Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
296 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. C2×C5×Dic12 | C2 | semidirect |
| 5. C5×#816 | C2 | semidirect |
| 18. #4739 | C5 | direct (N × H) |
| 39. C2×Dic12 | C2×C5 | semidirect |
| 41. #816 | C2×C5 | semidirect |
| 56. C22×C3×C5 | Q16 | semidirect |
| 111. C22×C5 | Dic12 | semidirect |
| 129. C3×C5 | #451 | semidirect |
| 132. C22×C3 | C5×Q16 | semidirect |
| 160. C5 | #4739 | direct (N × H) |
| 163. C22 | C5×Dic12 | semidirect |
| 170. C3 | C5×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic6 | 2 |
| C5×#924 | 2 |
| C2×C5×Dic12 | 2 |
| C3×C5×C22⋊C8 | 2 |
| C5×#816 | 2 |
| C5×#451 | 3 |
| #4739 | 5 |