Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 71 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×#2126 | C2 | semidirect |
| 3. #10602613 | C2 | semidirect |
| 4. #10598035 | C2 | semidirect |
| 8. C2×#4020 | C4 | semidirect |
| 13. #65347 | C4 | semidirect |
| 15. C4×#681 | C4 | semidirect |
| 16. C5×#354 | C22 | semidirect |
| 19. #64762 | C22 | semidirect |
| 54. #2126 | D5 | semidirect |
| 113. #354 | C2×D5 | semidirect |
| 287. C5 | #13579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615018 | 2 |
| C5×#2126 | 2 |
| #10602613 | 2 |
| #10598035 | 2 |
| #13579 | 5 |