Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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. C5×#1810 | C2 | semidirect |
| 3. #10602763 | C2 | semidirect |
| 5. #10598176 | C2 | semidirect |
| 8. C2×#4047 | C4 | semidirect |
| 15. #65399 | C4 | semidirect |
| 19. #65391 | C4 | semidirect |
| 20. #65390 | C4 | semidirect |
| 66. #1810 | D5 | semidirect |
| 338. C5 | #8626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615465 | 2 |
| C5×#1810 | 2 |
| #10602763 | 2 |
| #10600772 | 2 |
| #10598176 | 2 |
| #8626 | 5 |