of C10 and F5 | 40 | 4 | C10xF5 | 200,45 |
D5×Dic5 | Direct product of D5 and Dic5 | 40 | 4- | D5xDic5 | 200,22 |
C10×Dic5 | Direct product of C10 and Dic5 | 40 | | C10xDic5 | 200,30 |
C4×D25 | Direct product of C4 and D25 | 100 | 2 | C4xD25 | 200,5 |
C22×D25 | Direct product of C22 and D25 | 100 | | C2^2xD25 | 200,13 |
C2×Dic25 | Direct product of C2 and Dic25 | 200 | | C2xDic25 | 200,7 |
C2×D52 | Direct product of C2, D5 and D5 | 20 | 4+ | C2xD5^2 | 200,49 |
C2×C52⋊C4 | Direct product of C2 and C52⋊C4 | 20 | 4+ | C2xC5^2:C4 | 200,48 |
C5×C5⋊C8 | Direct product of C5 and C5⋊C8 | 40 | 4 | C5xC5:C8 | 200,18 |
D5×C2×C10 | Direct product of C2×C10 and D5 | 40 | | D5xC2xC10 | 200,50 |
C5×C5⋊2C8 | Direct product of C5 and C5⋊2C8 | 40 | 2 | C5xC5:2C8 | 200,15 |
C2×D5.D5 | Direct product of C2 and D5.D5 | 40 | 4 | C2xD5.D5 | 200,46 |
C2×C25⋊C4 | Direct product of C2 and C25⋊C4 | 50 | 4+ | C2xC25:C4 | 200,12 |
C2×C5⋊F5 | Direct product of C2 and C5⋊F5 | 50 | | C2xC5:F5 | 200,47 |
C4×C5⋊D5 | Direct product of C4 and C5⋊D5 | 100 | | C4xC5:D5 | 200,33 |
C22×C5⋊D5 | Direct product of C22 and C5⋊D5 | 100 | | C2^2xC5:D5 | 200,51 |
C2×C52⋊6C4 | Direct product of C2 and C52⋊6C4 | 200 | | C2xC5^2:6C4 | 200,35 |
| | d | ρ | Label | ID |
---|
C216 | Cyclic group | 216 | 1 | C216 | 216,2 |
C3⋊F9 | The semidirect product of C3 and F9 acting via F9/C32⋊C4=C2 | 24 | 8 | C3:F9 | 216,155 |
C33⋊4C8 | 2nd semidirect product of C33 and C8 acting via C8/C2=C4 | 24 | 4 | C3^3:4C8 | 216,118 |
C27⋊C8 | The semidirect product of C27 and C8 acting via C8/C4=C2 | 216 | 2 | C27:C8 | 216,1 |
C33⋊7C8 | 3rd semidirect product of C33 and C8 acting via C8/C4=C2 | 216 | | C3^3:7C8 | 216,84 |
C33⋊9(C2×C4) | 6th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C22 | 24 | 4 | C3^3:9(C2xC4) | 216,131 |
C33⋊8(C2×C4) | 5th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C22 | 36 | | C3^3:8(C2xC4) | 216,126 |
C18.D6 | 3rd non-split extension by C18 of D6 acting via D6/S3=C2 | 36 | 4+ | C18.D6 | 216,28 |
C36.S3 | 6th non-split extension by C36 of S3 acting via S3/C3=C2 | 216 | | C36.S3 | 216,16 |
C63 | Abelian group of type [6,6,6] | 216 | | C6^3 | 216,177 |
C3×C72 | Abelian group of type [3,72] | 216 | | C3xC72 | 216,18 |
C6×C36 | Abelian group of type [6,36] | 216 | | C6xC36 | 216,73 |
C2×C108 | Abelian group of type [2,108] | 216 | | C2xC108 | 216,9 |
C22×C54 | Abelian group of type [2,2,54] | 216 | | C2^2xC54 | 216,24 |
C32×C24 | Abelian group of type [3,3,24] | 216 | | C3^2xC24 | 216,85 |
C2×C6×C18 | Abelian group of type [2,6,18] | 216 | | C2xC6xC18 | 216,114 |
C3×C6×C12 | Abelian group of type [3,6,12] | 216 | | C3xC6xC12 | 216,150 |
C3×F9 | Direct product of C3 and F9 | 24 | 8 | C3xF9 | 216,154 |
A4×D9 | Direct product of A4 and D9 | 36 | 6+ | A4xD9 | 216,97 |
A4×C18 | Direct product of C18 and A4 | 54 | 3 | A4xC18 | 216,103 |
S3×C36 | Direct product of C36 and S3 | 72 | 2 | S3xC36 | 216,47 |
C12×D9 | Direct product of C12 and D9 | 72 | 2 | C12xD9 | 216,45 |
S3×C62 | Direct product of C62 and S3 | 72 | | S3xC6^2 | 216,174 |
Dic3×D9 | Direct product of Dic3 and D9 | 72 | 4- | Dic3xD9 | 216,27 |
S3×Dic9 | Direct product of S3 and Dic9 | 72 | 4- | S3xDic9 | 216,30 |
C6×Dic9 | Direct product of C6 and Dic9 | 72 | | C6xDic9 | 216,55 |
Dic3×C18 | Direct product of C18 and Dic3 | 72 | | Dic3xC18 | 216,56 |
C4×D27 | Direct product of C4 and D27 | 108 | 2 | C4xD27 | 216,5 |
C22×D27 | Direct product of C22 and D27 | 108 | | C2^2xD27 | 216,23 |
C2×Dic27 | Direct product of C2 and Dic27 | 216 | | C2xDic27 | 216,7 |
S33 | Direct product of S3, S3 and S3; = Hol(C3×S3) | 12 | 8+ | S3^3 | 216,162 |
S3×C32⋊C4 | Direct product of S3 and C32⋊C4 | 12 | 8+ | S3xC3^2:C4 | 216,156 |
S32×C6 | Direct product of C6, S3 and S3 | 24 | 4 | S3^2xC6 | 216,170 |
C3×S3×A4 | Direct product of C3, S3 and A4 | 24 | 6 | C3xS3xA4 | 216,166 |
C6×C32⋊C4 | Direct product of C6 and C32⋊C4 | 24 | 4 | C6xC3^2:C4 | 216,168 |
C3×S3×Dic3 | Direct product of C3, S3 and Dic3 | 24 | 4 | C3xS3xDic3 | 216,119 |
C2×C33⋊C4 | Direct product of C2 and C33⋊C4 | 24 | 4 | C2xC3^3:C4 | 216,169 |
C3×C6.D6 | Direct product of C3 and C6.D6 | 24 | 4 | C3xC6.D6 | 216,120 |
C3×C32⋊2C8 | Direct product of C3 and C32⋊2C8 | 24 | 4 | C3xC3^2:2C8 | 216,117 |
C2×C32⋊4D6 | Direct product of C2 and C32⋊4D6 | 24 | 4 | C2xC3^2:4D6 | 216,172 |
C2×S3×D9 | Direct product of C2, S3 and D9 | 36 | 4+ | C2xS3xD9 | 216,101 |
A4×C3⋊S3 | Direct product of A4 and C3⋊S3 | 36 | | A4xC3:S3 | 216,167 |
S3×C3.A4 | Direct product of S3 and C3.A4 | 36 | 6 | S3xC3.A4 | 216,98 |
A4×C3×C6 | Direct product of C3×C6 and A4 | 54 | | A4xC3xC6 | 216,173 |
C2×C9.A4 | Direct product of C2 and C9.A4 | 54 | 3 | C2xC9.A4 | 216,22 |
C6×C3.A4 | Direct product of C6 and C3.A4 | 54 | | C6xC3.A4 | 216,105 |
C3×C9⋊C8 | Direct product of C3 and C9⋊C8 | 72 | 2 | C3xC9:C8 | 216,12 |
C9×C3⋊C8 | Direct product of C9 and C3⋊C8 | 72 | 2 | C9xC3:C8 | 216,13 |
C2×C6×D9 | Direct product of C2×C6 and D9 | 72 | | C2xC6xD9 | 216,108 |
S3×C2×C18 | Direct product of C2×C18 and S3 | 72 | | S3xC2xC18 | 216,109 |
S3×C3×C12 | Direct product of C3×C12 and S3 | 72 | | S3xC3xC12 | 216,136 |
C12×C3⋊S3 | Direct product of C12 and C3⋊S3 | 72 | | C12xC3:S3 | 216,141 |
C32×C3⋊C8 | Direct product of C32 and C3⋊C8 | 72 | | C3^2xC3:C8 | 216,82 |
Dic3×C3×C6 | Direct product of C3×C6 and Dic3 | 72 | | Dic3xC3xC6 | 216,138 |
S3×C3⋊Dic3 | Direct product of S3 and C3⋊Dic3 | 72 | | S3xC3:Dic3 | 216,124 |
Dic3×C3⋊S3 | Direct product of Dic3 and C3⋊S3 | 72 | | Dic3xC3:S3 | 216,125 |
C6×C3⋊Dic3 | Direct product of C6 and C3⋊Dic3 | 72 | | C6xC3:Dic3 | 216,143 |
C3×C32⋊4C8 | Direct product of C3 and C32⋊4C8 | 72 | | C3xC3^2:4C8 | 216,83 |
C4×C9⋊S3 | Direct product of C4 and C9⋊S3 | 108 | | C4xC9:S3 | 216,64 |
C22×C9⋊S3 | Direct product of C22 and C9⋊S3 | 108 | | C2^2xC9:S3 | 216,112 |
C4×C33⋊C2 | Direct product of C4 and C33⋊C2 | 108 | | C4xC3^3:C2 | 216,146 |
C22×C33⋊C2 | Direct product of C22 and C33⋊C2 | 108 | | C2^2xC3^3:C2 | 216,176 |
C2×C9⋊Dic3 | Direct product of C2 and C9⋊Dic3 | 216 | | C2xC9:Dic3 | 216,69 |
C2×C33⋊5C4 | Direct product of C2 and C33⋊5C4 | 216 | | C2xC3^3:5C4 | 216,148 |
C2×S3×C3⋊S3 | Direct product of C2, S3 and C3⋊S3 | 36 | | C2xS3xC3:S3 | 216,171 |
C2×C6×C3⋊S3 | Direct product of C2×C6 and C3⋊S3 | 72 | | C2xC6xC3:S3 | 216,175 |
| | d | ρ | Label | ID |
---|
C224 | Cyclic group | 224 | 1 | C224 | 224,2 |
C7⋊C32 | The semidirect product of C7 and C32 acting via C32/C16=C2 | 224 | 2 | C7:C32 | 224,1 |
C4×C56 | Abelian group of type [4,56] | 224 | | C4xC56 | 224,45 |
C2×C112 | Abelian group of type [2,112] | 224 | | C2xC112 | 224,58 |
C22×C56 | Abelian group of type [2,2,56] | 224 | | C2^2xC56 | 224,164 |
C23×C28 | Abelian group of type [2,2,2,28] | 224 | | C2^3xC28 | 224,189 |
C24×C14 | Abelian group of type [2,2,2,2,14] | 224 | | C2^4xC14 | 224,197 |
C2×C4×C28 | Abelian group of type [2,4,28] | 224 | | C2xC4xC28 | 224,149 |
C4×F8 | Direct product of C4 and F8 | 28 | 7 | C4xF8 | 224,173 |
C22×F8 | Direct product of C22 and F8 | 28 | | C2^2xF8 | 224,195 |
D7×C16 | Direct product of C16 and D7 | 112 | 2 | D7xC16 | 224,3 |
D7×C42 | Direct product of C42 and D7 | 112 | | D7xC4^2 | 224,66 |
D7×C24 | Direct product of C24 and D7 | 112 | | D7xC2^4 | 224,196 |
C8×Dic7 | Direct product of C8 and Dic7 | 224 | | C8xDic7 | 224,19 |
C23×Dic7 | Direct product of C23 and Dic7 | 224 | | C2^3xDic7 | 224,187 |
D7×C2×C8 | Direct product of C2×C8 and D7 | 112 | | D7xC2xC8 | 224,94 |
D7×C22×C4 | Direct product of C22×C4 and D7 | 112 | | D7xC2^2xC4 | 224,175 |
C4×C7⋊C8 | Direct product of C4 and C7⋊C8 | 224 | | C4xC7:C8 | 224,8 |
C2×C7⋊C16 | Direct product of C2 and C7⋊C16 | 224 | | C2xC7:C16 | 224,17 |
C22×C7⋊C8 | Direct product of C22 and C7⋊C8 | 224 | | C2^2xC7:C8 | 224,115 |
C2×C4×Dic7 | Direct product of C2×C4 and Dic7 | 224 | | C2xC4xDic7 | 224,117 |
| | d | ρ | Label | ID |
---|
C240 | Cyclic group | 240 | 1 | C240 | 240,4 |
F16 | Frobenius group; = C24⋊C15 = AGL1(𝔽16) | 16 | 15+ | F16 | 240,191 |
D15⋊C8 | The semidirect product of D15 and C8 acting via C8/C2=C4 | 120 | 8+ | D15:C8 | 240,99 |
D15⋊2C8 | The semidirect product of D15 and C8 acting via C8/C4=C2 | 120 | 4 | D15:2C8 | 240,9 |
C15⋊3C16 | 1st semidirect product of C15 and C16 acting via C16/C8=C2 | 240 | 2 | C15:3C16 | 240,3 |
C15⋊C16 | 1st semidirect product of C15 and C16 acting via C16/C4=C4 | 240 | 4 | C15:C16 | 240,6 |
C60.C4 | 3rd non-split extension by C60 of C4 acting faithfully | 120 | 4 | C60.C4 | 240,118 |
C4×C60 | Abelian group of type [4,60] | 240 | | C4xC60 | 240,81 |
C2×C120 | Abelian group of type [2,120] | 240 | | C2xC120 | 240,84 |
C22×C60 | Abelian group of type [2,2,60] | 240 | | C2^2xC60 | 240,185 |
C23×C30 | Abelian group of type [2,2,2,30] | 240 | | C2^3xC30 | 240,208 |
C4×A5 | Direct product of C4 and A5 | 20 | 3 | C4xA5 | 240,92 |
A4×F5 | Direct product of A4 and F5 | 20 | 12+ | A4xF5 | 240,193 |
C22×A5 | Direct product of C22 and A5 | 20 | | C2^2xA5 | 240,190 |
