Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
224 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. C2×C3×C5×Q16 | C2 | semidirect |
| 3. C5×Q8×Dic3 | C2 | semidirect |
| 5. C5×#835 | C2 | semidirect |
| 7. C5×Dic3⋊C8 | C2 | semidirect |
| 22. #5185 | C5 | direct (N × H) |
| 23. C2×C5×Q16 | D3 | semidirect |
| 45. C2×C3×Q16 | C2×C5 | semidirect |
| 47. Q8×Dic3 | C2×C5 | semidirect |
| 49. #835 | C2×C5 | semidirect |
| 51. Dic3⋊C8 | C2×C5 | semidirect |
| 105. C2×Q16 | C5×D3 | semidirect |
| 155. C3×C5 | #464 | semidirect |
| 190. C5 | #5185 | direct (N × H) |
| 202. C3 | C5×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q16 | 2 |
| C5×#947 | 2 |
| C5×Q8×Dic3 | 2 |
| C2×C5×#215 | 2 |
| C5×#835 | 2 |
| C5×#821 | 2 |
| C5×Dic3⋊C8 | 2 |
| C5×#464 | 3 |
| #5185 | 5 |