Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
852 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 184 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×C5×D12 | C2 | semidirect |
| 2. C22×#1201 | C2 | semidirect |
| 3. C22×#1201 | C2 | semidirect |
| 4. C22×D3×Dic5 | C2 | semidirect |
| 5. C2×#6712 | C2 | semidirect |
| 6. C2×C3×#685 | C2 | semidirect |
| 7. C2×(C2×D3)⋊Dic5 | C2 | semidirect |
| 8. #91453 | C2 | direct (N × H) |
| 17. C2×C5×D12 | C22 | semidirect |
| 21. C2×#1201 | C22 | semidirect |
| 22. C2×#1201 | C22 | semidirect |
| 24. C2×D3×Dic5 | C22 | semidirect |
| 25. #6712 | C22 | semidirect |
| 26. C3×#685 | C22 | semidirect |
| 27. (C2×D3)⋊Dic5 | C22 | semidirect |
| 35. C2×#685 | D3 | semidirect |
| 43. C22×C5×D3 | D4 | semidirect |
| 53. C2×Dic15 | D4 | semidirect |
| 64. C22×D12 | D5 | semidirect |
| 86. #685 | C2×D3 | semidirect |
| 100. C2×C5×D3 | C2×D4 | semidirect |
| 107. Dic15 | C2×D4 | semidirect |
| 121. C2×D12 | C2×D5 | semidirect |
| 160. C2×C3×C5 | #121 | semidirect |
| 177. C22×D3 | C22⋊D5 | semidirect |
| 230. C3×C5 | C2×#121 | semidirect |
| 246. C2×D3 | C2×C22⋊D5 | semidirect |
| 253. C2×C5 | #884 | semidirect |
| 284. C2×C3 | #4085 | semidirect |
| 290. C5 | C2×#884 | semidirect |
| 311. C3 | C2×#4085 | semidirect |
| 315. C2 | #91453 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D12 | 2 |
| C22×#1201 | 2 |
| C22×D3×Dic5 | 2 |
| C2×#6712 | 2 |
| C2×C3×#685 | 2 |
| C2×(C2×D3)⋊Dic5 | 2 |
| #91453 | 2 |
| C2×#4085 | 3 |
| C2×#884 | 5 |