Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
578 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×D5⋊C16 | C2 | semidirect |
| 3. C2×#64904 | C2 | semidirect |
| 4. #10604723 | C2 | semidirect |
| 5. #10598619 | C2 | semidirect |
| 15. C5×#466 | C4 | semidirect |
| 16. #65446 | C4 | semidirect |
| 17. #65404 | C4 | semidirect |
| 19. #65172 | C4 | semidirect |
| 59. D5⋊C16 | D4 | semidirect |
| 135. #466 | AGL(1,𝔽5) | semidirect |
| 235. C22×C5 | #357 | semidirect |
| 246. C2×D5 | #357 | semidirect |
| 366. C5 | #13059 | semidirect |
| 386. C22 | #64904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5⋊C16 | 2 |
| D5×#466 | 2 |
| C2×#64904 | 2 |
| #10604723 | 2 |
| #10598619 | 2 |
| #13059 | 5 |