Finite Group DatabasebetaFinite Group DatabasebetaOrder 18755.
20 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C112×C31 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | #13133724 | — | 11 | 1 | no | maximal |
| 3 | #13133722 | — | 11 | 1 | no | maximal |
| 4 | #10597244 | — | 31 | 1 | no | maximal, Hall |
| 5 | C11×C31 | — | 5 | 2 | no | — |
| 6 | C11×C31 | C11⋊C5 | 1 | 1 | yes | characteristic, complemented |
| 7 | C11×C31 | C11⋊C5 | 1 | 1 | yes | characteristic, complemented |
| 8 | ΓL(1,𝔽32) | — | 121 | 1 | no | Hall |
| 9 | C112 | ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C11⋊C5 | — | 341 | 1 | no | — |
| 11 | C11⋊C5 | — | 341 | 1 | no | — |
| 12 | C31 | #10597244 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C11 | — | 5 | 2 | no | — |
| 14 | C11 | #13133722 | 1 | 1 | yes | characteristic, complemented |
| 15 | C11 | #13133724 | 1 | 1 | yes | characteristic, complemented |
| 16 | C5 | — | 3751 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C31 | C5 |
| LCS | G ▷ C112×C31 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C112×C31 | C5 | semidirect |
| 6. C11×C31 | C11⋊C5 | semidirect |
| 7. C11×C31 | C11⋊C5 | semidirect |
| 9. C112 | ΓL(1,𝔽32) | semidirect |
| 12. C31 | #10597244 | semidirect |
| 14. C11 | #13133722 | semidirect |
| 15. C11 | #13133724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C112×C31 | 5 |
| #13133724 | 11 |
| #13133722 | 11 |
| #10597244 | 31 |