Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2115 | C2 | semidirect |
| 3. #10602807 | C2 | semidirect |
| 4. #10598026 | C2 | semidirect |
| 18. C5×#349 | C22 | semidirect |
| 19. #64780 | C22 | semidirect |
| 55. #2115 | D5 | semidirect |
| 112. #349 | C2×D5 | semidirect |
| 275. C5 | #11870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615530 | 2 |
| C5×#2115 | 2 |
| #10602807 | 2 |
| #10598026 | 2 |
| #11870 | 5 |