Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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×#709 | C2 | semidirect |
| 2. #91819 | C2 | semidirect |
| 3. C2×#6658 | C2 | semidirect |
| 4. C2×#6653 | C2 | semidirect |
| 5. C5×#830 | C2 | semidirect |
| 6. #90971 | C2 | semidirect |
| 7. #90965 | C2 | semidirect |
| 25. C2×#709 | D3 | semidirect |
| 46. C3×D20 | D4 | semidirect |
| 49. C3×Dic10 | D4 | semidirect |
| 58. #830 | D5 | semidirect |
| 119. D20 | #67 | semidirect |
| 122. Dic10 | #67 | semidirect |
| 188. C3×C5 | #449 | semidirect |
| 236. C5 | #5238 | semidirect |
| 252. C3 | #65023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#709 | 2 |
| #91819 | 2 |
| C2×#6658 | 2 |
| C2×#6653 | 2 |
| C5×#830 | 2 |
| #90971 | 2 |
| #90965 | 2 |
| #65023 | 3 |
| #5238 | 5 |