Finite Group DatabasebetaFinite Group DatabasebetaOrder 24610.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×C23×C107 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D2461 | — | 5 | 1 | no | maximal, Hall |
| 3 | C23×C107 | D5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D535 | — | 23 | 1 | no | maximal, Hall |
| 5 | C5×C107 | D23 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D115 | — | 107 | 1 | no | maximal, Hall |
| 7 | D107 | — | 115 | 1 | no | Hall |
| 8 | C5×C23 | D107 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C107 | D115 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | D23 | — | 535 | 1 | no | Hall |
| 11 | C23 | D535 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D5 | — | 2461 | 1 | no | Hall |
| 13 | C5 | D2461 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 12305 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C23×C107 | C2 |
| LCS | G ▷ C5×C23×C107 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C23×C107 | C2 | semidirect |
| 3. C23×C107 | D5 | semidirect |
| 5. C5×C107 | D23 | semidirect |
| 8. C5×C23 | D107 | semidirect |
| 9. C107 | D115 | semidirect |
| 11. C23 | D535 | semidirect |
| 13. C5 | D2461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C23×C107 | 2 |
| D2461 | 5 |
| D535 | 23 |
| D115 | 107 |