Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 74 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×#6758 | C2 | semidirect |
| 3. C3×#4130 | C2 | semidirect |
| 4. #91158 | C2 | semidirect |
| 5. #91156 | C2 | semidirect |
| 7. #6817 | C4 | semidirect |
| 8. C5×#235 | C4 | semidirect |
| 12. D5×D12 | C4 | semidirect |
| 17. D5×Dic6 | C4 | semidirect |
| 20. #6758 | C22 | semidirect |
| 23. C3×C4×AGL(1,𝔽5) | C22 | semidirect |
| 26. #4130 | D3 | semidirect |
| 74. C4×AGL(1,𝔽5) | C2×D3 | semidirect |
| 99. #235 | AGL(1,𝔽5) | semidirect |
| 201. C3×C5 | #421 | semidirect |
| 253. C5 | #5005 | semidirect |
| 268. C3 | #65795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#235 | 2 |
| C2×#6758 | 2 |
| C3×#4130 | 2 |
| #91158 | 2 |
| #91156 | 2 |
| #65795 | 3 |
| #5005 | 5 |