Finite Group DatabasebetaFinite Group DatabasebetaOrder 10725.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C52×C11×C13 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C13⋊(C52⋊C3) | C11 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 3 | C11×C52⋊C3 | — | 13 | 1 | no | maximal, Hall |
| 4 | C5×C11×C13 | — | 3 | 2 | no | — |
| 5 | C11×C13⋊C3 | — | 25 | 1 | no | maximal, Hall |
| 6 | C52×C13 | C3×C11 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C52×C11 | C13⋊C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C11×C13 | C52⋊C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C52⋊C3 | — | 13 | 1 | no | Hall |
| 10 | C5×C13 | — | 3 | 2 | no | — |
| 11 | C5×C11 | — | 3 | 2 | no | — |
| 12 | C13⋊C3 | — | 25 | 1 | no | Hall |
| 13 | C3×C11 | — | 325 | 1 | no | Hall |
| 14 | C52 | C11×C13⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | C13 | C11×C52⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C11 | C13⋊(C52⋊C3) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 17 | C5 | — | 3 | 2 | no | — |
| 18 | C3 | — | 325 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C13⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C13 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11×C13 | C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×C11×C13 | C3 | semidirect |
| 2. C13⋊(C52⋊C3) | C11 | direct (N × H) |
| 6. C52×C13 | C3×C11 | semidirect |
| 7. C52×C11 | C13⋊C3 | semidirect |
| 8. C11×C13 | C52⋊C3 | semidirect |
| 14. C52 | C11×C13⋊C3 | semidirect |
| 15. C13 | C11×C52⋊C3 | semidirect |
| 16. C11 | C13⋊(C52⋊C3) | direct (N × H) |