Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
436 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10617314 | C2 | semidirect |
| 3. #10604598 | C2 | semidirect |
| 4. #10604596 | C2 | semidirect |
| 5. #10604539 | C2 | semidirect |
| 6. #10598550 | C2 | semidirect |
| 7. #10598545 | C2 | semidirect |
| 20. C5×#496 | C4 | semidirect |
| 25. #65360 | C4 | semidirect |
| 26. #65344 | C4 | semidirect |
| 28. #64991 | C4 | semidirect |
| 149. #496 | AGL(1,𝔽5) | semidirect |
| 387. C5 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617314 | 2 |
| #10613569 | 2 |
| #10604598 | 2 |
| #10604596 | 2 |
| #10604539 | 2 |
| #10598550 | 2 |
| #10598545 | 2 |
| #9432 | 5 |