Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. D5×#499 | C2 | semidirect |
| 3. C5×#2244 | C2 | semidirect |
| 4. #10602146 | C2 | semidirect |
| 5. #10602082 | C2 | semidirect |
| 6. #10599982 | C2 | semidirect |
| 7. #10599977 | C2 | semidirect |
| 8. #10599876 | C2 | semidirect |
| 9. #10599864 | C2 | semidirect |
| 77. #2244 | D5 | semidirect |
| 279. C5 | #33708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#499 | 2 |
| #10613513 | 2 |
| C5×#2244 | 2 |
| #10602146 | 2 |
| #10602082 | 2 |
| #10599982 | 2 |
| #10599977 | 2 |
| #10599876 | 2 |
| #10599864 | 2 |
| #33708 | 5 |