Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×D120 | C2 | semidirect |
| 2. C2×C3×#677 | C2 | semidirect |
| 3. #91458 | C2 | semidirect |
| 4. #91374 | C2 | semidirect |
| 5. C2×#6658 | C2 | semidirect |
| 6. C2×#6653 | C2 | semidirect |
| 7. C5×#815 | C2 | semidirect |
| 26. C2×#677 | D3 | semidirect |
| 45. C3×C5×C8 | D4 | semidirect |
| 46. C5×C3⋊C8 | D4 | semidirect |
| 53. #815 | D5 | semidirect |
| 108. C5×C8 | #67 | semidirect |
| 136. C3×C8 | D20 | semidirect |
| 137. C3⋊C8 | D20 | semidirect |
| 162. C3×C5 | #496 | semidirect |
| 195. C8 | #1202 | semidirect |
| 201. C5 | #5176 | semidirect |
| 213. C3 | #65001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D120 | 2 |
| C2×C3×#677 | 2 |
| #91458 | 2 |
| #91374 | 2 |
| C2×#6658 | 2 |
| C2×#6653 | 2 |
| C5×#815 | 2 |
| #65001 | 3 |
| #5176 | 5 |