Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 68 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. C3×#4070 | C2 | semidirect |
| 3. C2×#6662 | C2 | semidirect |
| 4. C2×#6658 | C2 | semidirect |
| 5. C5×#830 | C2 | semidirect |
| 6. #90974 | C2 | semidirect |
| 7. #90968 | C2 | semidirect |
| 26. #4070 | D3 | semidirect |
| 55. #830 | D5 | semidirect |
| 180. C3×C5 | #452 | semidirect |
| 223. C5 | #5047 | semidirect |
| 237. C3 | #65022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C3×#4070 | 2 |
| C2×#6662 | 2 |
| C2×#6658 | 2 |
| C5×#830 | 2 |
| #90974 | 2 |
| #90968 | 2 |
| #65022 | 3 |
| #5047 | 5 |