Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 8. #65471 | C3 | direct (N × H) |
| 74. C3×Dic5 | Q16 | semidirect |
| 136. Dic5 | C3×Q16 | semidirect |
| 150. C3×C5 | #462 | semidirect |
| 181. C5 | C3×#462 | semidirect |
| 191. C3 | #65471 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q16 | 2 |
| C3×Q8×Dic5 | 2 |
| C3×#4090 | 2 |
| C2×C3×#689 | 2 |
| C3×#3967 | 2 |
| C3×#3948 | 2 |
| C3×#3946 | 2 |
| #65471 | 3 |
| C3×#462 | 5 |