Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
1700 conjugacy classes of subgroups; only the 648 normal subgroups are shown.
This group has 1700 conjugacy classes of subgroups — too many to draw. Only its 648 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×Dic30 | C2 | semidirect |
| 3. C22×C3×Dic10 | C2 | semidirect |
| 4. C22×#1204 | C2 | semidirect |
| 6. C2×D3×Dic10 | C2 | direct (N × H) |
| 11. C2×Dic30 | C22 | semidirect |
| 15. C2×C3×Dic10 | C22 | semidirect |
| 16. C2×#1204 | C22 | semidirect |
| 18. D3×Dic10 | C22 | direct (N × H) |
| 25. C22×Dic10 | D3 | direct (N × H) |
| 27. C22×C5×D3 | Q8 | semidirect |
| 31. Dic30 | C23 | semidirect |
| 35. C3×Dic10 | C23 | semidirect |
| 36. #1204 | C23 | semidirect |
| 54. C2×Dic10 | C2×D3 | direct (N × H) |
| 56. C22×C3×C5 | C2×Q8 | semidirect |
| 58. C2×C5×D3 | C2×Q8 | semidirect |
| 86. Dic10 | C22×D3 | direct (N × H) |
| 93. C2×C3×C5 | C22×Q8 | semidirect |
| 95. C5×D3 | C22×Q8 | semidirect |
| 97. C22×D3 | Dic10 | direct (N × H) |
| 110. C22×C5 | D3×Q8 | semidirect |
| 127. C3×C5 | C23×Q8 | semidirect |
| 128. C22×C3 | C2×Dic10 | semidirect |
| 130. C2×D3 | C2×Dic10 | direct (N × H) |
| 137. C2×C5 | C2×D3×Q8 | semidirect |
| 151. C2×C3 | C22×Dic10 | semidirect |
| 153. D3 | C22×Dic10 | direct (N × H) |
| 154. C5 | C22×D3×Q8 | semidirect |
| 157. C22 | D3×Dic10 | direct (N × H) |
| 163. C3 | C23×Dic10 | semidirect |
| 165. C2 | C2×D3×Dic10 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic30 | 2 |
| C22×C4×C5×D3 | 2 |
| C22×C3×Dic10 | 2 |
| C22×#1204 | 2 |
| C22×D3×Dic5 | 2 |
| C2×D3×Dic10 | 2 |
| C23×Dic10 | 3 |
| C22×D3×Q8 | 5 |