Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 83 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. C22×C3×C5×C8 | C2 | semidirect |
| 2. #91819 | C2 | semidirect |
| 3. C2×D120 | C2 | semidirect |
| 4. #91105 | C2 | semidirect |
| 5. #91102 | C2 | semidirect |
| 17. C22×C5×C8 | D3 | semidirect |
| 33. C3×C5×C8 | D4 | semidirect |
| 34. C22×C3×C8 | D5 | semidirect |
| 51. C22×C3×C5 | D8 | semidirect |
| 80. C5×C8 | #67 | semidirect |
| 82. C22×C8 | D15 | semidirect |
| 102. C3×C8 | C22⋊D5 | semidirect |
| 105. C22×C5 | D24 | semidirect |
| 123. C3×C5 | #466 | semidirect |
| 126. C22×C3 | D40 | semidirect |
| 151. C8 | #1220 | semidirect |
| 157. C5 | #5115 | semidirect |
| 163. C22 | D120 | semidirect |
| 169. C3 | #65404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×C8 | 2 |
| #91819 | 2 |
| C2×D120 | 2 |
| #91105 | 2 |
| #91102 | 2 |
| #65404 | 3 |
| #5115 | 5 |