A4×C20 | Direct product of C20 and A4 | 60 | 3 | A4xC20 | 240,152 |
C12×F5 | Direct product of C12 and F5 | 60 | 4 | C12xF5 | 240,113 |
Dic3×F5 | Direct product of Dic3 and F5 | 60 | 8- | Dic3xF5 | 240,95 |
A4×Dic5 | Direct product of A4 and Dic5 | 60 | 6- | A4xDic5 | 240,110 |
S3×C40 | Direct product of C40 and S3 | 120 | 2 | S3xC40 | 240,49 |
D5×C24 | Direct product of C24 and D5 | 120 | 2 | D5xC24 | 240,33 |
C8×D15 | Direct product of C8 and D15 | 120 | 2 | C8xD15 | 240,65 |
C23×D15 | Direct product of C23 and D15 | 120 | | C2^3xD15 | 240,207 |
C12×Dic5 | Direct product of C12 and Dic5 | 240 | | C12xDic5 | 240,40 |
Dic3×C20 | Direct product of C20 and Dic3 | 240 | | Dic3xC20 | 240,56 |
C4×Dic15 | Direct product of C4 and Dic15 | 240 | | C4xDic15 | 240,72 |
Dic3×Dic5 | Direct product of Dic3 and Dic5 | 240 | | Dic3xDic5 | 240,25 |
C22×Dic15 | Direct product of C22 and Dic15 | 240 | | C2^2xDic15 | 240,183 |
C2×D5×A4 | Direct product of C2, D5 and A4 | 30 | 6+ | C2xD5xA4 | 240,198 |
C2×S3×F5 | Direct product of C2, S3 and F5; = Aut(D30) = Hol(C30) | 30 | 8+ | C2xS3xF5 | 240,195 |
C3×C24⋊C5 | Direct product of C3 and C24⋊C5 | 30 | 5 | C3xC2^4:C5 | 240,199 |
C4×S3×D5 | Direct product of C4, S3 and D5 | 60 | 4 | C4xS3xD5 | 240,135 |
C4×C3⋊F5 | Direct product of C4 and C3⋊F5 | 60 | 4 | C4xC3:F5 | 240,120 |
C2×C6×F5 | Direct product of C2×C6 and F5 | 60 | | C2xC6xF5 | 240,200 |
A4×C2×C10 | Direct product of C2×C10 and A4 | 60 | | A4xC2xC10 | 240,203 |
C5×C42⋊C3 | Direct product of C5 and C42⋊C3 | 60 | 3 | C5xC4^2:C3 | 240,32 |
C22×S3×D5 | Direct product of C22, S3 and D5 | 60 | | C2^2xS3xD5 | 240,202 |
C22×C3⋊F5 | Direct product of C22 and C3⋊F5 | 60 | | C2^2xC3:F5 | 240,201 |
C5×C22⋊A4 | Direct product of C5 and C22⋊A4 | 60 | | C5xC2^2:A4 | 240,204 |
S3×C5⋊C8 | Direct product of S3 and C5⋊C8 | 120 | 8- | S3xC5:C8 | 240,98 |
D5×C3⋊C8 | Direct product of D5 and C3⋊C8 | 120 | 4 | D5xC3:C8 | 240,7 |
S3×C2×C20 | Direct product of C2×C20 and S3 | 120 | | S3xC2xC20 | 240,166 |
D5×C2×C12 | Direct product of C2×C12 and D5 | 120 | | D5xC2xC12 | 240,156 |
C2×C4×D15 | Direct product of C2×C4 and D15 | 120 | | C2xC4xD15 | 240,176 |
S3×C5⋊2C8 | Direct product of S3 and C5⋊2C8 | 120 | 4 | S3xC5:2C8 | 240,8 |
C3×D5⋊C8 | Direct product of C3 and D5⋊C8 | 120 | 4 | C3xD5:C8 | 240,111 |
C2×D5×Dic3 | Direct product of C2, D5 and Dic3 | 120 | | C2xD5xDic3 | 240,139 |
C2×S3×Dic5 | Direct product of C2, S3 and Dic5 | 120 | | C2xS3xDic5 | 240,142 |
D5×C22×C6 | Direct product of C22×C6 and D5 | 120 | | D5xC2^2xC6 | 240,205 |
S3×C22×C10 | Direct product of C22×C10 and S3 | 120 | | S3xC2^2xC10 | 240,206 |
C2×D30.C2 | Direct product of C2 and D30.C2 | 120 | | C2xD30.C2 | 240,144 |
C6×C5⋊C8 | Direct product of C6 and C5⋊C8 | 240 | | C6xC5:C8 | 240,115 |
C5×C3⋊C16 | Direct product of C5 and C3⋊C16 | 240 | 2 | C5xC3:C16 | 240,1 |
C3×C5⋊C16 | Direct product of C3 and C5⋊C16 | 240 | 4 | C3xC5:C16 | 240,5 |
C10×C3⋊C8 | Direct product of C10 and C3⋊C8 | 240 | | C10xC3:C8 | 240,54 |
C6×C5⋊2C8 | Direct product of C6 and C5⋊2C8 | 240 | | C6xC5:2C8 | 240,38 |
C2×C15⋊C8 | Direct product of C2 and C15⋊C8 | 240 | | C2xC15:C8 | 240,122 |
C2×C6×Dic5 | Direct product of C2×C6 and Dic5 | 240 | | C2xC6xDic5 | 240,163 |
C3×C5⋊2C16 | Direct product of C3 and C5⋊2C16 | 240 | 2 | C3xC5:2C16 | 240,2 |
C2×C15⋊3C8 | Direct product of C2 and C15⋊3C8 | 240 | | C2xC15:3C8 | 240,70 |
Dic3×C2×C10 | Direct product of C2×C10 and Dic3 | 240 | | Dic3xC2xC10 | 240,173 |
| | d | ρ | Label | ID |
---|
C252 | Cyclic group | 252 | 1 | C252 | 252,6 |
D126 | Dihedral group; = C2×D63 | 126 | 2+ | D126 | 252,14 |
Dic63 | Dicyclic group; = C9⋊Dic7 | 252 | 2- | Dic63 | 252,5 |
D21⋊S3 | The semidirect product of D21 and S3 acting via S3/C3=C2 | 42 | 4 | D21:S3 | 252,37 |
C32⋊Dic7 | The semidirect product of C32 and Dic7 acting via Dic7/C7=C4 | 42 | 4 | C3^2:Dic7 | 252,32 |
C7⋊C36 | The semidirect product of C7 and C36 acting via C36/C6=C6 | 252 | 6 | C7:C36 | 252,1 |
C3⋊Dic21 | The semidirect product of C3 and Dic21 acting via Dic21/C42=C2 | 252 | | C3:Dic21 | 252,24 |
C6.F7 | The non-split extension by C6 of F7 acting via F7/C7⋊C3=C2 | 84 | 6- | C6.F7 | 252,18 |
C21.A4 | The non-split extension by C21 of A4 acting via A4/C22=C3 | 126 | 3 | C21.A4 | 252,11 |
C3×C84 | Abelian group of type [3,84] | 252 | | C3xC84 | 252,25 |
C6×C42 | Abelian group of type [6,42] | 252 | | C6xC42 | 252,46 |
C2×C126 | Abelian group of type [2,126] | 252 | | C2xC126 | 252,15 |
S3×F7 | Direct product of S3 and F7; = Aut(D21) = Hol(C21) | 21 | 12+ | S3xF7 | 252,26 |
C6×F7 | Direct product of C6 and F7 | 42 | 6 | C6xF7 | 252,28 |
S3×D21 | Direct product of S3 and D21 | 42 | 4+ | S3xD21 | 252,36 |
D7×D9 | Direct product of D7 and D9 | 63 | 4+ | D7xD9 | 252,8 |
S3×C42 | Direct product of C42 and S3 | 84 | 2 | S3xC42 | 252,42 |
A4×C21 | Direct product of C21 and A4 | 84 | 3 | A4xC21 | 252,39 |
C6×D21 | Direct product of C6 and D21 | 84 | 2 | C6xD21 | 252,43 |
Dic3×C21 | Direct product of C21 and Dic3 | 84 | 2 | Dic3xC21 | 252,21 |
C3×Dic21 | Direct product of C3 and Dic21 | 84 | 2 | C3xDic21 | 252,22 |
D7×C18 | Direct product of C18 and D7 | 126 | 2 | D7xC18 | 252,12 |
C14×D9 | Direct product of C14 and D9 | 126 | 2 | C14xD9 | 252,13 |
C7×Dic9 | Direct product of C7 and Dic9 | 252 | 2 | C7xDic9 | 252,3 |
C9×Dic7 | Direct product of C9 and Dic7 | 252 | 2 | C9xDic7 | 252,4 |
C32×Dic7 | Direct product of C32 and Dic7 | 252 | | C3^2xDic7 | 252,20 |
A4×C7⋊C3 | Direct product of A4 and C7⋊C3 | 28 | 9 | A4xC7:C3 | 252,27 |
S32×C7 | Direct product of C7, S3 and S3 | 42 | 4 | S3^2xC7 | 252,35 |
C3×S3×D7 | Direct product of C3, S3 and D7 | 42 | 4 | C3xS3xD7 | 252,33 |
C2×C3⋊F7 | Direct product of C2 and C3⋊F7 | 42 | 6+ | C2xC3:F7 | 252,30 |
C7×C32⋊C4 | Direct product of C7 and C32⋊C4 | 42 | 4 | C7xC3^2:C4 | 252,31 |
D7×C3⋊S3 | Direct product of D7 and C3⋊S3 | 63 | | D7xC3:S3 | 252,34 |
C3×C7⋊A4 | Direct product of C3 and C7⋊A4 | 84 | 3 | C3xC7:A4 | 252,40 |
C3×C7⋊C12 | Direct product of C3 and C7⋊C12 | 84 | 6 | C3xC7:C12 | 252,16 |
C12×C7⋊C3 | Direct product of C12 and C7⋊C3 | 84 | 3 | C12xC7:C3 | 252,19 |
Dic3×C7⋊C3 | Direct product of Dic3 and C7⋊C3 | 84 | 6 | Dic3xC7:C3 | 252,17 |
D7×C3×C6 | Direct product of C3×C6 and D7 | 126 | | D7xC3xC6 | 252,41 |
C2×C7⋊C18 | Direct product of C2 and C7⋊C18 | 126 | 6 | C2xC7:C18 | 252,7 |
C14×C3⋊S3 | Direct product of C14 and C3⋊S3 | 126 | | C14xC3:S3 | 252,44 |
C2×C3⋊D21 | Direct product of C2 and C3⋊D21 | 126 | | C2xC3:D21 | 252,45 |
C7×C3.A4 | Direct product of C7 and C3.A4 | 126 | 3 | C7xC3.A4 | 252,10 |
C4×C7⋊C9 | Direct product of C4 and C7⋊C9 | 252 | 3 | C4xC7:C9 | 252,2 |
C22×C7⋊C9 | Direct product of C22 and C7⋊C9 | 252 | | C2^2xC7:C9 | 252,9 |
C7×C3⋊Dic3 | Direct product of C7 and C3⋊Dic3 | 252 | | C7xC3:Dic3 | 252,23 |
C2×S3×C7⋊C3 | Direct product of C2, S3 and C7⋊C3 | 42 | 6 | C2xS3xC7:C3 | 252,29 |
C2×C6×C7⋊C3 | Direct product of C2×C6 and C7⋊C3 | 84 | | C2xC6xC7:C3 | 252,38 |
| | d | ρ | Label | ID |
---|
C272 | Cyclic group | 272 | 1 | C272 | 272,2 |
F17 | Frobenius group; = C17⋊C16 = AGL1(𝔽17) = Aut(D17) = Hol(C17) | 17 | 16+ | F17 | 272,50 |
C17⋊4C16 | The semidirect product of C17 and C16 acting via C16/C8=C2 | 272 | 2 | C17:4C16 | 272,1 |
C17⋊3C16 | The semidirect product of C17 and C16 acting via C16/C4=C4 | 272 | 4 | C17:3C16 | 272,3 |
C68.C4 | 3rd non-split extension by C68 of C4 acting faithfully | 136 | 4 | C68.C4 | 272,29 |
C34.C8 | The non-split extension by C34 of C8 acting faithfully | 272 | 8- | C34.C8 | 272,28 |
C4×C68 | Abelian group of type [4,68] | 272 | | C4xC68 | 272,20 |
C2×C136 | Abelian group of type [2,136] | 272 | | C2xC136 | 272,23 |
C22×C68 | Abelian group of type [2,2,68] | 272 | | C2^2xC68 | 272,46 |
C23×C34 | Abelian group of type [2,2,2,34] | 272 | | C2^3xC34 | 272,54 |
C8×D17 | Direct product of C8 and D17 | 136 | 2 | C8xD17 | 272,4 |
C23×D17 | Direct product of C23 and D17 | 136 | | C2^3xD17 | 272,53 |
C4×Dic17 | Direct product of C4 and Dic17 | 272 | | C4xDic17 | 272,11 |
C22×Dic17 | Direct product of C22 and Dic17 | 272 | | C2^2xDic17 | 272,44 |
C2×C17⋊C8 | Direct product of C2 and C17⋊C8 | 34 | 8+ | C2xC17:C8 | 272,51 |
C4×C17⋊C4 | Direct product of C4 and C17⋊C4 | 68 | 4 | C4xC17:C4 | 272,31 |
C22×C17⋊C4 | Direct product of C22 and C17⋊C4 | 68 | | C2^2xC17:C4 | 272,52 |
C2×C4×D17 | Direct product of C2×C4 and D17 | 136 | | C2xC4xD17 | 272,37 |
C2×C17⋊3C8 | Direct product of C2 and C17⋊3C8 | 272 | | C2xC17:3C8 | 272,9 |
C2×C17⋊2C8 | Direct product of C2 and C17⋊2C8 | 272 | | C2xC17:2C8 | 272,33 |
| | d | ρ | Label | ID |
---|
C280 | Cyclic group | 280 | 1 | C280 | 280,4 |
C35⋊3C8 | 1st semidirect product of C35 and C8 acting via C8/C4=C2 | 280 | 2 | C35:3C8 | 280,3 |
C35⋊C8 | 1st semidirect product of C35 and C8 acting via C8/C2=C4 | 280 | 4 | C35:C8 | 280,6 |
D70.C2 | The non-split extension by D70 of C2 acting faithfully | 140 | 4+ | D70.C2 | 280,9 |
