Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
526 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 526 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 |
|---|---|---|
| 3. C2×#64908 | C2 | semidirect |
| 5. #10598619 | C2 | semidirect |
| 15. C5×#467 | C4 | semidirect |
| 16. #65477 | C4 | semidirect |
| 17. #65405 | C4 | semidirect |
| 19. #65176 | C4 | semidirect |
| 133. #467 | AGL(1,𝔽5) | semidirect |
| 222. C22×C5 | #358 | semidirect |
| 228. C2×D5 | #358 | semidirect |
| 338. C5 | #13060 | semidirect |
| 350. C22 | #64908 | 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×#467 | 2 |
| C2×#64908 | 2 |
| #10604723 | 2 |
| #10598619 | 2 |
| #13060 | 5 |