Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 2. C2×C4×Dic15 | C2 | semidirect |
| 3. C2×C3×C4×Dic5 | C2 | semidirect |
| 5. #90994 | C2 | semidirect |
| 13. C2×C4×C5×D3 | C4 | semidirect |
| 17. (C2×D3)⋊Dic5 | C4 | direct (N × H) |
| 22. C2×C4×Dic5 | D3 | semidirect |
| 35. C2×Dic15 | C2×C4 | semidirect |
| 42. C2×C3×Dic5 | C2×C4 | semidirect |
| 69. C2×C5×D3 | C42 | semidirect |
| 70. C3×C4×C5 | C22⋊C4 | semidirect |
| 81. C2×C4×D3 | Dic5 | semidirect |
| 103. C2×Dic5 | C4×D3 | semidirect |
| 145. C4×C5 | (C2×D3)⋊C4 | semidirect |
| 159. C3×C5 | C4×C22⋊C4 | semidirect |
| 169. C2×D3 | C4×Dic5 | semidirect |
| 171. C3×C4 | C22⋊Dic5 | semidirect |
| 205. C5 | C4×(C2×D3)⋊C4 | semidirect |
| 219. C4 | (C2×D3)⋊Dic5 | direct (N × H) |
| 220. C3 | C4×C22⋊Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D3 | 2 |
| C2×C4×Dic15 | 2 |
| C2×C3×C4×Dic5 | 2 |
| C2×(C2×D3)⋊Dic5 | 2 |
| #90994 | 2 |
| C4×C22⋊Dic5 | 3 |
| C4×(C2×D3)⋊C4 | 5 |