C2×C140 | Abelian group of type [2,140] | 280 | | C2xC140 | 280,29 |
C22×C70 | Abelian group of type [2,2,70] | 280 | | C2^2xC70 | 280,40 |
D7×F5 | Direct product of D7 and F5 | 35 | 8+ | D7xF5 | 280,32 |
C5×F8 | Direct product of C5 and F8 | 40 | 7 | C5xF8 | 280,33 |
C14×F5 | Direct product of C14 and F5 | 70 | 4 | C14xF5 | 280,34 |
D7×C20 | Direct product of C20 and D7 | 140 | 2 | D7xC20 | 280,15 |
D5×C28 | Direct product of C28 and D5 | 140 | 2 | D5xC28 | 280,20 |
C4×D35 | Direct product of C4 and D35 | 140 | 2 | C4xD35 | 280,25 |
D7×Dic5 | Direct product of D7 and Dic5 | 140 | 4- | D7xDic5 | 280,7 |
D5×Dic7 | Direct product of D5 and Dic7 | 140 | 4- | D5xDic7 | 280,8 |
C22×D35 | Direct product of C22 and D35 | 140 | | C2^2xD35 | 280,39 |
C10×Dic7 | Direct product of C10 and Dic7 | 280 | | C10xDic7 | 280,17 |
C14×Dic5 | Direct product of C14 and Dic5 | 280 | | C14xDic5 | 280,22 |
C2×Dic35 | Direct product of C2 and Dic35 | 280 | | C2xDic35 | 280,27 |
C2×D5×D7 | Direct product of C2, D5 and D7 | 70 | 4+ | C2xD5xD7 | 280,36 |
C2×C7⋊F5 | Direct product of C2 and C7⋊F5 | 70 | 4 | C2xC7:F5 | 280,35 |
D7×C2×C10 | Direct product of C2×C10 and D7 | 140 | | D7xC2xC10 | 280,37 |
D5×C2×C14 | Direct product of C2×C14 and D5 | 140 | | D5xC2xC14 | 280,38 |
C5×C7⋊C8 | Direct product of C5 and C7⋊C8 | 280 | 2 | C5xC7:C8 | 280,2 |
C7×C5⋊C8 | Direct product of C7 and C5⋊C8 | 280 | 4 | C7xC5:C8 | 280,5 |
C7×C5⋊2C8 | Direct product of C7 and C5⋊2C8 | 280 | 2 | C7xC5:2C8 | 280,1 |
| | d | ρ | Label | ID |
---|
C288 | Cyclic group | 288 | 1 | C288 | 288,2 |
C32⋊C32 | The semidirect product of C32 and C32 acting via C32/C4=C8 | 96 | 8 | C3^2:C32 | 288,373 |
C32⋊2C32 | The semidirect product of C32 and C32 acting via C32/C8=C4 | 96 | 4 | C3^2:2C32 | 288,188 |
C9⋊C32 | The semidirect product of C9 and C32 acting via C32/C16=C2 | 288 | 2 | C9:C32 | 288,1 |
C3⋊S3⋊3C16 | 2nd semidirect product of C3⋊S3 and C16 acting via C16/C8=C2 | 48 | 4 | C3:S3:3C16 | 288,412 |
C4.3F9 | 2nd central extension by C4 of F9 | 48 | 8 | C4.3F9 | 288,861 |
C24.60D6 | 13rd non-split extension by C24 of D6 acting via D6/S3=C2 | 48 | 4 | C24.60D6 | 288,190 |
C48.S3 | 9th non-split extension by C48 of S3 acting via S3/C3=C2 | 288 | | C48.S3 | 288,65 |
C6.(S3×C8) | 3rd non-split extension by C6 of S3×C8 acting via S3×C8/C3⋊C8=C2 | 96 | | C6.(S3xC8) | 288,201 |
C4×C72 | Abelian group of type [4,72] | 288 | | C4xC72 | 288,46 |
C3×C96 | Abelian group of type [3,96] | 288 | | C3xC96 | 288,66 |
C6×C48 | Abelian group of type [6,48] | 288 | | C6xC48 | 288,327 |
C2×C144 | Abelian group of type [2,144] | 288 | | C2xC144 | 288,59 |
C12×C24 | Abelian group of type [12,24] | 288 | | C12xC24 | 288,314 |
C22×C72 | Abelian group of type [2,2,72] | 288 | | C2^2xC72 | 288,179 |
C23×C36 | Abelian group of type [2,2,2,36] | 288 | | C2^3xC36 | 288,367 |
C2×C122 | Abelian group of type [2,12,12] | 288 | | C2xC12^2 | 288,811 |
C24×C18 | Abelian group of type [2,2,2,2,18] | 288 | | C2^4xC18 | 288,840 |
C23×C62 | Abelian group of type [2,2,2,6,6] | 288 | | C2^3xC6^2 | 288,1045 |
C2×C4×C36 | Abelian group of type [2,4,36] | 288 | | C2xC4xC36 | 288,164 |
C2×C6×C24 | Abelian group of type [2,6,24] | 288 | | C2xC6xC24 | 288,826 |
C22×C6×C12 | Abelian group of type [2,2,6,12] | 288 | | C2^2xC6xC12 | 288,1018 |
C4×F9 | Direct product of C4 and F9 | 36 | 8 | C4xF9 | 288,863 |
C22×F9 | Direct product of C22 and F9 | 36 | | C2^2xF9 | 288,1030 |
A4×C24 | Direct product of C24 and A4 | 72 | 3 | A4xC24 | 288,637 |
S3×C48 | Direct product of C48 and S3 | 96 | 2 | S3xC48 | 288,231 |
Dic3×C24 | Direct product of C24 and Dic3 | 96 | | Dic3xC24 | 288,247 |
C16×D9 | Direct product of C16 and D9 | 144 | 2 | C16xD9 | 288,4 |
C42×D9 | Direct product of C42 and D9 | 144 | | C4^2xD9 | 288,81 |
C24×D9 | Direct product of C24 and D9 | 144 | | C2^4xD9 | 288,839 |
C8×Dic9 | Direct product of C8 and Dic9 | 288 | | C8xDic9 | 288,21 |
C23×Dic9 | Direct product of C23 and Dic9 | 288 | | C2^3xDic9 | 288,365 |
C2×A42 | Direct product of C2, A4 and A4 | 18 | 9+ | C2xA4^2 | 288,1029 |
C4×S3×A4 | Direct product of C4, S3 and A4 | 36 | 6 | C4xS3xA4 | 288,919 |
C2×C42⋊C9 | Direct product of C2 and C42⋊C9 | 36 | 3 | C2xC4^2:C9 | 288,71 |
S3×C42⋊C3 | Direct product of S3 and C42⋊C3 | 36 | 6 | S3xC4^2:C3 | 288,407 |
C6×C42⋊C3 | Direct product of C6 and C42⋊C3 | 36 | 3 | C6xC4^2:C3 | 288,632 |
C22×S3×A4 | Direct product of C22, S3 and A4 | 36 | | C2^2xS3xA4 | 288,1037 |
S3×C22⋊A4 | Direct product of S3 and C22⋊A4 | 36 | | S3xC2^2:A4 | 288,1038 |
C6×C22⋊A4 | Direct product of C6 and C22⋊A4 | 36 | | C6xC2^2:A4 | 288,1042 |
C2×C24⋊C9 | Direct product of C2 and C24⋊C9 | 36 | | C2xC2^4:C9 | 288,838 |
S32×C8 | Direct product of C8, S3 and S3 | 48 | 4 | S3^2xC8 | 288,437 |
S32×C23 | Direct product of C23, S3 and S3 | 48 | | S3^2xC2^3 | 288,1040 |
C8×C32⋊C4 | Direct product of C8 and C32⋊C4 | 48 | 4 | C8xC3^2:C4 | 288,414 |
C4×C6.D6 | Direct product of C4 and C6.D6 | 48 | | C4xC6.D6 | 288,530 |
C23×C32⋊C4 | Direct product of C23 and C32⋊C4 | 48 | | C2^3xC3^2:C4 | 288,1039 |
C22×C6.D6 | Direct product of C22 and C6.D6 | 48 | | C2^2xC6.D6 | 288,972 |
C2×C12.29D6 | Direct product of C2 and C12.29D6 | 48 | | C2xC12.29D6 | 288,464 |
A4×C3⋊C8 | Direct product of A4 and C3⋊C8 | 72 | 6 | A4xC3:C8 | 288,408 |
A4×C2×C12 | Direct product of C2×C12 and A4 | 72 | | A4xC2xC12 | 288,979 |
C8×C3.A4 | Direct product of C8 and C3.A4 | 72 | 3 | C8xC3.A4 | 288,76 |
A4×C22×C6 | Direct product of C22×C6 and A4 | 72 | | A4xC2^2xC6 | 288,1041 |
C2×Dic3×A4 | Direct product of C2, Dic3 and A4 | 72 | | C2xDic3xA4 | 288,927 |
C23×C3.A4 | Direct product of C23 and C3.A4 | 72 | | C2^3xC3.A4 | 288,837 |
C3×C3⋊C32 | Direct product of C3 and C3⋊C32 | 96 | 2 | C3xC3:C32 | 288,64 |
C12×C3⋊C8 | Direct product of C12 and C3⋊C8 | 96 | | C12xC3:C8 | 288,236 |
C6×C3⋊C16 | Direct product of C6 and C3⋊C16 | 96 | | C6xC3:C16 | 288,245 |
S3×C3⋊C16 | Direct product of S3 and C3⋊C16 | 96 | 4 | S3xC3:C16 | 288,189 |
S3×C4×C12 | Direct product of C4×C12 and S3 | 96 | | S3xC4xC12 | 288,642 |
S3×C2×C24 | Direct product of C2×C24 and S3 | 96 | | S3xC2xC24 | 288,670 |
C2×Dic32 | Direct product of C2, Dic3 and Dic3 | 96 | | C2xDic3^2 | 288,602 |
S3×C23×C6 | Direct product of C23×C6 and S3 | 96 | | S3xC2^3xC6 | 288,1043 |
Dic3×C3⋊C8 | Direct product of Dic3 and C3⋊C8 | 96 | | Dic3xC3:C8 | 288,200 |
C4×S3×Dic3 | Direct product of C4, S3 and Dic3 | 96 | | C4xS3xDic3 | 288,523 |
C2×C2.F9 | Direct product of C2 and C2.F9 | 96 | | C2xC2.F9 | 288,865 |
S3×C22×C12 | Direct product of C22×C12 and S3 | 96 | | S3xC2^2xC12 | 288,989 |
Dic3×C2×C12 | Direct product of C2×C12 and Dic3 | 96 | | Dic3xC2xC12 | 288,693 |
C4×C32⋊2C8 | Direct product of C4 and C32⋊2C8 | 96 | | C4xC3^2:2C8 | 288,423 |
C22×S3×Dic3 | Direct product of C22, S3 and Dic3 | 96 | | C2^2xS3xDic3 | 288,969 |
Dic3×C22×C6 | Direct product of C22×C6 and Dic3 | 96 | | Dic3xC2^2xC6 | 288,1001 |
C2×C32⋊2C16 | Direct product of C2 and C32⋊2C16 | 96 | | C2xC3^2:2C16 | 288,420 |
C22×C32⋊2C8 | Direct product of C22 and C32⋊2C8 | 96 | | C2^2xC3^2:2C8 | 288,939 |
C2×C8×D9 | Direct product of C2×C8 and D9 | 144 | | C2xC8xD9 | 288,110 |
C16×C3⋊S3 | Direct product of C16 and C3⋊S3 | 144 | | C16xC3:S3 | 288,272 |
C22×C4×D9 | Direct product of C22×C4 and D9 | 144 | | C2^2xC4xD9 | 288,353 |
C42×C3⋊S3 | Direct product of C42 and C3⋊S3 | 144 | | C4^2xC3:S3 | 288,728 |
C24×C3⋊S3 | Direct product of C24 and C3⋊S3 | 144 | | C2^4xC3:S3 | 288,1044 |
C4×C9⋊C8 | Direct product of C4 and C9⋊C8 | 288 | | C4xC9:C8 | 288,9 |
C2×C9⋊C16 | Direct product of C2 and C9⋊C16 | 288 | | C2xC9:C16 | 288,18 |
C22×C9⋊C8 | Direct product of C22 and C9⋊C8 | 288 | | C2^2xC9:C8 | 288,130 |
C2×C4×Dic9 | Direct product of C2×C4 and Dic9 | 288 | | C2xC4xDic9 | 288,132 |
C8×C3⋊Dic3 | Direct product of C8 and C3⋊Dic3 | 288 | | C8xC3:Dic3 | 288,288 |
C2×C24.S3 | Direct product of C2 and C24.S3 | 288 | | C2xC24.S3 | 288,286 |
C4×C32⋊4C8 | Direct product of C4 and C32⋊4C8 | 288 | | C4xC3^2:4C8 | 288,277 |
C23×C3⋊Dic3 | Direct product of C23 and C3⋊Dic3 | 288 | | C2^3xC3:Dic3 | 288,1016 |
C22×C32⋊4C8 | Direct product of C22 and C32⋊4C8 | 288 | | C2^2xC3^2:4C8 | 288,777 |
S32×C2×C4 | Direct product of C2×C4, S3 and S3 | 48 | | S3^2xC2xC4 | 288,950 |
C2×C4×C32⋊C4 | Direct product of C2×C4 and C32⋊C4 | 48 | | C2xC4xC3^2:C4 | 288,932 |
C2×C3⋊S3⋊3C8 | Direct product of C2 and C3⋊S3⋊3C8 | 48 | | C2xC3:S3:3C8 | 288,929 |
C2×C4×C3.A4 | Direct product of C2×C4 and C3.A4 | 72 | | C2xC4xC3.A4 | 288,343 |
C2×S3×C3⋊C8 | Direct product of C2, S3 and C3⋊C8 | 96 | | C2xS3xC3:C8 | 288,460 |
C2×C6×C3⋊C8 | Direct product of C2×C6 and C3⋊C8 | 96 | | C2xC6xC3:C8 | 288,691 |
C2×C8×C3⋊S3 | Direct product of C2×C8 and C3⋊S3 | 144 | | C2xC8xC3:S3 | 288,756 |
C22×C4×C3⋊S3 | Direct product of C22×C4 and C3⋊S3 | 144 | | C2^2xC4xC3:S3 | 288,1004 |
C2×C4×C3⋊Dic3 | Direct product of C2×C4 and C3⋊Dic3 | 288 | | C2xC4xC3:Dic3 | 288,779 |
