Finite Group DatabasebetaFinite Group Databasebeta← C22⋊(#13108656⋊C5) #45656355
Order 32580.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×C3×C181⋊C5 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13108656⋊C5 | — | 4 | 1 | no | maximal, Hall |
| 3 | C22⋊#13108656 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 4 | C2×C3×C181⋊C5 | — | 3 | 1 | no | — |
| 5 | C22×C181⋊C5 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C3×C181⋊C5 | A4 | 1 | 1 | yes | characteristic |
| 7 | C22×C3×C181 | C3×C5 | 1 | 1 | yes | characteristic |
| 8 | C2×C181⋊C5 | — | 3 | 1 | no | — |
| 9 | #13108656 | — | 4 | 1 | no | Hall |
| 10 | C2×C3×C181 | — | 3 | 1 | no | — |
| 11 | C181⋊C5 | C22⋊C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 12 | C22×C181 | C5×C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 13 | C3×C181 | C5×A4 | 1 | 1 | yes | characteristic |
| 14 | C2×C181 | — | 3 | 1 | no | — |
| 15 | C181 | C5×C22⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C5×C22⋊C9 | — | 181 | 1 | no | maximal, Hall |
| 17 | C22×C3×C5 | — | 181 | 1 | no | — |
| 18 | C5×C9 | — | 724 | 1 | no | Hall |
| 19 | C22⋊C9 | — | 181 | 1 | no | Hall |
| 20 | C2×C3×C5 | — | 543 | 1 | no | — |
| 21 | C22×C5 | — | 181 | 1 | no | Hall |
| 22 | C3×C5 | — | 181 | 1 | no | — |
| 23 | C22×C3 | (C181⋊C3)⋊C5 | 1 | 1 | yes | characteristic |
| 24 | C2×C5 | — | 543 | 1 | no | — |
| 25 | C9 | — | 724 | 1 | no | Sylow |
| 26 | C2×C3 | — | 3 | 1 | no | — |
| 27 | C5 | — | 181 | 1 | no | Sylow |
| 28 | C22 | #13108656⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 29 | C3 | C22⋊((C181⋊C3)⋊C5) | 1 | 1 | yes | characteristic |
| 30 | C2 | — | 3 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊((C181⋊C3)⋊C5) |
| commutator, hypocenter | C22×C181 | C5×C9 |
| Fitting, socle, cosocle | C22×C3×C181 | C3×C5 |
| prime radical | C22×C3×C181⋊C5 | C3 |
| LCS | G ▷ C22×C181 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22⋊#13108656 | C5 | semidirect |
| 5. C22×C181⋊C5 | C9 | semidirect |
| 11. C181⋊C5 | C22⋊C9 | semidirect |
| 12. C22×C181 | C5×C9 | semidirect |
| 15. C181 | C5×C22⋊C9 | semidirect |
| 28. C22 | #13108656⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C181⋊C5 | 3 |
| #13108656⋊C5 | 4 |
| C22⋊#13108656 | 5 |
| C5×C22⋊C9 | 181 |