Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C3×Dic20 | C2 | semidirect |
| 3. #91390 | C2 | semidirect |
| 4. C2×#6656 | C2 | semidirect |
| 5. #91104 | C2 | semidirect |
| 6. C5×#821 | C2 | semidirect |
| 7. #90970 | C2 | semidirect |
| 27. C2×Dic20 | D3 | semidirect |
| 56. #821 | D5 | semidirect |
| 180. C3×C5 | #452 | semidirect |
| 223. C5 | #5187 | semidirect |
| 237. C3 | #65072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6768 | 2 |
| C2×C3×Dic20 | 2 |
| #91390 | 2 |
| C2×#6656 | 2 |
| #91104 | 2 |
| C5×#821 | 2 |
| #90970 | 2 |
| #65072 | 3 |
| #5187 | 5 |