Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
694 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10604616 | C2 | semidirect |
| 3. #10604616 | C2 | semidirect |
| 4. #10603845 | C2 | semidirect |
| 5. #10603806 | C2 | semidirect |
| 13. C5×#493 | C4 | semidirect |
| 15. #65362 | C4 | semidirect |
| 16. #64984 | C4 | semidirect |
| 81. D5⋊C8 | D8 | semidirect |
| 97. #493 | AGL(1,𝔽5) | semidirect |
| 271. C5 | #9832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#493 | 2 |
| #10604616 | 2 |
| #10603845 | 2 |
| #10603806 | 2 |
| #9832 | 5 |