Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
588 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 240 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. Q8×Dic15 | C2 | semidirect |
| 3. C3×Q8×Dic5 | C2 | semidirect |
| 4. #91435 | C2 | semidirect |
| 5. D3×C4⋊Dic5 | C2 | semidirect |
| 6. Dic5×D12 | C2 | semidirect |
| 7. #91371 | C2 | semidirect |
| 10. C5×#239 | C4 | semidirect |
| 25. Q8×Dic5 | D3 | semidirect |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 36. C5×D12 | C2×C4 | semidirect |
| 37. C4×C5×D3 | C2×C4 | semidirect |
| 73. #239 | Dic5 | semidirect |
| 86. C5×Q8 | C4×D3 | semidirect |
| 108. C3×Q8 | C2×Dic5 | semidirect |
| 115. D12 | C2×Dic5 | semidirect |
| 117. C4×D3 | C2×Dic5 | semidirect |
| 141. C3×C5 | #520 | semidirect |
| 157. Q8 | D3×Dic5 | semidirect |
| 171. C5 | #5574 | semidirect |
| 182. C3 | #66161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#239 | 2 |
| Q8×Dic15 | 2 |
| C3×Q8×Dic5 | 2 |
| #91435 | 2 |
| D3×C4⋊Dic5 | 2 |
| Dic5×D12 | 2 |
| #91371 | 2 |
| #66161 | 3 |
| #5574 | 5 |