Finite Group DatabasebetaFinite Group DatabasebetaOrder 32395.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×C19×C31 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C19×ΓL(1,𝔽32) | — | 11 | 1 | no | maximal, Hall |
| 3 | #13133723 | C19 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | C19×C11⋊C5 | — | 31 | 1 | no | maximal, Hall |
| 5 | C19×C31 | C11⋊C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C11×C31 | C5×C19 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C11×C19 | ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | ΓL(1,𝔽32) | — | 11 | 1 | no | Hall |
| 9 | C5×C19 | — | 341 | 1 | no | Hall |
| 10 | C11⋊C5 | — | 31 | 1 | no | Hall |
| 11 | C31 | C19×C11⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C19 | #13133723 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 13 | C11 | C19×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C5 | — | 341 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #13133723 |
| commutator, cosocle, hypocenter | C11×C31 | C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C11×C19×C31 | C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C19 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×C19×C31 | C5 | semidirect |
| 3. #13133723 | C19 | direct (N × H) |
| 5. C19×C31 | C11⋊C5 | semidirect |
| 6. C11×C31 | C5×C19 | semidirect |
| 7. C11×C19 | ΓL(1,𝔽32) | semidirect |
| 11. C31 | C19×C11⋊C5 | semidirect |
| 12. C19 | #13133723 | direct (N × H) |
| 13. C11 | C19×ΓL(1,𝔽32) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×C19×C31 | 5 |
| C19×ΓL(1,𝔽32) | 11 |
| #13133723 | 19 |
| C19×C11⋊C5 | 31 |