Finite Group DatabasebetaFinite Group DatabasebetaOrder 30422.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×C41×C53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D2173 | — | 7 | 1 | no | maximal, Hall |
| 3 | C41×C53 | D7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D371 | — | 41 | 1 | no | maximal, Hall |
| 5 | D287 | — | 53 | 1 | no | maximal, Hall |
| 6 | C7×C53 | D41 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C7×C41 | D53 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D53 | — | 287 | 1 | no | Hall |
| 9 | D41 | — | 371 | 1 | no | Hall |
| 10 | C53 | D287 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C41 | D371 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D7 | — | 2173 | 1 | no | Hall |
| 13 | C7 | D2173 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 15211 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C41×C53 | C2 |
| LCS | G ▷ C7×C41×C53 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×C41×C53 | C2 | semidirect |
| 3. C41×C53 | D7 | semidirect |
| 6. C7×C53 | D41 | semidirect |
| 7. C7×C41 | D53 | semidirect |
| 10. C53 | D287 | semidirect |
| 11. C41 | D371 | semidirect |
| 13. C7 | D2173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C41×C53 | 2 |
| D2173 | 7 |
| D371 | 41 |
| D287 | 53 |