| | d | ρ | Label | ID |
---|
C300 | Cyclic group | 300 | 1 | C300 | 300,4 |
D150 | Dihedral group; = C2×D75 | 150 | 2+ | D150 | 300,11 |
Dic75 | Dicyclic group; = C75⋊3C4 | 300 | 2- | Dic75 | 300,3 |
C52⋊D6 | The semidirect product of C52 and D6 acting faithfully | 15 | 6+ | C5^2:D6 | 300,25 |
C52⋊C12 | The semidirect product of C52 and C12 acting faithfully | 15 | 12+ | C5^2:C12 | 300,24 |
C52⋊Dic3 | The semidirect product of C52 and Dic3 acting faithfully | 15 | 12+ | C5^2:Dic3 | 300,23 |
C52⋊A4 | The semidirect product of C52 and A4 acting via A4/C22=C3 | 30 | 3 | C5^2:A4 | 300,43 |
D15⋊D5 | The semidirect product of D15 and D5 acting via D5/C5=C2 | 30 | 4 | D15:D5 | 300,40 |
C15⋊2F5 | 2nd semidirect product of C15 and F5 acting via F5/C5=C4 | 30 | 4 | C15:2F5 | 300,35 |
C52⋊2C12 | The semidirect product of C52 and C12 acting via C12/C2=C6 | 60 | 6- | C5^2:2C12 | 300,14 |
C52⋊2Dic3 | The semidirect product of C52 and Dic3 acting via Dic3/C2=S3 | 60 | 3 | C5^2:2Dic3 | 300,13 |
C75⋊C4 | 1st semidirect product of C75 and C4 acting faithfully | 75 | 4 | C75:C4 | 300,6 |
C15⋊F5 | 1st semidirect product of C15 and F5 acting via F5/C5=C4 | 75 | | C15:F5 | 300,34 |
D5.D15 | The non-split extension by D5 of D15 acting via D15/C15=C2 | 60 | 4 | D5.D15 | 300,33 |
C30.D5 | 3rd non-split extension by C30 of D5 acting via D5/C5=C2 | 300 | | C30.D5 | 300,20 |
C5×C60 | Abelian group of type [5,60] | 300 | | C5xC60 | 300,21 |
C2×C150 | Abelian group of type [2,150] | 300 | | C2xC150 | 300,12 |
C10×C30 | Abelian group of type [10,30] | 300 | | C10xC30 | 300,49 |
C5×A5 | Direct product of C5 and A5; = U2(𝔽4) | 25 | 3 | C5xA5 | 300,22 |
D5×D15 | Direct product of D5 and D15 | 30 | 4+ | D5xD15 | 300,39 |
D5×C30 | Direct product of C30 and D5 | 60 | 2 | D5xC30 | 300,44 |
C15×F5 | Direct product of C15 and F5 | 60 | 4 | C15xF5 | 300,28 |
C10×D15 | Direct product of C10 and D15 | 60 | 2 | C10xD15 | 300,47 |
C15×Dic5 | Direct product of C15 and Dic5 | 60 | 2 | C15xDic5 | 300,16 |
C5×Dic15 | Direct product of C5 and Dic15 | 60 | 2 | C5xDic15 | 300,19 |
S3×D25 | Direct product of S3 and D25 | 75 | 4+ | S3xD25 | 300,7 |
A4×C25 | Direct product of C25 and A4 | 100 | 3 | A4xC25 | 300,8 |
A4×C52 | Direct product of C52 and A4 | 100 | | A4xC5^2 | 300,42 |
S3×C50 | Direct product of C50 and S3 | 150 | 2 | S3xC50 | 300,10 |
C6×D25 | Direct product of C6 and D25 | 150 | 2 | C6xD25 | 300,9 |
Dic3×C25 | Direct product of C25 and Dic3 | 300 | 2 | Dic3xC25 | 300,1 |
C3×Dic25 | Direct product of C3 and Dic25 | 300 | 2 | C3xDic25 | 300,2 |
Dic3×C52 | Direct product of C52 and Dic3 | 300 | | Dic3xC5^2 | 300,18 |
C3×D52 | Direct product of C3, D5 and D5 | 30 | 4 | C3xD5^2 | 300,36 |
C5×S3×D5 | Direct product of C5, S3 and D5 | 30 | 4 | C5xS3xD5 | 300,37 |
C2×C52⋊S3 | Direct product of C2 and C52⋊S3 | 30 | 3 | C2xC5^2:S3 | 300,26 |
C2×C52⋊C6 | Direct product of C2 and C52⋊C6 | 30 | 6+ | C2xC5^2:C6 | 300,27 |
C3×C52⋊C4 | Direct product of C3 and C52⋊C4 | 30 | 4 | C3xC5^2:C4 | 300,31 |
C5×C3⋊F5 | Direct product of C5 and C3⋊F5 | 60 | 4 | C5xC3:F5 | 300,32 |
C4×C52⋊C3 | Direct product of C4 and C52⋊C3 | 60 | 3 | C4xC5^2:C3 | 300,15 |
C3×D5.D5 | Direct product of C3 and D5.D5 | 60 | 4 | C3xD5.D5 | 300,29 |
C22×C52⋊C3 | Direct product of C22 and C52⋊C3 | 60 | | C2^2xC5^2:C3 | 300,41 |
C3×C25⋊C4 | Direct product of C3 and C25⋊C4 | 75 | 4 | C3xC25:C4 | 300,5 |
S3×C5⋊D5 | Direct product of S3 and C5⋊D5 | 75 | | S3xC5:D5 | 300,38 |
C3×C5⋊F5 | Direct product of C3 and C5⋊F5 | 75 | | C3xC5:F5 | 300,30 |
S3×C5×C10 | Direct product of C5×C10 and S3 | 150 | | S3xC5xC10 | 300,46 |
C6×C5⋊D5 | Direct product of C6 and C5⋊D5 | 150 | | C6xC5:D5 | 300,45 |
C2×C5⋊D15 | Direct product of C2 and C5⋊D15 | 150 | | C2xC5:D15 | 300,48 |
C3×C52⋊6C4 | Direct product of C3 and C52⋊6C4 | 300 | | C3xC5^2:6C4 | 300,17 |
| | d | ρ | Label | ID |
---|
C312 | Cyclic group | 312 | 1 | C312 | 312,6 |
D13⋊A4 | The semidirect product of D13 and A4 acting via A4/C22=C3 | 52 | 6+ | D13:A4 | 312,51 |
C13⋊C24 | The semidirect product of C13 and C24 acting via C24/C2=C12 | 104 | 12- | C13:C24 | 312,7 |
C13⋊2C24 | The semidirect product of C13 and C24 acting via C24/C4=C6 | 104 | 6 | C13:2C24 | 312,1 |
C39⋊3C8 | 1st semidirect product of C39 and C8 acting via C8/C4=C2 | 312 | 2 | C39:3C8 | 312,5 |
C39⋊C8 | 1st semidirect product of C39 and C8 acting via C8/C2=C4 | 312 | 4 | C39:C8 | 312,14 |
D78.C2 | The non-split extension by D78 of C2 acting faithfully | 156 | 4+ | D78.C2 | 312,17 |
C2×C156 | Abelian group of type [2,156] | 312 | | C2xC156 | 312,42 |
C22×C78 | Abelian group of type [2,2,78] | 312 | | C2^2xC78 | 312,61 |
C2×F13 | Direct product of C2 and F13; = Aut(D26) = Hol(C26) | 26 | 12+ | C2xF13 | 312,45 |
A4×D13 | Direct product of A4 and D13 | 52 | 6+ | A4xD13 | 312,50 |
A4×C26 | Direct product of C26 and A4 | 78 | 3 | A4xC26 | 312,56 |
S3×C52 | Direct product of C52 and S3 | 156 | 2 | S3xC52 | 312,33 |
C4×D39 | Direct product of C4 and D39 | 156 | 2 | C4xD39 | 312,38 |
C12×D13 | Direct product of C12 and D13 | 156 | 2 | C12xD13 | 312,28 |
Dic3×D13 | Direct product of Dic3 and D13 | 156 | 4- | Dic3xD13 | 312,15 |
S3×Dic13 | Direct product of S3 and Dic13 | 156 | 4- | S3xDic13 | 312,16 |
C22×D39 | Direct product of C22 and D39 | 156 | | C2^2xD39 | 312,60 |
C6×Dic13 | Direct product of C6 and Dic13 | 312 | | C6xDic13 | 312,30 |
Dic3×C26 | Direct product of C26 and Dic3 | 312 | | Dic3xC26 | 312,35 |
C2×Dic39 | Direct product of C2 and Dic39 | 312 | | C2xDic39 | 312,40 |
S3×C13⋊C4 | Direct product of S3 and C13⋊C4 | 39 | 8+ | S3xC13:C4 | 312,46 |
C4×C13⋊C6 | Direct product of C4 and C13⋊C6 | 52 | 6 | C4xC13:C6 | 312,9 |
C22×C13⋊C6 | Direct product of C22 and C13⋊C6 | 52 | | C2^2xC13:C6 | 312,49 |
C6×C13⋊C4 | Direct product of C6 and C13⋊C4 | 78 | 4 | C6xC13:C4 | 312,52 |
C2×C13⋊A4 | Direct product of C2 and C13⋊A4 | 78 | 3 | C2xC13:A4 | 312,57 |
C2×S3×D13 | Direct product of C2, S3 and D13 | 78 | 4+ | C2xS3xD13 | 312,54 |
C2×C39⋊C4 | Direct product of C2 and C39⋊C4 | 78 | 4 | C2xC39:C4 | 312,53 |
C8×C13⋊C3 | Direct product of C8 and C13⋊C3 | 104 | 3 | C8xC13:C3 | 312,2 |
C2×C26.C6 | Direct product of C2 and C26.C6 | 104 | | C2xC26.C6 | 312,11 |
C23×C13⋊C3 | Direct product of C23 and C13⋊C3 | 104 | | C2^3xC13:C3 | 312,55 |
S3×C2×C26 | Direct product of C2×C26 and S3 | 156 | | S3xC2xC26 | 312,59 |
C2×C6×D13 | Direct product of C2×C6 and D13 | 156 | | C2xC6xD13 | 312,58 |
C13×C3⋊C8 | Direct product of C13 and C3⋊C8 | 312 | 2 | C13xC3:C8 | 312,3 |
C3×C13⋊C8 | Direct product of C3 and C13⋊C8 | 312 | 4 | C3xC13:C8 | 312,13 |
C3×C13⋊2C8 | Direct product of C3 and C13⋊2C8 | 312 | 2 | C3xC13:2C8 | 312,4 |
C2×C4×C13⋊C3 | Direct product of C2×C4 and C13⋊C3 | 104 | | C2xC4xC13:C3 | 312,22 |
| | d | ρ | Label | ID |
---|
C320 | Cyclic group | 320 | 1 | C320 | 320,2 |
D5⋊C32 | The semidirect product of D5 and C32 acting via C32/C16=C2 | 160 | 4 | D5:C32 | 320,179 |
C5⋊C64 | The semidirect product of C5 and C64 acting via C64/C16=C4 | 320 | 4 | C5:C64 | 320,3 |
C5⋊2C64 | The semidirect product of C5 and C64 acting via C64/C32=C2 | 320 | 2 | C5:2C64 | 320,1 |
Dic5⋊C16 | 2nd semidirect product of Dic5 and C16 acting via C16/C8=C2 | 320 | | Dic5:C16 | 320,223 |
C8×C40 | Abelian group of type [8,40] | 320 | | C8xC40 | 320,126 |
C4×C80 | Abelian group of type [4,80] | 320 | | C4xC80 | 320,150 |
C2×C160 | Abelian group of type [2,160] | 320 | | C2xC160 | 320,174 |
C42×C20 | Abelian group of type [4,4,20] | 320 | | C4^2xC20 | 320,875 |
C22×C80 | Abelian group of type [2,2,80] | 320 | | C2^2xC80 | 320,1003 |
C23×C40 | Abelian group of type [2,2,2,40] | 320 | | C2^3xC40 | 320,1567 |
C24×C20 | Abelian group of type [2,2,2,2,20] | 320 | | C2^4xC20 | 320,1628 |
C25×C10 | Abelian group of type [2,2,2,2,2,10] | 320 | | C2^5xC10 | 320,1640 |
C2×C4×C40 | Abelian group of type [2,4,40] | 320 | | C2xC4xC40 | 320,903 |
C22×C4×C20 | Abelian group of type [2,2,4,20] | 320 | | C2^2xC4xC20 | 320,1513 |
C16×F5 | Direct product of C16 and F5 | 80 | 4 | C16xF5 | 320,181 |
C42×F5 | Direct product of C42 and F5 | 80 | | C4^2xF5 | 320,1023 |
C24×F5 | Direct product of C24 and F5 | 80 | | C2^4xF5 | 320,1638 |
D5×C32 | Direct product of C32 and D5 | 160 | 2 | D5xC32 | 320,4 |
D5×C25 | Direct product of C25 and D5 | 160 | | D5xC2^5 | 320,1639 |
C16×Dic5 | Direct product of C16 and Dic5 | 320 | | C16xDic5 | 320,58 |
C42×Dic5 | Direct product of C42 and Dic5 | 320 | | C4^2xDic5 | 320,557 |
C24×Dic5 | Direct product of C24 and Dic5 | 320 | | C2^4xDic5 | 320,1626 |
C4×C24⋊C5 | Direct product of C4 and C24⋊C5 | 20 | 5 | C4xC2^4:C5 | 320,1584 |
C22×C24⋊C5 | Direct product of C22 and C24⋊C5 | 20 | | C2^2xC2^4:C5 | 320,1637 |
C2×C8×F5 | Direct product of C2×C8 and F5 | 80 | | C2xC8xF5 | 320,1054 |
C22×C4×F5 | Direct product of C22×C4 and F5 | 80 | | C2^2xC4xF5 | 320,1590 |
D5×C4×C8 | Direct product of C4×C8 and D5 | 160 | | D5xC4xC8 | 320,311 |
