Finite Group DatabasebetaFinite Group DatabasebetaOrder 60952.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic7619 | C2 | 1 | 2 | yes | maximal |
| 2 | C4×C19×C401 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C19×C401 | C22 | 1 | 1 | yes | characteristic |
| 4 | C19×C401 | Q8 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | Dic802 | — | 19 | 1 | no | maximal, Hall |
| 6 | C4×C401 | D19 | 1 | 1 | yes | characteristic |
| 7 | Dic401 | — | 19 | 2 | no | — |
| 8 | C2×C401 | C2×D19 | 1 | 1 | yes | characteristic |
| 9 | C401 | Dic38 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | Dic38 | — | 401 | 1 | no | maximal, Hall |
| 11 | C4×C19 | D401 | 1 | 1 | yes | characteristic |
| 12 | Dic19 | — | 401 | 2 | no | — |
| 13 | C2×C19 | C2×D401 | 1 | 1 | yes | characteristic |
| 14 | C19 | Dic802 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | Q8 | — | 7619 | 1 | no | Sylow |
| 16 | C4 | — | 7619 | 2 | no | — |
| 17 | C4 | D7619 | 1 | 1 | yes | characteristic |
| 18 | C2 | C2×D7619 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D7619 |
| commutator, socle, prime radical, cosocle | C2×C19×C401 | C22 |
| Fitting | C4×C19×C401 | C2 |
| hypercenter | C4 | D7619 |
| hypocenter | C19×C401 | Q8 |
| LCS | G ▷ C2×C19×C401 ▷ C19×C401 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C19×C401 | Q8 | semidirect |
| 9. C401 | Dic38 | semidirect |
| 14. C19 | Dic802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic7619 | 2 |
| C4×C19×C401 | 2 |
| Dic802 | 19 |
| Dic38 | 401 |