Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 99 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. C3×C5×#117 | C2 | semidirect |
| 3. C2×#6710 | C2 | semidirect |
| 4. #91089 | C2 | semidirect |
| 10. #6817 | C4 | semidirect |
| 12. C2×D60 | C4 | semidirect |
| 14. C2×Dic30 | C4 | semidirect |
| 17. C3×C42×C5 | C22 | semidirect |
| 19. #6710 | C22 | semidirect |
| 23. C5×#117 | D3 | semidirect |
| 46. C3×#117 | D5 | semidirect |
| 60. C42×C5 | C2×D3 | semidirect |
| 88. C3×C42 | C2×D5 | semidirect |
| 113. #117 | D15 | semidirect |
| 165. C42 | C2×D15 | semidirect |
| 166. C3×C5 | #421 | semidirect |
| 208. C5 | #5005 | semidirect |
| 221. C3 | #65294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C3×C5×#117 | 2 |
| C2×#6710 | 2 |
| #91089 | 2 |
| #65294 | 3 |
| #5005 | 5 |