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×D60 | C2 | semidirect |
| 2. C2×C3×#709 | C2 | semidirect |
| 3. C5×#926 | C2 | semidirect |
| 4. #91572 | C2 | semidirect |
| 5. #91458 | C2 | semidirect |
| 6. #91450 | C2 | semidirect |
| 7. #91374 | C2 | semidirect |
| 16. C2×C3×D20 | C22 | semidirect |
| 17. C2×C3×C4×D5 | C22 | semidirect |
| 18. C2×C3×Dic10 | C22 | semidirect |
| 19. C2×#1202 | C22 | semidirect |
| 21. C5×C4⋊Dic3 | C22 | semidirect |
| 22. C4×C5×Dic3 | C22 | semidirect |
| 23. #6667 | C22 | semidirect |
| 25. C2×#709 | D3 | semidirect |
| 37. C2×C3×C4×C5 | D4 | semidirect |
| 55. #926 | D5 | semidirect |
| 64. C2×D20 | C2×D3 | semidirect |
| 65. C2×C4×D5 | C2×D3 | semidirect |
| 66. C2×Dic10 | C2×D3 | semidirect |
| 97. C4⋊Dic3 | C2×D5 | semidirect |
| 98. C4×Dic3 | C2×D5 | semidirect |
| 105. C2×C4×C5 | #67 | semidirect |
| 138. C2×C3×C4 | D20 | semidirect |
| 172. C3×C5 | #535 | semidirect |
| 204. C2×C4 | #1202 | semidirect |
| 212. C5 | #5830 | semidirect |
| 225. C3 | #65859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D60 | 2 |
| C2×C3×#709 | 2 |
| C5×#926 | 2 |
| #91572 | 2 |
| #91458 | 2 |
| #91450 | 2 |
| #91374 | 2 |
| #65859 | 3 |
| #5830 | 5 |