Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
684 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 192 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. C23×C3×Dic5 | C2 | semidirect |
| 3. C2×#6719 | C2 | semidirect |
| 4. C2×#6669 | C2 | semidirect |
| 5. #91539 | C2 | direct (N × H) |
| 6. C2×(C2×D3)⋊Dic5 | C2 | semidirect |
| 16. C22×C3×Dic5 | C22 | semidirect |
| 17. #6719 | C22 | semidirect |
| 18. #6669 | C22 | semidirect |
| 19. (C2×D3)⋊Dic5 | C22 | semidirect |
| 22. C23×Dic5 | D3 | semidirect |
| 56. C22×Dic5 | C2×D3 | semidirect |
| 107. C2×C3×C5 | #123 | semidirect |
| 150. C3×C5 | C2×#123 | semidirect |
| 165. C2×C5 | #929 | semidirect |
| 184. C2×C3 | #4081 | semidirect |
| 188. C5 | C2×#929 | semidirect |
| 201. C3 | C2×#4081 | semidirect |
| 204. C2 | #91539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#67 | 2 |
| C23×C3×Dic5 | 2 |
| C2×#6719 | 2 |
| C2×#6669 | 2 |
| #91539 | 2 |
| C2×(C2×D3)⋊Dic5 | 2 |
| C2×#4081 | 3 |
| C2×#929 | 5 |