Finite Group DatabasebetaFinite Group DatabasebetaOrder 23954.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C59×C29⋊C7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C29×D59 | C7 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C29×C59 | C2×C7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C7×D59 | — | 29 | 1 | no | maximal, Hall |
| 5 | C7×C59 | — | 29 | 1 | no | Hall |
| 6 | C2×C29⋊C7 | — | 59 | 1 | no | maximal, Hall |
| 7 | C29⋊C7 | D59 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 8 | D59 | C29⋊C7 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 9 | C59 | C2×C29⋊C7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C2×C29 | — | 59 | 1 | no | Hall |
| 11 | C29 | C7×D59 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C2×C7 | — | 1711 | 1 | no | Hall |
| 13 | C7 | — | 29 | 1 | no | Sylow |
| 14 | C2 | — | 59 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C59 | C2×C7 |
| LCS | G ▷ C29×C59 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×C29⋊C7 | C2 | semidirect |
| 2. C29×D59 | C7 | semidirect |
| 3. C29×C59 | C2×C7 | semidirect |
| 7. C29⋊C7 | D59 | direct (N × H) |
| 8. D59 | C29⋊C7 | direct (N × H) |
| 9. C59 | C2×C29⋊C7 | semidirect |
| 11. C29 | C7×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×C29⋊C7 | 2 |
| C29×D59 | 7 |
| C7×D59 | 29 |
| C2×C29⋊C7 | 59 |