Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #91808 | C2 | semidirect |
| 2. D8×D15 | C2 | semidirect |
| 3. C3×C5×SD32 | C2 | semidirect |
| 4. #91112 | C2 | semidirect |
| 5. #91110 | C2 | semidirect |
| 6. D240 | C2 | semidirect |
| 7. #91082 | C2 | semidirect |
| 11. C3×C5×Q16 | C22 | semidirect |
| 16. D120 | C22 | semidirect |
| 18. C3×C5×C16 | C22 | semidirect |
| 19. C3⋊#672 | C22 | semidirect |
| 23. C5×SD32 | D3 | semidirect |
| 41. C3×SD32 | D5 | semidirect |
| 48. C5×Q16 | C2×D3 | semidirect |
| 55. C5×C16 | C2×D3 | semidirect |
| 68. C3×Q16 | C2×D5 | semidirect |
| 75. C3×C16 | C2×D5 | semidirect |
| 91. SD32 | D15 | semidirect |
| 121. Q16 | C2×D15 | semidirect |
| 129. C16 | C2×D15 | semidirect |
| 130. C3×C5 | #509 | semidirect |
| 160. C5 | #4914 | semidirect |
| 169. C3 | #65203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91808 | 2 |
| D8×D15 | 2 |
| C3×C5×SD32 | 2 |
| #91112 | 2 |
| #91110 | 2 |
| D240 | 2 |
| #91082 | 2 |
| #65203 | 3 |
| #4914 | 5 |