Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
424 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 424 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. #10617313 | C2 | semidirect |
| 3. #10604605 | C2 | semidirect |
| 4. #10604595 | C2 | semidirect |
| 5. #10604540 | C2 | semidirect |
| 6. #10598549 | C2 | semidirect |
| 7. #10598546 | C2 | semidirect |
| 20. C5×#496 | C4 | semidirect |
| 25. #65360 | C4 | semidirect |
| 26. #65349 | C4 | semidirect |
| 28. #64992 | C4 | semidirect |
| 149. #496 | AGL(1,𝔽5) | semidirect |
| 381. C5 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617313 | 2 |
| #10613583 | 2 |
| #10604605 | 2 |
| #10604595 | 2 |
| #10604540 | 2 |
| #10598549 | 2 |
| #10598546 | 2 |
| #9370 | 5 |