Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
464 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10604722 | C2 | semidirect |
| 3. #10604706 | C2 | semidirect |
| 4. #10598805 | C2 | semidirect |
| 5. C22×C5×D8 | C4 | semidirect |
| 14. #65446 | C4 | semidirect |
| 16. C2×#3950 | C4 | semidirect |
| 18. #64893 | C22 | semidirect |
| 19. #64887 | C22 | semidirect |
| 93. C22×D8 | AGL(1,𝔽5) | semidirect |
| 279. C5 | #11888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65446 | 2 |
| #10604722 | 2 |
| #10604706 | 2 |
| #10598805 | 2 |
| #11888 | 5 |