D5×C2×C16 | Direct product of C2×C16 and D5 | 160 | | D5xC2xC16 | 320,526 |
C4×D5⋊C8 | Direct product of C4 and D5⋊C8 | 160 | | C4xD5:C8 | 320,1013 |
D5×C2×C42 | Direct product of C2×C42 and D5 | 160 | | D5xC2xC4^2 | 320,1143 |
D5×C22×C8 | Direct product of C22×C8 and D5 | 160 | | D5xC2^2xC8 | 320,1408 |
D5×C23×C4 | Direct product of C23×C4 and D5 | 160 | | D5xC2^3xC4 | 320,1609 |
C2×D5⋊C16 | Direct product of C2 and D5⋊C16 | 160 | | C2xD5:C16 | 320,1051 |
C22×D5⋊C8 | Direct product of C22 and D5⋊C8 | 160 | | C2^2xD5:C8 | 320,1587 |
C8×C5⋊C8 | Direct product of C8 and C5⋊C8 | 320 | | C8xC5:C8 | 320,216 |
C4×C5⋊C16 | Direct product of C4 and C5⋊C16 | 320 | | C4xC5:C16 | 320,195 |
C2×C5⋊C32 | Direct product of C2 and C5⋊C32 | 320 | | C2xC5:C32 | 320,214 |
C8×C5⋊2C8 | Direct product of C8 and C5⋊2C8 | 320 | | C8xC5:2C8 | 320,11 |
C23×C5⋊C8 | Direct product of C23 and C5⋊C8 | 320 | | C2^3xC5:C8 | 320,1605 |
C2×C8×Dic5 | Direct product of C2×C8 and Dic5 | 320 | | C2xC8xDic5 | 320,725 |
C4×C5⋊2C16 | Direct product of C4 and C5⋊2C16 | 320 | | C4xC5:2C16 | 320,18 |
C2×C5⋊2C32 | Direct product of C2 and C5⋊2C32 | 320 | | C2xC5:2C32 | 320,56 |
C22×C5⋊C16 | Direct product of C22 and C5⋊C16 | 320 | | C2^2xC5:C16 | 320,1080 |
C23×C5⋊2C8 | Direct product of C23 and C5⋊2C8 | 320 | | C2^3xC5:2C8 | 320,1452 |
C22×C4×Dic5 | Direct product of C22×C4 and Dic5 | 320 | | C2^2xC4xDic5 | 320,1454 |
C22×C5⋊2C16 | Direct product of C22 and C5⋊2C16 | 320 | | C2^2xC5:2C16 | 320,723 |
C2×C4×C5⋊C8 | Direct product of C2×C4 and C5⋊C8 | 320 | | C2xC4xC5:C8 | 320,1084 |
C2×C4×C5⋊2C8 | Direct product of C2×C4 and C5⋊2C8 | 320 | | C2xC4xC5:2C8 | 320,547 |
| | d | ρ | Label | ID |
---|
C324 | Cyclic group | 324 | 1 | C324 | 324,2 |
D162 | Dihedral group; = C2×D81 | 162 | 2+ | D162 | 324,4 |
Dic81 | Dicyclic group; = C81⋊C4 | 324 | 2- | Dic81 | 324,1 |
C92⋊C4 | The semidirect product of C92 and C4 acting faithfully | 18 | 4+ | C9^2:C4 | 324,35 |
C34⋊4C4 | 4th semidirect product of C34 and C4 acting faithfully | 18 | | C3^4:4C4 | 324,164 |
C34⋊C4 | 3rd semidirect product of C34 and C4 acting faithfully | 36 | | C3^4:C4 | 324,163 |
C32⋊5D18 | 2nd semidirect product of C32 and D18 acting via D18/C9=C22 | 36 | 4 | C3^2:5D18 | 324,123 |
C33⋊17D6 | 5th semidirect product of C33 and D6 acting via D6/C3=C22 | 36 | | C3^3:17D6 | 324,170 |
C32⋊3Dic9 | The semidirect product of C32 and Dic9 acting via Dic9/C9=C4 | 36 | 4 | C3^2:3Dic9 | 324,112 |
C9⋊Dic9 | The semidirect product of C9 and Dic9 acting via Dic9/C18=C2 | 324 | | C9:Dic9 | 324,19 |
C27⋊Dic3 | The semidirect product of C27 and Dic3 acting via Dic3/C6=C2 | 324 | | C27:Dic3 | 324,21 |
C34⋊8C4 | 4th semidirect product of C34 and C4 acting via C4/C2=C2 | 324 | | C3^4:8C4 | 324,158 |
C32⋊5Dic9 | 2nd semidirect product of C32 and Dic9 acting via Dic9/C18=C2 | 324 | | C3^2:5Dic9 | 324,103 |
C27.A4 | The central extension by C27 of A4 | 162 | 3 | C27.A4 | 324,3 |
C182 | Abelian group of type [18,18] | 324 | | C18^2 | 324,81 |
C9×C36 | Abelian group of type [9,36] | 324 | | C9xC36 | 324,26 |
C6×C54 | Abelian group of type [6,54] | 324 | | C6xC54 | 324,84 |
C2×C162 | Abelian group of type [2,162] | 324 | | C2xC162 | 324,5 |
C3×C108 | Abelian group of type [3,108] | 324 | | C3xC108 | 324,29 |
C32×C36 | Abelian group of type [3,3,36] | 324 | | C3^2xC36 | 324,105 |
C33×C12 | Abelian group of type [3,3,3,12] | 324 | | C3^3xC12 | 324,159 |
C32×C62 | Abelian group of type [3,3,6,6] | 324 | | C3^2xC6^2 | 324,176 |
C3×C6×C18 | Abelian group of type [3,6,18] | 324 | | C3xC6xC18 | 324,151 |
D92 | Direct product of D9 and D9 | 18 | 4+ | D9^2 | 324,36 |
D9×C18 | Direct product of C18 and D9 | 36 | 2 | D9xC18 | 324,61 |
C9×Dic9 | Direct product of C9 and Dic9 | 36 | 2 | C9xDic9 | 324,6 |
S3×D27 | Direct product of S3 and D27 | 54 | 4+ | S3xD27 | 324,38 |
S3×C54 | Direct product of C54 and S3 | 108 | 2 | S3xC54 | 324,66 |
A4×C27 | Direct product of C27 and A4 | 108 | 3 | A4xC27 | 324,42 |
C6×D27 | Direct product of C6 and D27 | 108 | 2 | C6xD27 | 324,65 |
A4×C33 | Direct product of C33 and A4 | 108 | | A4xC3^3 | 324,171 |
C3×Dic27 | Direct product of C3 and Dic27 | 108 | 2 | C3xDic27 | 324,10 |
Dic3×C27 | Direct product of C27 and Dic3 | 108 | 2 | Dic3xC27 | 324,11 |
C32×Dic9 | Direct product of C32 and Dic9 | 108 | | C3^2xDic9 | 324,90 |
Dic3×C33 | Direct product of C33 and Dic3 | 108 | | Dic3xC3^3 | 324,155 |
C3×C33⋊C4 | Direct product of C3 and C33⋊C4; = AΣL1(𝔽81) | 12 | 4 | C3xC3^3:C4 | 324,162 |
C3×C32⋊4D6 | Direct product of C3 and C32⋊4D6 | 12 | 4 | C3xC3^2:4D6 | 324,167 |
S32×C9 | Direct product of C9, S3 and S3 | 36 | 4 | S3^2xC9 | 324,115 |
C3×S3×D9 | Direct product of C3, S3 and D9 | 36 | 4 | C3xS3xD9 | 324,114 |
S32×C32 | Direct product of C32, S3 and S3 | 36 | | S3^2xC3^2 | 324,165 |
C9×C32⋊C4 | Direct product of C9 and C32⋊C4 | 36 | 4 | C9xC3^2:C4 | 324,109 |
C32×C32⋊C4 | Direct product of C32 and C32⋊C4 | 36 | | C3^2xC3^2:C4 | 324,161 |
C32×C3⋊Dic3 | Direct product of C32 and C3⋊Dic3 | 36 | | C3^2xC3:Dic3 | 324,156 |
S3×C9⋊S3 | Direct product of S3 and C9⋊S3 | 54 | | S3xC9:S3 | 324,120 |
D9×C3⋊S3 | Direct product of D9 and C3⋊S3 | 54 | | D9xC3:S3 | 324,119 |
S3×C33⋊C2 | Direct product of S3 and C33⋊C2 | 54 | | S3xC3^3:C2 | 324,168 |
A4×C3×C9 | Direct product of C3×C9 and A4 | 108 | | A4xC3xC9 | 324,126 |
D9×C3×C6 | Direct product of C3×C6 and D9 | 108 | | D9xC3xC6 | 324,136 |
C6×C9⋊S3 | Direct product of C6 and C9⋊S3 | 108 | | C6xC9:S3 | 324,142 |
S3×C3×C18 | Direct product of C3×C18 and S3 | 108 | | S3xC3xC18 | 324,137 |
C18×C3⋊S3 | Direct product of C18 and C3⋊S3 | 108 | | C18xC3:S3 | 324,143 |
S3×C32×C6 | Direct product of C32×C6 and S3 | 108 | | S3xC3^2xC6 | 324,172 |
Dic3×C3×C9 | Direct product of C3×C9 and Dic3 | 108 | | Dic3xC3xC9 | 324,91 |
C3×C9⋊Dic3 | Direct product of C3 and C9⋊Dic3 | 108 | | C3xC9:Dic3 | 324,96 |
C9×C3⋊Dic3 | Direct product of C9 and C3⋊Dic3 | 108 | | C9xC3:Dic3 | 324,97 |
C6×C33⋊C2 | Direct product of C6 and C33⋊C2 | 108 | | C6xC3^3:C2 | 324,174 |
C3×C33⋊5C4 | Direct product of C3 and C33⋊5C4 | 108 | | C3xC3^3:5C4 | 324,157 |
C2×C9⋊D9 | Direct product of C2 and C9⋊D9 | 162 | | C2xC9:D9 | 324,74 |
C2×C27⋊S3 | Direct product of C2 and C27⋊S3 | 162 | | C2xC27:S3 | 324,76 |
C3×C9.A4 | Direct product of C3 and C9.A4 | 162 | | C3xC9.A4 | 324,44 |
C9×C3.A4 | Direct product of C9 and C3.A4 | 162 | | C9xC3.A4 | 324,46 |
C2×C34⋊C2 | Direct product of C2 and C34⋊C2 | 162 | | C2xC3^4:C2 | 324,175 |
C32×C3.A4 | Direct product of C32 and C3.A4 | 162 | | C3^2xC3.A4 | 324,133 |
C2×C32⋊4D9 | Direct product of C2 and C32⋊4D9 | 162 | | C2xC3^2:4D9 | 324,149 |
C3⋊S32 | Direct product of C3⋊S3 and C3⋊S3 | 18 | | C3:S3^2 | 324,169 |
C3×S3×C3⋊S3 | Direct product of C3, S3 and C3⋊S3 | 36 | | C3xS3xC3:S3 | 324,166 |
C3⋊S3×C3×C6 | Direct product of C3×C6 and C3⋊S3 | 36 | | C3:S3xC3xC6 | 324,173 |
| | d | ρ | Label | ID |
---|
C336 | Cyclic group | 336 | 1 | C336 | 336,6 |
Dic7⋊A4 | The semidirect product of Dic7 and A4 acting via A4/C22=C3 | 84 | 6- | Dic7:A4 | 336,136 |
C7⋊C48 | The semidirect product of C7 and C48 acting via C48/C8=C6 | 112 | 6 | C7:C48 | 336,1 |
D21⋊C8 | The semidirect product of D21 and C8 acting via C8/C4=C2 | 168 | 4 | D21:C8 | 336,25 |
C21⋊C16 | 1st semidirect product of C21 and C16 acting via C16/C8=C2 | 336 | 2 | C21:C16 | 336,5 |
C42⋊(C7⋊C3) | The semidirect product of C42 and C7⋊C3 acting via C7⋊C3/C7=C3 | 84 | 3 | C4^2:(C7:C3) | 336,57 |
C7⋊(C22⋊A4) | The semidirect product of C7 and C22⋊A4 acting via C22⋊A4/C24=C3 | 84 | | C7:(C2^2:A4) | 336,224 |
C4×C84 | Abelian group of type [4,84] | 336 | | C4xC84 | 336,106 |
C2×C168 | Abelian group of type [2,168] | 336 | | C2xC168 | 336,109 |
C22×C84 | Abelian group of type [2,2,84] | 336 | | C2^2xC84 | 336,204 |
C23×C42 | Abelian group of type [2,2,2,42] | 336 | | C2^3xC42 | 336,228 |
C2×AΓL1(𝔽8) | Direct product of C2 and AΓL1(𝔽8) | 14 | 7+ | C2xAGammaL(1,8) | 336,210 |
S3×F8 | Direct product of S3 and F8 | 24 | 14+ | S3xF8 | 336,211 |
C6×F8 | Direct product of C6 and F8 | 42 | 7 | C6xF8 | 336,213 |
C8×F7 | Direct product of C8 and F7 | 56 | 6 | C8xF7 | 336,7 |
C23×F7 | Direct product of C23 and F7 | 56 | | C2^3xF7 | 336,216 |
A4×C28 | Direct product of C28 and A4 | 84 | 3 | A4xC28 | 336,168 |
A4×Dic7 | Direct product of A4 and Dic7 | 84 | 6- | A4xDic7 | 336,133 |
S3×C56 | Direct product of C56 and S3 | 168 | 2 | S3xC56 | 336,74 |
D7×C24 | Direct product of C24 and D7 | 168 | 2 | D7xC24 | 336,58 |
C8×D21 | Direct product of C8 and D21 | 168 | 2 | C8xD21 | 336,90 |
C23×D21 | Direct product of C23 and D21 | 168 | | C2^3xD21 | 336,227 |
C12×Dic7 | Direct product of C12 and Dic7 | 336 | | C12xDic7 | 336,65 |
Dic3×C28 | Direct product of C28 and Dic3 | 336 | | Dic3xC28 | 336,81 |
C4×Dic21 | Direct product of C4 and Dic21 | 336 | | C4xDic21 | 336,97 |
Dic3×Dic7 | Direct product of Dic3 and Dic7 | 336 | | Dic3xDic7 | 336,41 |
C22×Dic21 | Direct product of C22 and Dic21 | 336 | | C2^2xDic21 | 336,202 |
