Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 5. ΓL(1,𝔽16)⋊Q8 | C2 | semidirect |
| 6. AGL(1,𝔽5)×Dic6 | C2 | semidirect |
| 8. C2×Dic30 | C4 | semidirect |
| 9. C2×C5×Dic6 | C4 | semidirect |
| 11. C2×#1204 | C4 | semidirect |
| 13. D5×Dic6 | C4 | semidirect |
| 14. D5×Dic6 | C4 | semidirect |
| 95. C2×Dic6 | AGL(1,𝔽5) | semidirect |
| 181. C3×C5 | #519 | semidirect |
| 221. C5 | #5516 | semidirect |
| 234. C3 | #66262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic6 | 2 |
| #91989 | 2 |
| C3×#4130 | 2 |
| #91923 | 2 |
| ΓL(1,𝔽16)⋊Q8 | 2 |
| AGL(1,𝔽5)×Dic6 | 2 |
| #66262 | 3 |
| #5516 | 5 |