Finite Group DatabasebetaFinite Group DatabasebetaOrder 25821.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C19×C151 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22575305 | C3 | 1 | 3 | yes | maximal, direct product factor |
| 3 | C19×C151 | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C3×C151⋊C3 | — | 19 | 1 | no | maximal, Hall |
| 5 | C3×C151 | C19⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 6 | C151⋊C3 | — | 19 | 3 | no | — |
| 7 | C3×C19⋊C3 | — | 151 | 1 | no | maximal, Hall |
| 8 | C151 | C3×C19⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C3×C19 | C151⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C19⋊C3 | — | 151 | 3 | no | — |
| 11 | C19 | C3×C151⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C32 | — | 2869 | 1 | no | Sylow |
| 13 | C3 | — | 2869 | 3 | no | — |
| 14 | C3 | #22575305 | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #22575305 |
| commutator, cosocle, hypocenter | C19×C151 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C151 | C3 |
| LCS | G ▷ C19×C151 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C19×C151 | C3 | semidirect |
| 2. #22575305 | C3 | direct (N × H) |
| 3. C19×C151 | C32 | semidirect |
| 5. C3×C151 | C19⋊C3 | semidirect |
| 8. C151 | C3×C19⋊C3 | semidirect |
| 9. C3×C19 | C151⋊C3 | semidirect |
| 11. C19 | C3×C151⋊C3 | semidirect |
| 14. C3 | #22575305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C19×C151 | 3 |
| #22575305 | 3 |
| C3×C151⋊C3 | 19 |
| C3×C19⋊C3 | 151 |