Finite Group DatabasebetaFinite Group DatabasebetaOrder 7514.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C13×C289 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D289 | C13 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 3 | C13×D17 | — | 17 | 1 | no | maximal |
| 4 | C289 | C2×C13 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 5 | C13×C17 | D17 | 1 | 1 | yes | characteristic |
| 6 | D17 | — | 17 | 1 | no | — |
| 7 | C2×C13 | — | 289 | 1 | no | Hall |
| 8 | C17 | C13×D17 | 1 | 1 | yes | characteristic |
| 9 | C13 | D289 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 10 | C2 | — | 289 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D289 |
| commutator, hypocenter | C289 | C2×C13 |
| Frattini | C17 | C13×D17 |
| Fitting | C13×C289 | C2 |
| socle | C13×C17 | D17 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C13 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×C289 | C2 | semidirect |
| 2. D289 | C13 | direct (N × H) |
| 4. C289 | C2×C13 | semidirect |
| 9. C13 | D289 | direct (N × H) |