Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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. #91989 | C2 | semidirect |
| 3. C2×C3×D5⋊C8 | C2 | semidirect |
| 4. #91154 | C2 | semidirect |
| 5. #91152 | C2 | semidirect |
| 7. #6817 | C4 | semidirect |
| 8. C5×#235 | C4 | semidirect |
| 14. #6773 | C4 | semidirect |
| 15. #6772 | C4 | semidirect |
| 27. C2×D5⋊C8 | D3 | semidirect |
| 99. #235 | AGL(1,𝔽5) | semidirect |
| 201. C3×C5 | #416 | semidirect |
| 253. C5 | #5113 | semidirect |
| 268. C3 | #65794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#235 | 2 |
| #91989 | 2 |
| C2×C3×D5⋊C8 | 2 |
| #91154 | 2 |
| #91152 | 2 |
| #65794 | 3 |
| #5113 | 5 |