Finite Group DatabasebetaFinite Group DatabasebetaOrder 36905.
20 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C112×C61 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | #16809822 | C11 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 3 | C11×C61⋊C5 | — | 11 | 1 | no | maximal |
| 4 | C11×C61 | — | 5 | 2 | no | — |
| 5 | C11×C61 | C11⋊C5 | 1 | 1 | yes | characteristic, complemented |
| 6 | C11×C61 | C5×C11 | 1 | 1 | yes | characteristic, complemented |
| 7 | C11×C11⋊C5 | — | 61 | 1 | no | maximal, Hall |
| 8 | C61⋊C5 | — | 11 | 1 | no | Hall |
| 9 | C112 | C61⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C61 | C11×C11⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C5×C11 | — | 671 | 1 | no | — |
| 12 | C11⋊C5 | — | 61 | 1 | no | — |
| 13 | C11 | — | 5 | 2 | no | — |
| 14 | C11 | C11×C61⋊C5 | 1 | 1 | yes | characteristic, complemented |
| 15 | C11 | #16809822 | 1 | 1 | yes | characteristic, direct product factor |
| 16 | C5 | — | 671 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #16809822 |
| commutator, cosocle, hypocenter | C11×C61 | C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C61 | C5 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C112×C61 | C5 | semidirect |
| 2. #16809822 | C11 | direct (N × H) |
| 5. C11×C61 | C11⋊C5 | semidirect |
| 6. C11×C61 | C5×C11 | semidirect |
| 9. C112 | C61⋊C5 | semidirect |
| 10. C61 | C11×C11⋊C5 | semidirect |
| 14. C11 | C11×C61⋊C5 | semidirect |
| 15. C11 | #16809822 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C112×C61 | 5 |
| #16809822 | 11 |
| C11×C61⋊C5 | 11 |
| C11×C11⋊C5 | 61 |