Finite Group DatabasebetaFinite Group DatabasebetaOrder 32065.
20 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C112×C53 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C53×C11⋊C5 | — | 11 | 2 | no | maximal |
| 3 | #10597244 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | C11×C53 | — | 5 | 2 | no | — |
| 5 | C11×C53 | C11⋊C5 | 1 | 2 | yes | complemented |
| 6 | C5×C53 | — | 121 | 1 | no | Hall |
| 7 | C112 | C5×C53 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C11⋊C5 | — | 11 | 2 | no | — |
| 9 | C53 | #10597244 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 10 | C11 | — | 5 | 2 | no | — |
| 11 | C11 | C53×C11⋊C5 | 1 | 2 | yes | complemented |
| 12 | C5 | — | 121 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | #10597244 |
| commutator, cosocle, hypocenter | C112 | C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C112×C53 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C53 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C112×C53 | C5 | semidirect |
| 3. #10597244 | C53 | direct (N × H) |
| 5. C11×C53 | C11⋊C5 | semidirect |
| 7. C112 | C5×C53 | semidirect |
| 9. C53 | #10597244 | direct (N × H) |
| 11. C11 | C53×C11⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C112×C53 | 5 |
| C53×C11⋊C5 | 11 |
| #10597244 | 53 |