Finite Group DatabasebetaFinite Group Databasebeta← C22⋊(C52⋊(C31⋊C3)) #22604928
Order 9300.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×C52×C31 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C52⋊(C31⋊C3) | — | 4 | 1 | no | maximal, Hall |
| 3 | C2×C52×C31 | — | 3 | 1 | no | — |
| 4 | C52×C31 | A4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C22×C5×C31 | — | 3 | 2 | no | — |
| 6 | C22⋊(C31⋊C3) | — | 25 | 1 | no | maximal, Hall |
| 7 | C2×C5×C31 | — | 3 | 6 | no | — |
| 8 | C22⋊(C52⋊C3) | — | 31 | 1 | no | maximal, Hall |
| 9 | C5×C31 | — | 3 | 2 | no | — |
| 10 | C22×C31 | C52⋊C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 11 | C22×C52 | C31⋊C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 12 | C31⋊C3 | — | 100 | 1 | no | Hall |
| 13 | C52⋊C3 | — | 124 | 1 | no | Hall |
| 14 | C2×C31 | — | 3 | 1 | no | — |
| 15 | C2×C52 | — | 3 | 1 | no | — |
| 16 | C31 | C22⋊(C52⋊C3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 17 | C52 | C22⋊(C31⋊C3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 18 | C22×C5 | — | 3 | 2 | no | — |
| 19 | A4 | — | 775 | 1 | no | Hall |
| 20 | C2×C5 | — | 3 | 6 | no | — |
| 21 | C5 | — | 3 | 2 | no | — |
| 22 | C22 | C52⋊(C31⋊C3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 23 | C3 | — | 3100 | 1 | no | Sylow |
| 24 | C2 | — | 3 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C52×C31 | C3 |
| LCS | G ▷ C22×C52×C31 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×C31 | C3 | semidirect |
| 4. C52×C31 | A4 | semidirect |
| 10. C22×C31 | C52⋊C3 | semidirect |
| 11. C22×C52 | C31⋊C3 | semidirect |
| 16. C31 | C22⋊(C52⋊C3) | semidirect |
| 17. C52 | C22⋊(C31⋊C3) | semidirect |
| 22. C22 | C52⋊(C31⋊C3) | semidirect |