Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
472 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 2. #10604834 | C2 | semidirect |
| 3. #10604830 | C2 | semidirect |
| 4. #10603851 | C2 | semidirect |
| 5. D5⋊#364 | C2 | semidirect |
| 13. C5×#494 | C4 | semidirect |
| 15. #65480 | C4 | semidirect |
| 17. #64984 | C4 | semidirect |
| 51. #3996 | D4 | semidirect |
| 54. #3993 | D4 | semidirect |
| 121. #494 | AGL(1,𝔽5) | semidirect |
| 299. C5 | #13259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613530 | 2 |
| #10604834 | 2 |
| #10604830 | 2 |
| #10603851 | 2 |
| D5⋊#364 | 2 |
| #13259 | 5 |