Finite Group DatabasebetaFinite Group DatabasebetaOrder 33620.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #30681146 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22554263 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #20269609 | — | 5 | 1 | no | maximal, Hall |
| 4 | C41⋊D41 | D5 | 1 | 1 | yes | characteristic |
| 5 | C412 | Dic5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | D41⋊C5 | — | 82 | 1 | no | — |
| 7 | C41⋊C5 | — | 82 | 1 | no | — |
| 8 | #4223 | — | 205 | 2 | no | — |
| 9 | D41 | — | 82 | 1 | no | — |
| 10 | D41 | — | 410 | 3 | no | — |
| 11 | D41 | — | 205 | 2 | no | — |
| 12 | C41 | — | 2 | 1 | no | — |
| 13 | C41 | — | 5 | 2 | no | — |
| 14 | C41 | — | 10 | 3 | no | — |
| 15 | Dic5 | — | 1681 | 1 | no | maximal, Hall |
| 16 | C2×C5 | — | 1681 | 1 | no | — |
| 17 | C5 | — | 1681 | 1 | no | Sylow |
| 18 | C4 | — | 8405 | 1 | no | Sylow |
| 19 | C2 | — | 1681 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | #22554263 | C4 |
| Fitting, socle | C412 | Dic5 |
| prime radical, cosocle | #30681146 | C2 |
| LCS | G ▷ #22554263 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22554263 | C4 | semidirect |
| 5. C412 | Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30681146 | 2 |
| #20269609 | 5 |
| Dic5 | 1681 |