Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
432 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 128 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. #91782 | C2 | semidirect |
| 2. C5×#897 | C2 | semidirect |
| 3. C3×#4034 | C2 | semidirect |
| 5. #91390 | C2 | semidirect |
| 6. #91375 | C2 | semidirect |
| 7. #91371 | C2 | semidirect |
| 8. #91355 | C2 | semidirect |
| 9. #91344 | C2 | semidirect |
| 10. #91337 | C2 | semidirect |
| 11. #91326 | C2 | semidirect |
| 45. #4034 | D3 | semidirect |
| 69. #897 | D5 | semidirect |
| 228. C3×C5 | #542 | semidirect |
| 272. C5 | #5733 | semidirect |
| 289. C3 | #65977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91782 | 2 |
| C5×#897 | 2 |
| C3×#4034 | 2 |
| #91460 | 2 |
| #91390 | 2 |
| #91375 | 2 |
| #91371 | 2 |
| #91355 | 2 |
| #91344 | 2 |
| #91337 | 2 |
| #91326 | 2 |
| #65977 | 3 |
| #5733 | 5 |