Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 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. #10617404 | C2 | semidirect |
| 3. #10604784 | C2 | semidirect |
| 4. #10604765 | C2 | semidirect |
| 5. #10598605 | C2 | semidirect |
| 15. C5×#469 | C4 | semidirect |
| 16. #65448 | C4 | semidirect |
| 17. #65426 | C4 | semidirect |
| 19. #65157 | C4 | semidirect |
| 59. #3990 | D4 | semidirect |
| 132. #469 | AGL(1,𝔽5) | semidirect |
| 329. C5 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617404 | 2 |
| #10612597 | 2 |
| #10604784 | 2 |
| #10604765 | 2 |
| #10598605 | 2 |
| #13077 | 5 |