Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #10601587 | C2 | semidirect |
| 4. C4×#3939 | C2 | semidirect |
| 6. C5×#1285 | C2 | semidirect |
| 7. #10598241 | C2 | semidirect |
| 16. #65127 | C4 | semidirect |
| 17. #65123 | C4 | semidirect |
| 18. #65120 | C4 | semidirect |
| 19. #65119 | C4 | semidirect |
| 80. #1285 | D5 | semidirect |
| 330. C5 | #8695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611056 | 2 |
| #10601626 | 2 |
| #10601587 | 2 |
| C4×#3939 | 2 |
| #10600263 | 2 |
| C5×#1285 | 2 |
| #10598241 | 2 |
| #8695 | 5 |