C2×A4×D7 | Direct product of C2, A4 and D7 | 42 | 6+ | C2xA4xD7 | 336,217 |
C2×D7⋊A4 | Direct product of C2 and D7⋊A4 | 42 | 6+ | C2xD7:A4 | 336,218 |
C2×C4×F7 | Direct product of C2×C4 and F7 | 56 | | C2xC4xF7 | 336,122 |
C4×C7⋊A4 | Direct product of C4 and C7⋊A4 | 84 | 3 | C4xC7:A4 | 336,171 |
C4×S3×D7 | Direct product of C4, S3 and D7 | 84 | 4 | C4xS3xD7 | 336,147 |
A4×C2×C14 | Direct product of C2×C14 and A4 | 84 | | A4xC2xC14 | 336,221 |
C7×C42⋊C3 | Direct product of C7 and C42⋊C3 | 84 | 3 | C7xC4^2:C3 | 336,56 |
C22×C7⋊A4 | Direct product of C22 and C7⋊A4 | 84 | | C2^2xC7:A4 | 336,222 |
C22×S3×D7 | Direct product of C22, S3 and D7 | 84 | | C2^2xS3xD7 | 336,219 |
C7×C22⋊A4 | Direct product of C7 and C22⋊A4 | 84 | | C7xC2^2:A4 | 336,223 |
C16×C7⋊C3 | Direct product of C16 and C7⋊C3 | 112 | 3 | C16xC7:C3 | 336,2 |
C2×C7⋊C24 | Direct product of C2 and C7⋊C24 | 112 | | C2xC7:C24 | 336,12 |
C4×C7⋊C12 | Direct product of C4 and C7⋊C12 | 112 | | C4xC7:C12 | 336,14 |
C42×C7⋊C3 | Direct product of C42 and C7⋊C3 | 112 | | C4^2xC7:C3 | 336,48 |
C24×C7⋊C3 | Direct product of C24 and C7⋊C3 | 112 | | C2^4xC7:C3 | 336,220 |
C22×C7⋊C12 | Direct product of C22 and C7⋊C12 | 112 | | C2^2xC7:C12 | 336,129 |
S3×C7⋊C8 | Direct product of S3 and C7⋊C8 | 168 | 4 | S3xC7:C8 | 336,24 |
D7×C3⋊C8 | Direct product of D7 and C3⋊C8 | 168 | 4 | D7xC3:C8 | 336,23 |
S3×C2×C28 | Direct product of C2×C28 and S3 | 168 | | S3xC2xC28 | 336,185 |
D7×C2×C12 | Direct product of C2×C12 and D7 | 168 | | D7xC2xC12 | 336,175 |
C2×C4×D21 | Direct product of C2×C4 and D21 | 168 | | C2xC4xD21 | 336,195 |
C2×Dic3×D7 | Direct product of C2, Dic3 and D7 | 168 | | C2xDic3xD7 | 336,151 |
C2×S3×Dic7 | Direct product of C2, S3 and Dic7 | 168 | | C2xS3xDic7 | 336,154 |
D7×C22×C6 | Direct product of C22×C6 and D7 | 168 | | D7xC2^2xC6 | 336,225 |
C2×D21⋊C4 | Direct product of C2 and D21⋊C4 | 168 | | C2xD21:C4 | 336,156 |
S3×C22×C14 | Direct product of C22×C14 and S3 | 168 | | S3xC2^2xC14 | 336,226 |
C6×C7⋊C8 | Direct product of C6 and C7⋊C8 | 336 | | C6xC7:C8 | 336,63 |
C7×C3⋊C16 | Direct product of C7 and C3⋊C16 | 336 | 2 | C7xC3:C16 | 336,3 |
C3×C7⋊C16 | Direct product of C3 and C7⋊C16 | 336 | 2 | C3xC7:C16 | 336,4 |
C14×C3⋊C8 | Direct product of C14 and C3⋊C8 | 336 | | C14xC3:C8 | 336,79 |
C2×C21⋊C8 | Direct product of C2 and C21⋊C8 | 336 | | C2xC21:C8 | 336,95 |
C2×C6×Dic7 | Direct product of C2×C6 and Dic7 | 336 | | C2xC6xDic7 | 336,182 |
Dic3×C2×C14 | Direct product of C2×C14 and Dic3 | 336 | | Dic3xC2xC14 | 336,192 |
C2×C8×C7⋊C3 | Direct product of C2×C8 and C7⋊C3 | 112 | | C2xC8xC7:C3 | 336,51 |
C22×C4×C7⋊C3 | Direct product of C22×C4 and C7⋊C3 | 112 | | C2^2xC4xC7:C3 | 336,164 |
| | d | ρ | Label | ID |
---|
C352 | Cyclic group | 352 | 1 | C352 | 352,2 |
C11⋊C32 | The semidirect product of C11 and C32 acting via C32/C16=C2 | 352 | 2 | C11:C32 | 352,1 |
C4×C88 | Abelian group of type [4,88] | 352 | | C4xC88 | 352,45 |
C2×C176 | Abelian group of type [2,176] | 352 | | C2xC176 | 352,58 |
C22×C88 | Abelian group of type [2,2,88] | 352 | | C2^2xC88 | 352,164 |
C23×C44 | Abelian group of type [2,2,2,44] | 352 | | C2^3xC44 | 352,188 |
C24×C22 | Abelian group of type [2,2,2,2,22] | 352 | | C2^4xC22 | 352,195 |
C2×C4×C44 | Abelian group of type [2,4,44] | 352 | | C2xC4xC44 | 352,149 |
C16×D11 | Direct product of C16 and D11 | 176 | 2 | C16xD11 | 352,3 |
C42×D11 | Direct product of C42 and D11 | 176 | | C4^2xD11 | 352,66 |
C24×D11 | Direct product of C24 and D11 | 176 | | C2^4xD11 | 352,194 |
C8×Dic11 | Direct product of C8 and Dic11 | 352 | | C8xDic11 | 352,19 |
C23×Dic11 | Direct product of C23 and Dic11 | 352 | | C2^3xDic11 | 352,186 |
C2×C8×D11 | Direct product of C2×C8 and D11 | 176 | | C2xC8xD11 | 352,94 |
C22×C4×D11 | Direct product of C22×C4 and D11 | 176 | | C2^2xC4xD11 | 352,174 |
C4×C11⋊C8 | Direct product of C4 and C11⋊C8 | 352 | | C4xC11:C8 | 352,8 |
C2×C11⋊C16 | Direct product of C2 and C11⋊C16 | 352 | | C2xC11:C16 | 352,17 |
C22×C11⋊C8 | Direct product of C22 and C11⋊C8 | 352 | | C2^2xC11:C8 | 352,115 |
C2×C4×Dic11 | Direct product of C2×C4 and Dic11 | 352 | | C2xC4xDic11 | 352,117 |
| | d | ρ | Label | ID |
---|
C360 | Cyclic group | 360 | 1 | C360 | 360,4 |
C5⋊F9 | The semidirect product of C5 and F9 acting via F9/C3⋊S3=C4 | 45 | 8 | C5:F9 | 360,125 |
C5⋊2F9 | The semidirect product of C5 and F9 acting via F9/C32⋊C4=C2 | 45 | 8 | C5:2F9 | 360,124 |
Dic15⋊S3 | 3rd semidirect product of Dic15 and S3 acting via S3/C3=C2 | 60 | 4 | Dic15:S3 | 360,85 |
C45⋊3C8 | 1st semidirect product of C45 and C8 acting via C8/C4=C2 | 360 | 2 | C45:3C8 | 360,3 |
C45⋊C8 | 1st semidirect product of C45 and C8 acting via C8/C2=C4 | 360 | 4 | C45:C8 | 360,6 |
C3⋊F5⋊S3 | The semidirect product of C3⋊F5 and S3 acting via S3/C3=C2 | 30 | 8+ | C3:F5:S3 | 360,129 |
C32⋊F5⋊C2 | The semidirect product of C32⋊F5 and C2 acting faithfully | 30 | 8+ | C3^2:F5:C2 | 360,131 |
(C3×C15)⋊9C8 | 6th semidirect product of C3×C15 and C8 acting via C8/C2=C4 | 120 | 4 | (C3xC15):9C8 | 360,56 |
C6.D30 | 3rd non-split extension by C6 of D30 acting via D30/D15=C2 | 60 | 4+ | C6.D30 | 360,79 |
D30.S3 | The non-split extension by D30 of S3 acting via S3/C3=C2 | 120 | 4 | D30.S3 | 360,84 |
D90.C2 | The non-split extension by D90 of C2 acting faithfully | 180 | 4+ | D90.C2 | 360,9 |
C30.D6 | 11st non-split extension by C30 of D6 acting via D6/C3=C22 | 180 | | C30.D6 | 360,67 |
C60.S3 | 6th non-split extension by C60 of S3 acting via S3/C3=C2 | 360 | | C60.S3 | 360,37 |
C30.Dic3 | 3rd non-split extension by C30 of Dic3 acting via Dic3/C3=C4 | 360 | | C30.Dic3 | 360,54 |
(C3×C6).F5 | The non-split extension by C3×C6 of F5 acting via F5/C5=C4 | 120 | 4- | (C3xC6).F5 | 360,57 |
C6×C60 | Abelian group of type [6,60] | 360 | | C6xC60 | 360,115 |
C2×C180 | Abelian group of type [2,180] | 360 | | C2xC180 | 360,30 |
C3×C120 | Abelian group of type [3,120] | 360 | | C3xC120 | 360,38 |
C22×C90 | Abelian group of type [2,2,90] | 360 | | C2^2xC90 | 360,50 |
C2×C6×C30 | Abelian group of type [2,6,30] | 360 | | C2xC6xC30 | 360,162 |
S3×A5 | Direct product of S3 and A5 | 15 | 6+ | S3xA5 | 360,121 |
C6×A5 | Direct product of C6 and A5 | 30 | 3 | C6xA5 | 360,122 |
D9×F5 | Direct product of D9 and F5 | 45 | 8+ | D9xF5 | 360,39 |
C5×F9 | Direct product of C5 and F9 | 45 | 8 | C5xF9 | 360,123 |
A4×D15 | Direct product of A4 and D15 | 60 | 6+ | A4xD15 | 360,144 |
A4×C30 | Direct product of C30 and A4 | 90 | 3 | A4xC30 | 360,156 |
C18×F5 | Direct product of C18 and F5 | 90 | 4 | C18xF5 | 360,43 |
S3×C60 | Direct product of C60 and S3 | 120 | 2 | S3xC60 | 360,96 |
C12×D15 | Direct product of C12 and D15 | 120 | 2 | C12xD15 | 360,101 |
Dic3×D15 | Direct product of Dic3 and D15 | 120 | 4- | Dic3xD15 | 360,77 |
S3×Dic15 | Direct product of S3 and Dic15 | 120 | 4- | S3xDic15 | 360,78 |
Dic3×C30 | Direct product of C30 and Dic3 | 120 | | Dic3xC30 | 360,98 |
C6×Dic15 | Direct product of C6 and Dic15 | 120 | | C6xDic15 | 360,103 |
D5×C36 | Direct product of C36 and D5 | 180 | 2 | D5xC36 | 360,16 |
D9×C20 | Direct product of C20 and D9 | 180 | 2 | D9xC20 | 360,21 |
C4×D45 | Direct product of C4 and D45 | 180 | 2 | C4xD45 | 360,26 |
D9×Dic5 | Direct product of D9 and Dic5 | 180 | 4- | D9xDic5 | 360,8 |
D5×Dic9 | Direct product of D5 and Dic9 | 180 | 4- | D5xDic9 | 360,11 |
D5×C62 | Direct product of C62 and D5 | 180 | | D5xC6^2 | 360,157 |
C22×D45 | Direct product of C22 and D45 | 180 | | C2^2xD45 | 360,49 |
C18×Dic5 | Direct product of C18 and Dic5 | 360 | | C18xDic5 | 360,18 |
C10×Dic9 | Direct product of C10 and Dic9 | 360 | | C10xDic9 | 360,23 |
C2×Dic45 | Direct product of C2 and Dic45 | 360 | | C2xDic45 | 360,28 |
S32×D5 | Direct product of S3, S3 and D5 | 30 | 8+ | S3^2xD5 | 360,137 |
S3×C3⋊F5 | Direct product of S3 and C3⋊F5 | 30 | 8 | S3xC3:F5 | 360,128 |
C3×S3×F5 | Direct product of C3, S3 and F5 | 30 | 8 | C3xS3xF5 | 360,126 |
D5×C32⋊C4 | Direct product of D5 and C32⋊C4 | 30 | 8+ | D5xC3^2:C4 | 360,130 |
C3⋊S3×F5 | Direct product of C3⋊S3 and F5 | 45 | | C3:S3xF5 | 360,127 |
C5×S3×A4 | Direct product of C5, S3 and A4 | 60 | 6 | C5xS3xA4 | 360,143 |
C3×D5×A4 | Direct product of C3, D5 and A4 | 60 | 6 | C3xD5xA4 | 360,142 |
S3×C6×D5 | Direct product of C6, S3 and D5 | 60 | 4 | S3xC6xD5 | 360,151 |
C6×C3⋊F5 | Direct product of C6 and C3⋊F5 | 60 | 4 | C6xC3:F5 | 360,146 |
S32×C10 | Direct product of C10, S3 and S3 | 60 | 4 | S3^2xC10 | 360,153 |
C2×S3×D15 | Direct product of C2, S3 and D15 | 60 | 4+ | C2xS3xD15 | 360,154 |
C3×D5×Dic3 | Direct product of C3, D5 and Dic3 | 60 | 4 | C3xD5xDic3 | 360,58 |
C2×C32⋊F5 | Direct product of C2 and C32⋊F5 | 60 | 4+ | C2xC3^2:F5 | 360,150 |
C2×D15⋊S3 | Direct product of C2 and D15⋊S3 | 60 | 4 | C2xD15:S3 | 360,155 |
C10×C32⋊C4 | Direct product of C10 and C32⋊C4 | 60 | 4 | C10xC3^2:C4 | 360,148 |
C5×C6.D6 | Direct product of C5 and C6.D6 | 60 | 4 | C5xC6.D6 | 360,73 |
C2×C32⋊Dic5 | Direct product of C2 and C32⋊Dic5 | 60 | 4 | C2xC3^2:Dic5 | 360,149 |
