Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
580 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 226 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×C5×#239 | C2 | semidirect |
| 2. C2×C5×D3×Q8 | C2 | semidirect |
| 3. C3×C4×C5×Q8 | C2 | semidirect |
| 4. C5×#897 | C2 | semidirect |
| 5. C5×#895 | C2 | semidirect |
| 6. C5×#875 | C2 | semidirect |
| 7. C4×C5×D12 | C2 | semidirect |
| 23. #5576 | C5 | direct (N × H) |
| 29. C4×C5×Q8 | D3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 44. C2×#239 | C2×C5 | semidirect |
| 45. C2×D3×Q8 | C2×C5 | semidirect |
| 46. C3×C4×Q8 | C2×C5 | semidirect |
| 47. #897 | C2×C5 | semidirect |
| 48. #895 | C2×C5 | semidirect |
| 49. #875 | C2×C5 | semidirect |
| 50. C4×D12 | C2×C5 | semidirect |
| 72. C2×C5×D3 | #41 | semidirect |
| 95. C5×Q8 | D12 | semidirect |
| 110. C4×Q8 | C5×D3 | semidirect |
| 119. C3×Q8 | C5×D4 | semidirect |
| 156. C3×C5 | #548 | semidirect |
| 163. C2×D3 | C5×#41 | semidirect |
| 177. Q8 | C5×D12 | semidirect |
| 192. C5 | #5576 | direct (N × H) |
| 205. C3 | C5×#548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#239 | 2 |
| C2×C5×D3×Q8 | 2 |
| C3×C4×C5×Q8 | 2 |
| C5×#897 | 2 |
| C5×#895 | 2 |
| C5×#875 | 2 |
| C4×C5×D12 | 2 |
| C5×#548 | 3 |
| #5576 | 5 |