Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
442 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 85 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. #10611068 | C2 | semidirect |
| 3. C5×#1536 | C2 | semidirect |
| 4. #10602606 | C2 | semidirect |
| 5. #10601628 | C2 | semidirect |
| 6. #10598244 | C2 | semidirect |
| 7. #10598243 | C2 | semidirect |
| 12. #65377 | C4 | semidirect |
| 13. #65368 | C4 | semidirect |
| 14. #65362 | C4 | semidirect |
| 15. #65359 | C4 | semidirect |
| 70. #1536 | D5 | semidirect |
| 309. C5 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615026 | 2 |
| #10611068 | 2 |
| C5×#1536 | 2 |
| #10602606 | 2 |
| #10601628 | 2 |
| #10598244 | 2 |
| #10598243 | 2 |
| #9417 | 5 |