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×#1813 | C2 | semidirect |
| 3. #10602800 | C2 | semidirect |
| 4. #10597974 | C2 | semidirect |
| 17. C5×#338 | C22 | semidirect |
| 19. #64773 | C22 | semidirect |
| 56. #1813 | D5 | semidirect |
| 113. #338 | 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×#1813 | 2 |
| #10602800 | 2 |
| #10597974 | 2 |
| #11870 | 5 |