Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1164 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 271 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. C5×#3458 | C2 | semidirect |
| 3. #10602689 | C2 | semidirect |
| 4. #10602386 | C2 | semidirect |
| 22. C22×D20 | Q8 | semidirect |
| 23. C22×C4×D5 | Q8 | semidirect |
| 24. C22×Dic10 | Q8 | semidirect |
| 44. #3458 | D5 | semidirect |
| 244. C5 | #23474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3458 | 2 |
| C2×#65295 | 2 |
| #10602689 | 2 |
| #10602386 | 2 |
| #23474 | 5 |