Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10617380 | C2 | semidirect |
| 3. #10604624 | C2 | semidirect |
| 4. #10604607 | C2 | semidirect |
| 5. #10604594 | C2 | semidirect |
| 6. #10598532 | C2 | semidirect |
| 7. #10598526 | C2 | semidirect |
| 18. C5×#486 | C4 | semidirect |
| 19. #65382 | C4 | semidirect |
| 20. #65362 | C4 | semidirect |
| 23. #64982 | C4 | semidirect |
| 126. #486 | AGL(1,𝔽5) | semidirect |
| 330. C5 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617380 | 2 |
| #10613298 | 2 |
| #10604624 | 2 |
| #10604607 | 2 |
| #10604594 | 2 |
| #10598532 | 2 |
| #10598526 | 2 |
| #9281 | 5 |