Finite Group DatabasebetaFinite Group DatabasebetaOrder 24915.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22552175 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C11×C151⋊C3 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | (C151⋊C3)⋊C5 | — | 11 | 1 | no | maximal, Hall |
| 4 | C11×C151 | C3×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C151⋊C5 | — | 11 | 1 | no | Hall |
| 6 | C151⋊C3 | C11⋊C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C3×C11⋊C5 | — | 151 | 1 | no | maximal, Hall |
| 8 | C151 | C3×C11⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C11⋊C5 | — | 151 | 1 | no | Hall |
| 10 | C3×C11 | — | 755 | 1 | no | Hall |
| 11 | C3×C5 | — | 1661 | 1 | no | Hall |
| 12 | C11 | (C151⋊C3)⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C5 | — | 1661 | 1 | no | Sylow |
| 14 | C3 | — | 755 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C151 | C3×C5 |
| LCS | G ▷ C11×C151 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22552175 | C3 | semidirect |
| 2. C11×C151⋊C3 | C5 | semidirect |
| 4. C11×C151 | C3×C5 | semidirect |
| 6. C151⋊C3 | C11⋊C5 | semidirect |
| 8. C151 | C3×C11⋊C5 | semidirect |
| 12. C11 | (C151⋊C3)⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22552175 | 3 |
| C11×C151⋊C3 | 5 |
| (C151⋊C3)⋊C5 | 11 |
| C3×C11⋊C5 | 151 |