Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. #10600926 | C2 | semidirect |
| 4. C5×#1392 | C2 | semidirect |
| 5. #10598182 | C2 | semidirect |
| 8. C22×#676 | C4 | semidirect |
| 12. #65415 | C4 | semidirect |
| 14. #65411 | C4 | semidirect |
| 15. #65391 | C4 | semidirect |
| 19. #64696 | C4 | semidirect |
| 20. #64695 | C4 | semidirect |
| 56. #1392 | D5 | semidirect |
| 263. C5 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610387 | 2 |
| #10600938 | 2 |
| #10600926 | 2 |
| C5×#1392 | 2 |
| #10598182 | 2 |
| #12624 | 5 |