Finite Group DatabasebetaFinite Group DatabasebetaOrder 10404.
30 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3⋊D3×C289 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C32×C289 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | D3×C289 | — | 6 | 2 | no | — |
| 4 | C4×C289 | — | 9 | 1 | no | maximal, Hall |
| 5 | C3×C289 | — | 2 | 2 | no | — |
| 6 | C17×#157 | C17 | 1 | 1 | yes | maximal, characteristic |
| 7 | C2×C289 | — | 9 | 1 | no | — |
| 8 | C17×C3⋊D3 | C2×C17 | 1 | 1 | yes | characteristic |
| 9 | C289 | #157 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 10 | C32×C17 | C4×C17 | 1 | 1 | yes | characteristic |
| 11 | D3×C17 | — | 6 | 2 | no | — |
| 12 | C4×C17 | — | 9 | 1 | no | — |
| 13 | C3×C17 | — | 2 | 2 | no | — |
| 14 | #157 | C289 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 15 | C2×C17 | — | 9 | 1 | no | — |
| 16 | C3⋊D3 | C2×C289 | 1 | 1 | yes | characteristic |
| 17 | C17 | C17×#157 | 1 | 1 | yes | characteristic |
| 18 | C32 | C4×C289 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 19 | D3 | — | 6 | 2 | no | — |
| 20 | C4 | — | 9 | 1 | no | Sylow |
| 21 | C3 | — | 2 | 2 | no | — |
| 22 | C2 | — | 9 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | #157 |
| commutator, hypocenter | C32 | C4×C289 |
| Frattini | C17 | C17×#157 |
| Fitting | C32×C289 | C4 |
| socle | C32×C17 | C4×C17 |
| prime radical, cosocle | C17×C3⋊D3 | C2×C17 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C289 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×C289 | C4 | semidirect |
| 9. C289 | #157 | direct (N × H) |
| 14. #157 | C289 | direct (N × H) |
| 18. C32 | C4×C289 | semidirect |