C2×D5×D9 | Direct product of C2, D5 and D9 | 90 | 4+ | C2xD5xD9 | 360,45 |
C2×C9⋊F5 | Direct product of C2 and C9⋊F5 | 90 | 4 | C2xC9:F5 | 360,44 |
C3×C6×F5 | Direct product of C3×C6 and F5 | 90 | | C3xC6xF5 | 360,145 |
D5×C3.A4 | Direct product of D5 and C3.A4 | 90 | 6 | D5xC3.A4 | 360,42 |
C10×C3.A4 | Direct product of C10 and C3.A4 | 90 | 3 | C10xC3.A4 | 360,46 |
C2×C32⋊3F5 | Direct product of C2 and C32⋊3F5 | 90 | | C2xC3^2:3F5 | 360,147 |
C15×C3⋊C8 | Direct product of C15 and C3⋊C8 | 120 | 2 | C15xC3:C8 | 360,34 |
S3×C2×C30 | Direct product of C2×C30 and S3 | 120 | | S3xC2xC30 | 360,158 |
C2×C6×D15 | Direct product of C2×C6 and D15 | 120 | | C2xC6xD15 | 360,159 |
C3×C15⋊C8 | Direct product of C3 and C15⋊C8 | 120 | 4 | C3xC15:C8 | 360,53 |
C3×S3×Dic5 | Direct product of C3, S3 and Dic5 | 120 | 4 | C3xS3xDic5 | 360,59 |
C5×S3×Dic3 | Direct product of C5, S3 and Dic3 | 120 | 4 | C5xS3xDic3 | 360,72 |
C3×C15⋊3C8 | Direct product of C3 and C15⋊3C8 | 120 | 2 | C3xC15:3C8 | 360,35 |
C3×D30.C2 | Direct product of C3 and D30.C2 | 120 | 4 | C3xD30.C2 | 360,60 |
C5×C32⋊2C8 | Direct product of C5 and C32⋊2C8 | 120 | 4 | C5xC3^2:2C8 | 360,55 |
D5×C2×C18 | Direct product of C2×C18 and D5 | 180 | | D5xC2xC18 | 360,47 |
D9×C2×C10 | Direct product of C2×C10 and D9 | 180 | | D9xC2xC10 | 360,48 |
D5×C3×C12 | Direct product of C3×C12 and D5 | 180 | | D5xC3xC12 | 360,91 |
C3⋊S3×C20 | Direct product of C20 and C3⋊S3 | 180 | | C3:S3xC20 | 360,106 |
C4×C3⋊D15 | Direct product of C4 and C3⋊D15 | 180 | | C4xC3:D15 | 360,111 |
D5×C3⋊Dic3 | Direct product of D5 and C3⋊Dic3 | 180 | | D5xC3:Dic3 | 360,65 |
C3⋊S3×Dic5 | Direct product of C3⋊S3 and Dic5 | 180 | | C3:S3xDic5 | 360,66 |
C22×C3⋊D15 | Direct product of C22 and C3⋊D15 | 180 | | C2^2xC3:D15 | 360,161 |
C5×C9⋊C8 | Direct product of C5 and C9⋊C8 | 360 | 2 | C5xC9:C8 | 360,1 |
C9×C5⋊C8 | Direct product of C9 and C5⋊C8 | 360 | 4 | C9xC5:C8 | 360,5 |
C9×C5⋊2C8 | Direct product of C9 and C5⋊2C8 | 360 | 2 | C9xC5:2C8 | 360,2 |
C32×C5⋊C8 | Direct product of C32 and C5⋊C8 | 360 | | C3^2xC5:C8 | 360,52 |
C3×C6×Dic5 | Direct product of C3×C6 and Dic5 | 360 | | C3xC6xDic5 | 360,93 |
C10×C3⋊Dic3 | Direct product of C10 and C3⋊Dic3 | 360 | | C10xC3:Dic3 | 360,108 |
C2×C3⋊Dic15 | Direct product of C2 and C3⋊Dic15 | 360 | | C2xC3:Dic15 | 360,113 |
C32×C5⋊2C8 | Direct product of C32 and C5⋊2C8 | 360 | | C3^2xC5:2C8 | 360,33 |
C5×C32⋊4C8 | Direct product of C5 and C32⋊4C8 | 360 | | C5xC3^2:4C8 | 360,36 |
C2×D5×C3⋊S3 | Direct product of C2, D5 and C3⋊S3 | 90 | | C2xD5xC3:S3 | 360,152 |
C3⋊S3×C2×C10 | Direct product of C2×C10 and C3⋊S3 | 180 | | C3:S3xC2xC10 | 360,160 |
| | d | ρ | Label | ID |
---|
C378 | Cyclic group | 378 | 1 | C378 | 378,6 |
D189 | Dihedral group | 189 | 2+ | D189 | 378,5 |
C9⋊5F7 | The semidirect product of C9 and F7 acting via F7/C7⋊C3=C2 | 63 | 6+ | C9:5F7 | 378,20 |
C32⋊4F7 | 2nd semidirect product of C32 and F7 acting via F7/C7⋊C3=C2 | 63 | | C3^2:4F7 | 378,51 |
D21⋊C9 | The semidirect product of D21 and C9 acting via C9/C3=C3 | 126 | 6 | D21:C9 | 378,21 |
C7⋊C54 | The semidirect product of C7 and C54 acting via C54/C9=C6 | 189 | 6 | C7:C54 | 378,1 |
C3⋊D63 | The semidirect product of C3 and D63 acting via D63/C63=C2 | 189 | | C3:D63 | 378,42 |
C33⋊D7 | 3rd semidirect product of C33 and D7 acting via D7/C7=C2 | 189 | | C3^3:D7 | 378,59 |
C3×C126 | Abelian group of type [3,126] | 378 | | C3xC126 | 378,44 |
C32×C42 | Abelian group of type [3,3,42] | 378 | | C3^2xC42 | 378,60 |
C9×F7 | Direct product of C9 and F7 | 63 | 6 | C9xF7 | 378,7 |
C32×F7 | Direct product of C32 and F7 | 63 | | C3^2xF7 | 378,47 |
S3×C63 | Direct product of C63 and S3 | 126 | 2 | S3xC63 | 378,33 |
D9×C21 | Direct product of C21 and D9 | 126 | 2 | D9xC21 | 378,32 |
C3×D63 | Direct product of C3 and D63 | 126 | 2 | C3xD63 | 378,36 |
C9×D21 | Direct product of C9 and D21 | 126 | 2 | C9xD21 | 378,37 |
C32×D21 | Direct product of C32 and D21 | 126 | | C3^2xD21 | 378,55 |
C7×D27 | Direct product of C7 and D27 | 189 | 2 | C7xD27 | 378,3 |
D7×C27 | Direct product of C27 and D7 | 189 | 2 | D7xC27 | 378,4 |
D7×C33 | Direct product of C33 and D7 | 189 | | D7xC3^3 | 378,53 |
C3×C3⋊F7 | Direct product of C3 and C3⋊F7 | 42 | 6 | C3xC3:F7 | 378,49 |
D9×C7⋊C3 | Direct product of D9 and C7⋊C3 | 63 | 6 | D9xC7:C3 | 378,15 |
S3×C7⋊C9 | Direct product of S3 and C7⋊C9 | 126 | 6 | S3xC7:C9 | 378,16 |
C18×C7⋊C3 | Direct product of C18 and C7⋊C3 | 126 | 3 | C18xC7:C3 | 378,23 |
S3×C3×C21 | Direct product of C3×C21 and S3 | 126 | | S3xC3xC21 | 378,54 |
C3⋊S3×C21 | Direct product of C21 and C3⋊S3 | 126 | | C3:S3xC21 | 378,56 |
C3×C3⋊D21 | Direct product of C3 and C3⋊D21 | 126 | | C3xC3:D21 | 378,57 |
D7×C3×C9 | Direct product of C3×C9 and D7 | 189 | | D7xC3xC9 | 378,29 |
C3×C7⋊C18 | Direct product of C3 and C7⋊C18 | 189 | | C3xC7:C18 | 378,10 |
C7×C9⋊S3 | Direct product of C7 and C9⋊S3 | 189 | | C7xC9:S3 | 378,40 |
C7×C33⋊C2 | Direct product of C7 and C33⋊C2 | 189 | | C7xC3^3:C2 | 378,58 |
C6×C7⋊C9 | Direct product of C6 and C7⋊C9 | 378 | | C6xC7:C9 | 378,26 |
C2×C7⋊C27 | Direct product of C2 and C7⋊C27 | 378 | 3 | C2xC7:C27 | 378,2 |
C3×S3×C7⋊C3 | Direct product of C3, S3 and C7⋊C3 | 42 | 6 | C3xS3xC7:C3 | 378,48 |
C3⋊S3×C7⋊C3 | Direct product of C3⋊S3 and C7⋊C3 | 63 | | C3:S3xC7:C3 | 378,50 |
C3×C6×C7⋊C3 | Direct product of C3×C6 and C7⋊C3 | 126 | | C3xC6xC7:C3 | 378,52 |
| | d | ρ | Label | ID |
---|
C392 | Cyclic group | 392 | 1 | C392 | 392,2 |
C72⋊C8 | The semidirect product of C72 and C8 acting faithfully | 28 | 8+ | C7^2:C8 | 392,36 |
Dic7⋊2D7 | The semidirect product of Dic7 and D7 acting through Inn(Dic7) | 28 | 4+ | Dic7:2D7 | 392,19 |
C72⋊2C8 | The semidirect product of C72 and C8 acting via C8/C2=C4 | 56 | 4- | C7^2:2C8 | 392,17 |
C49⋊C8 | The semidirect product of C49 and C8 acting via C8/C4=C2 | 392 | 2 | C49:C8 | 392,1 |
C72⋊4C8 | 2nd semidirect product of C72 and C8 acting via C8/C4=C2 | 392 | | C7^2:4C8 | 392,15 |
C7.F8 | The central extension by C7 of F8 | 98 | 7 | C7.F8 | 392,11 |
C7×C56 | Abelian group of type [7,56] | 392 | | C7xC56 | 392,16 |
C2×C196 | Abelian group of type [2,196] | 392 | | C2xC196 | 392,8 |
C14×C28 | Abelian group of type [14,28] | 392 | | C14xC28 | 392,33 |
C22×C98 | Abelian group of type [2,2,98] | 392 | | C2^2xC98 | 392,13 |
C2×C142 | Abelian group of type [2,14,14] | 392 | | C2xC14^2 | 392,44 |
C7×F8 | Direct product of C7 and F8 | 56 | 7 | C7xF8 | 392,39 |
D7×C28 | Direct product of C28 and D7 | 56 | 2 | D7xC28 | 392,24 |
D7×Dic7 | Direct product of D7 and Dic7 | 56 | 4- | D7xDic7 | 392,18 |
C14×Dic7 | Direct product of C14 and Dic7 | 56 | | C14xDic7 | 392,26 |
C4×D49 | Direct product of C4 and D49 | 196 | 2 | C4xD49 | 392,4 |
C22×D49 | Direct product of C22 and D49 | 196 | | C2^2xD49 | 392,12 |
C2×Dic49 | Direct product of C2 and Dic49 | 392 | | C2xDic49 | 392,6 |
C2×D72 | Direct product of C2, D7 and D7 | 28 | 4+ | C2xD7^2 | 392,41 |
C2×C72⋊C4 | Direct product of C2 and C72⋊C4 | 28 | 4+ | C2xC7^2:C4 | 392,40 |
C7×C7⋊C8 | Direct product of C7 and C7⋊C8 | 56 | 2 | C7xC7:C8 | 392,14 |
D7×C2×C14 | Direct product of C2×C14 and D7 | 56 | | D7xC2xC14 | 392,42 |
C4×C7⋊D7 | Direct product of C4 and C7⋊D7 | 196 | | C4xC7:D7 | 392,29 |
C22×C7⋊D7 | Direct product of C22 and C7⋊D7 | 196 | | C2^2xC7:D7 | 392,43 |
C2×C7⋊Dic7 | Direct product of C2 and C7⋊Dic7 | 392 | | C2xC7:Dic7 | 392,31 |
| | d | ρ | Label | ID |
---|
C396 | Cyclic group | 396 | 1 | C396 | 396,4 |
D198 | Dihedral group; = C2×D99 | 198 | 2+ | D198 | 396,9 |
Dic99 | Dicyclic group; = C99⋊1C4 | 396 | 2- | Dic99 | 396,3 |
D33⋊S3 | The semidirect product of D33 and S3 acting via S3/C3=C2 | 66 | 4 | D33:S3 | 396,23 |
C32⋊Dic11 | The semidirect product of C32 and Dic11 acting via Dic11/C11=C4 | 66 | 4 | C3^2:Dic11 | 396,18 |
C3⋊Dic33 | The semidirect product of C3 and Dic33 acting via Dic33/C66=C2 | 396 | | C3:Dic33 | 396,15 |
C6×C66 | Abelian group of type [6,66] | 396 | | C6xC66 | 396,30 |
C2×C198 | Abelian group of type [2,198] | 396 | | C2xC198 | 396,10 |
C3×C132 | Abelian group of type [3,132] | 396 | | C3xC132 | 396,16 |
S3×D33 | Direct product of S3 and D33 | 66 | 4+ | S3xD33 | 396,22 |
D9×D11 | Direct product of D9 and D11 | 99 | 4+ | D9xD11 | 396,5 |
S3×C66 | Direct product of C66 and S3 | 132 | 2 | S3xC66 | 396,26 |
A4×C33 | Direct product of C33 and A4 | 132 | 3 | A4xC33 | 396,24 |
C6×D33 | Direct product of C6 and D33 | 132 | 2 | C6xD33 | 396,27 |
Dic3×C33 | Direct product of C33 and Dic3 | 132 | 2 | Dic3xC33 | 396,12 |
C3×Dic33 | Direct product of C3 and Dic33 | 132 | 2 | C3xDic33 | 396,13 |
D9×C22 | Direct product of C22 and D9 | 198 | 2 | D9xC22 | 396,8 |
C18×D11 | Direct product of C18 and D11 | 198 | 2 | C18xD11 | 396,7 |
C11×Dic9 | Direct product of C11 and Dic9 | 396 | 2 | C11xDic9 | 396,1 |
C9×Dic11 | Direct product of C9 and Dic11 | 396 | 2 | C9xDic11 | 396,2 |
C32×Dic11 | Direct product of C32 and Dic11 | 396 | | C3^2xDic11 | 396,11 |
