Finite Group DatabasebetaFinite Group DatabasebetaOrder 19220.
18 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C5×C961 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×C961 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | Dic961 | — | 5 | 1 | no | maximal, Hall |
| 4 | C2×C961 | D5 | 1 | 1 | yes | characteristic |
| 5 | C961 | Dic5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | Dic155 | — | 31 | 1 | no | maximal |
| 7 | C2×C5×C31 | D31 | 1 | 1 | yes | characteristic |
| 8 | C5×C31 | Dic31 | 1 | 1 | yes | characteristic |
| 9 | Dic31 | — | 155 | 1 | no | — |
| 10 | C2×C31 | D155 | 1 | 1 | yes | characteristic |
| 11 | C31 | Dic155 | 1 | 1 | yes | characteristic |
| 12 | Dic5 | — | 961 | 1 | no | Hall |
| 13 | C2×C5 | D961 | 1 | 1 | yes | characteristic |
| 14 | C5 | Dic961 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | C4 | — | 4805 | 1 | no | Sylow |
| 16 | C2 | D4805 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D4805 |
| commutator, hypocenter | C5×C961 | C4 |
| Frattini | C2×C31 | D155 |
| Fitting, cosocle | C2×C5×C961 | C2 |
| socle, prime radical | C2×C5×C31 | D31 |
| LCS | G ▷ C5×C961 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×C961 | C4 | semidirect |
| 5. C961 | Dic5 | semidirect |
| 14. C5 | Dic961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C961 | 2 |
| Dic961 | 5 |
| Dic155 | 31 |