Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
668 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #535 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×D12 | C2 | semidirect |
| 2. C2×C3×#709 | C2 | semidirect |
| 3. #91815 | C2 | semidirect |
| 4. #91568 | C2 | semidirect |
| 5. #91463 | C2 | semidirect |
| 6. #91449 | C2 | semidirect |
| 7. #91370 | C2 | semidirect |
| 16. C2×C3×D20 | C22 | semidirect |
| 17. C2×C3×C4×D5 | C22 | semidirect |
| 18. C2×C3×Dic10 | C22 | semidirect |
| 19. C2×#1201 | C22 | semidirect |
| 21. C4⋊Dic15 | C22 | semidirect |
| 22. C4×Dic15 | C22 | semidirect |
| 23. (C2×D3)⋊Dic5 | C22 | semidirect |
| 26. C2×#709 | D3 | semidirect |
| 37. C2×C3×C4×C5 | D4 | semidirect |
| 50. C22×D12 | D5 | semidirect |
| 64. C2×D20 | C2×D3 | semidirect |
| 65. C2×C4×D5 | C2×D3 | semidirect |
| 66. C2×Dic10 | C2×D3 | semidirect |
| 106. C2×C4×C5 | #67 | semidirect |
| 138. C2×C3×C4 | C22⋊D5 | semidirect |
| 172. C3×C5 | #535 | semidirect |
| 204. C2×C4 | #1201 | semidirect |
| 212. C5 | #5830 | semidirect |
| 225. C3 | #66139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D12 | 2 |
| C2×C3×#709 | 2 |
| #91815 | 2 |
| #91568 | 2 |
| #91463 | 2 |
| #91449 | 2 |
| #91370 | 2 |
| #66139 | 3 |
| #5830 | 5 |