S32×C11 | Direct product of C11, S3 and S3 | 66 | 4 | S3^2xC11 | 396,21 |
C3×S3×D11 | Direct product of C3, S3 and D11 | 66 | 4 | C3xS3xD11 | 396,19 |
C11×C32⋊C4 | Direct product of C11 and C32⋊C4 | 66 | 4 | C11xC3^2:C4 | 396,17 |
C3⋊S3×D11 | Direct product of C3⋊S3 and D11 | 99 | | C3:S3xD11 | 396,20 |
C3×C6×D11 | Direct product of C3×C6 and D11 | 198 | | C3xC6xD11 | 396,25 |
C3⋊S3×C22 | Direct product of C22 and C3⋊S3 | 198 | | C3:S3xC22 | 396,28 |
C2×C3⋊D33 | Direct product of C2 and C3⋊D33 | 198 | | C2xC3:D33 | 396,29 |
C11×C3.A4 | Direct product of C11 and C3.A4 | 198 | 3 | C11xC3.A4 | 396,6 |
C11×C3⋊Dic3 | Direct product of C11 and C3⋊Dic3 | 396 | | C11xC3:Dic3 | 396,14 |
| | d | ρ | Label | ID |
---|
C400 | Cyclic group | 400 | 1 | C400 | 400,2 |
C52⋊3C42 | 2nd semidirect product of C52 and C42 acting via C42/C2=C2×C4 | 20 | 8+ | C5^2:3C4^2 | 400,124 |
C24⋊C25 | The semidirect product of C24 and C25 acting via C25/C5=C5 | 50 | 5 | C2^4:C25 | 400,52 |
C52⋊C16 | The semidirect product of C52 and C16 acting via C16/C2=C8 | 80 | 8- | C5^2:C16 | 400,116 |
C52⋊3C16 | 2nd semidirect product of C52 and C16 acting via C16/C4=C4 | 80 | 4 | C5^2:3C16 | 400,57 |
C52⋊5C16 | 4th semidirect product of C52 and C16 acting via C16/C4=C4 | 80 | 4 | C5^2:5C16 | 400,59 |
D25⋊C8 | The semidirect product of D25 and C8 acting via C8/C4=C2 | 200 | 4 | D25:C8 | 400,28 |
C25⋊C16 | The semidirect product of C25 and C16 acting via C16/C4=C4 | 400 | 4 | C25:C16 | 400,3 |
C25⋊2C16 | The semidirect product of C25 and C16 acting via C16/C8=C2 | 400 | 2 | C25:2C16 | 400,1 |
C52⋊7C16 | 2nd semidirect product of C52 and C16 acting via C16/C8=C2 | 400 | | C5^2:7C16 | 400,50 |
C52⋊4C16 | 3rd semidirect product of C52 and C16 acting via C16/C4=C4 | 400 | | C5^2:4C16 | 400,58 |
C20.11F5 | 11st non-split extension by C20 of F5 acting via F5/C5=C4 | 40 | 4 | C20.11F5 | 400,156 |
C20.29D10 | 3rd non-split extension by C20 of D10 acting via D10/D5=C2 | 40 | 4 | C20.29D10 | 400,61 |
Dic5.4F5 | The non-split extension by Dic5 of F5 acting through Inn(Dic5) | 40 | 8+ | Dic5.4F5 | 400,121 |
D10.2F5 | 2nd non-split extension by D10 of F5 acting via F5/D5=C2 | 80 | 8- | D10.2F5 | 400,127 |
C20.14F5 | 3rd non-split extension by C20 of F5 acting via F5/D5=C2 | 80 | 4 | C20.14F5 | 400,142 |
C20.F5 | 10th non-split extension by C20 of F5 acting via F5/C5=C4 | 200 | | C20.F5 | 400,149 |
C202 | Abelian group of type [20,20] | 400 | | C20^2 | 400,108 |
C5×C80 | Abelian group of type [5,80] | 400 | | C5xC80 | 400,51 |
C4×C100 | Abelian group of type [4,100] | 400 | | C4xC100 | 400,20 |
C2×C200 | Abelian group of type [2,200] | 400 | | C2xC200 | 400,23 |
C10×C40 | Abelian group of type [10,40] | 400 | | C10xC40 | 400,111 |
C23×C50 | Abelian group of type [2,2,2,50] | 400 | | C2^3xC50 | 400,55 |
C22×C100 | Abelian group of type [2,2,100] | 400 | | C2^2xC100 | 400,45 |
C22×C102 | Abelian group of type [2,2,10,10] | 400 | | C2^2xC10^2 | 400,221 |
C2×C10×C20 | Abelian group of type [2,10,20] | 400 | | C2xC10xC20 | 400,201 |
F52 | Direct product of F5 and F5; = Hol(F5) | 20 | 16+ | F5^2 | 400,205 |
D5×C40 | Direct product of C40 and D5 | 80 | 2 | D5xC40 | 400,76 |
C20×F5 | Direct product of C20 and F5 | 80 | 4 | C20xF5 | 400,137 |
Dic52 | Direct product of Dic5 and Dic5 | 80 | | Dic5^2 | 400,71 |
Dic5×F5 | Direct product of Dic5 and F5 | 80 | 8- | Dic5xF5 | 400,117 |
Dic5×C20 | Direct product of C20 and Dic5 | 80 | | Dic5xC20 | 400,83 |
C8×D25 | Direct product of C8 and D25 | 200 | 2 | C8xD25 | 400,5 |
C23×D25 | Direct product of C23 and D25 | 200 | | C2^3xD25 | 400,54 |
C4×Dic25 | Direct product of C4 and Dic25 | 400 | | C4xDic25 | 400,11 |
C22×Dic25 | Direct product of C22 and Dic25 | 400 | | C2^2xDic25 | 400,43 |
C2×D5⋊F5 | Direct product of C2 and D5⋊F5 | 20 | 8+ | C2xD5:F5 | 400,210 |
C2×C52⋊C8 | Direct product of C2 and C52⋊C8 | 20 | 8+ | C2xC5^2:C8 | 400,208 |
C4×D52 | Direct product of C4, D5 and D5 | 40 | 4 | C4xD5^2 | 400,169 |
C2×D5×F5 | Direct product of C2, D5 and F5 | 40 | 8+ | C2xD5xF5 | 400,209 |
C22×D52 | Direct product of C22, D5 and D5 | 40 | | C2^2xD5^2 | 400,218 |
C4×C52⋊C4 | Direct product of C4 and C52⋊C4 | 40 | 4 | C4xC5^2:C4 | 400,158 |
C22×C52⋊C4 | Direct product of C22 and C52⋊C4 | 40 | | C2^2xC5^2:C4 | 400,217 |
C2×Dic5⋊2D5 | Direct product of C2 and Dic5⋊2D5 | 40 | | C2xDic5:2D5 | 400,175 |
C5×C24⋊C5 | Direct product of C5 and C24⋊C5 | 50 | 5 | C5xC2^4:C5 | 400,213 |
D5×C5⋊C8 | Direct product of D5 and C5⋊C8 | 80 | 8- | D5xC5:C8 | 400,120 |
C5×C5⋊C16 | Direct product of C5 and C5⋊C16 | 80 | 4 | C5xC5:C16 | 400,56 |
C10×C5⋊C8 | Direct product of C10 and C5⋊C8 | 80 | | C10xC5:C8 | 400,139 |
D5×C2×C20 | Direct product of C2×C20 and D5 | 80 | | D5xC2xC20 | 400,182 |
F5×C2×C10 | Direct product of C2×C10 and F5 | 80 | | F5xC2xC10 | 400,214 |
C5×D5⋊C8 | Direct product of C5 and D5⋊C8 | 80 | 4 | C5xD5:C8 | 400,135 |
D5×C5⋊2C8 | Direct product of D5 and C5⋊2C8 | 80 | 4 | D5xC5:2C8 | 400,60 |
C2×D5×Dic5 | Direct product of C2, D5 and Dic5 | 80 | | C2xD5xDic5 | 400,172 |
C5×C5⋊2C16 | Direct product of C5 and C5⋊2C16 | 80 | 2 | C5xC5:2C16 | 400,49 |
C10×C5⋊2C8 | Direct product of C10 and C5⋊2C8 | 80 | | C10xC5:2C8 | 400,81 |
C4×D5.D5 | Direct product of C4 and D5.D5 | 80 | 4 | C4xD5.D5 | 400,144 |
Dic5×C2×C10 | Direct product of C2×C10 and Dic5 | 80 | | Dic5xC2xC10 | 400,189 |
D5×C22×C10 | Direct product of C22×C10 and D5 | 80 | | D5xC2^2xC10 | 400,219 |
C2×C52⋊3C8 | Direct product of C2 and C52⋊3C8 | 80 | | C2xC5^2:3C8 | 400,146 |
C2×C52⋊5C8 | Direct product of C2 and C52⋊5C8 | 80 | | C2xC5^2:5C8 | 400,160 |
C22×D5.D5 | Direct product of C22 and D5.D5 | 80 | | C2^2xD5.D5 | 400,215 |
C4×C25⋊C4 | Direct product of C4 and C25⋊C4 | 100 | 4 | C4xC25:C4 | 400,30 |
C4×C5⋊F5 | Direct product of C4 and C5⋊F5 | 100 | | C4xC5:F5 | 400,151 |
C22×C25⋊C4 | Direct product of C22 and C25⋊C4 | 100 | | C2^2xC25:C4 | 400,53 |
C22×C5⋊F5 | Direct product of C22 and C5⋊F5 | 100 | | C2^2xC5:F5 | 400,216 |
C8×C5⋊D5 | Direct product of C8 and C5⋊D5 | 200 | | C8xC5:D5 | 400,92 |
C2×C4×D25 | Direct product of C2×C4 and D25 | 200 | | C2xC4xD25 | 400,36 |
C23×C5⋊D5 | Direct product of C23 and C5⋊D5 | 200 | | C2^3xC5:D5 | 400,220 |
C2×C25⋊C8 | Direct product of C2 and C25⋊C8 | 400 | | C2xC25:C8 | 400,32 |
C2×C25⋊2C8 | Direct product of C2 and C25⋊2C8 | 400 | | C2xC25:2C8 | 400,9 |
C2×C52⋊7C8 | Direct product of C2 and C52⋊7C8 | 400 | | C2xC5^2:7C8 | 400,97 |
C4×C52⋊6C4 | Direct product of C4 and C52⋊6C4 | 400 | | C4xC5^2:6C4 | 400,99 |
C2×C52⋊4C8 | Direct product of C2 and C52⋊4C8 | 400 | | C2xC5^2:4C8 | 400,153 |
C22×C52⋊6C4 | Direct product of C22 and C52⋊6C4 | 400 | | C2^2xC5^2:6C4 | 400,199 |
C2×C4×C5⋊D5 | Direct product of C2×C4 and C5⋊D5 | 200 | | C2xC4xC5:D5 | 400,192 |
| | d | ρ | Label | ID |
---|
C408 | Cyclic group | 408 | 1 | C408 | 408,4 |
C51⋊C8 | 1st semidirect product of C51 and C8 acting faithfully | 51 | 8 | C51:C8 | 408,34 |
D51⋊2C4 | The semidirect product of D51 and C4 acting via C4/C2=C2 | 204 | 4+ | D51:2C4 | 408,9 |
C51⋊5C8 | 1st semidirect product of C51 and C8 acting via C8/C4=C2 | 408 | 2 | C51:5C8 | 408,3 |
C51⋊3C8 | 1st semidirect product of C51 and C8 acting via C8/C2=C4 | 408 | 4 | C51:3C8 | 408,6 |
C2×C204 | Abelian group of type [2,204] | 408 | | C2xC204 | 408,30 |
C22×C102 | Abelian group of type [2,2,102] | 408 | | C2^2xC102 | 408,46 |
A4×D17 | Direct product of A4 and D17 | 68 | 6+ | A4xD17 | 408,38 |
A4×C34 | Direct product of C34 and A4 | 102 | 3 | A4xC34 | 408,42 |
S3×C68 | Direct product of C68 and S3 | 204 | 2 | S3xC68 | 408,21 |
C4×D51 | Direct product of C4 and D51 | 204 | 2 | C4xD51 | 408,26 |
C12×D17 | Direct product of C12 and D17 | 204 | 2 | C12xD17 | 408,16 |
Dic3×D17 | Direct product of Dic3 and D17 | 204 | 4- | Dic3xD17 | 408,7 |
S3×Dic17 | Direct product of S3 and Dic17 | 204 | 4- | S3xDic17 | 408,8 |
C22×D51 | Direct product of C22 and D51 | 204 | | C2^2xD51 | 408,45 |
C6×Dic17 | Direct product of C6 and Dic17 | 408 | | C6xDic17 | 408,18 |
Dic3×C34 | Direct product of C34 and Dic3 | 408 | | Dic3xC34 | 408,23 |
C2×Dic51 | Direct product of C2 and Dic51 | 408 | | C2xDic51 | 408,28 |
C3×C17⋊C8 | Direct product of C3 and C17⋊C8 | 51 | 8 | C3xC17:C8 | 408,33 |
S3×C17⋊C4 | Direct product of S3 and C17⋊C4 | 51 | 8+ | S3xC17:C4 | 408,35 |
C6×C17⋊C4 | Direct product of C6 and C17⋊C4 | 102 | 4 | C6xC17:C4 | 408,39 |
C2×S3×D17 | Direct product of C2, S3 and D17 | 102 | 4+ | C2xS3xD17 | 408,41 |
C2×C51⋊C4 | Direct product of C2 and C51⋊C4 | 102 | 4 | C2xC51:C4 | 408,40 |
S3×C2×C34 | Direct product of C2×C34 and S3 | 204 | | S3xC2xC34 | 408,44 |
C2×C6×D17 | Direct product of C2×C6 and D17 | 204 | | C2xC6xD17 | 408,43 |
C17×C3⋊C8 | Direct product of C17 and C3⋊C8 | 408 | 2 | C17xC3:C8 | 408,1 |
C3×C17⋊3C8 | Direct product of C3 and C17⋊3C8 | 408 | 2 | C3xC17:3C8 | 408,2 |
C3×C17⋊2C8 | Direct product of C3 and C17⋊2C8 | 408 | 4 | C3xC17:2C8 | 408,5 |