Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
594 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #10601586 | C2 | semidirect |
| 5. #10601308 | C2 | semidirect |
| 6. #10598228 | C2 | semidirect |
| 7. #10598204 | C2 | semidirect |
| 17. #65365 | C4 | semidirect |
| 19. #65359 | C4 | semidirect |
| 51. #4015 | C2×C4 | semidirect |
| 52. #4015 | C2×C4 | semidirect |
| 67. C4×#168 | C2×C4 | semidirect |
| 124. C4×Dic5 | SD16 | semidirect |
| 357. C5 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614903 | 2 |
| #10614900 | 2 |
| C5×#1545 | 2 |
| #10601586 | 2 |
| #10601308 | 2 |
| #10598228 | 2 |
| #10598204 | 2 |
| #9295 | 5 |