Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 80 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×C5×D24 | C2 | semidirect |
| 3. #91451 | C2 | semidirect |
| 4. C2×#6654 | C2 | semidirect |
| 5. C3×C8×Dic5 | C2 | semidirect |
| 21. C8×Dic5 | D3 | semidirect |
| 31. C3×C5×C8 | D4 | semidirect |
| 32. C3×#168 | D4 | semidirect |
| 35. C2×D24 | D5 | semidirect |
| 55. C3×Dic5 | D8 | semidirect |
| 74. C5×C8 | D12 | semidirect |
| 75. #168 | D12 | semidirect |
| 95. C3×C8 | C22⋊D5 | semidirect |
| 103. Dic5 | D24 | semidirect |
| 113. C3×C5 | #493 | semidirect |
| 136. C8 | #1203 | semidirect |
| 141. C5 | #4695 | semidirect |
| 150. C3 | #65440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D120 | 2 |
| C2×C5×D24 | 2 |
| #91451 | 2 |
| C2×#6654 | 2 |
| C3×C8×Dic5 | 2 |
| #65440 | 3 |
| #4695 | 5 |