Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
356 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. C5×#1838 | C2 | semidirect |
| 4. #10601287 | C2 | semidirect |
| 5. #10601286 | C2 | semidirect |
| 7. #10598151 | C2 | semidirect |
| 51. #1838 | D5 | semidirect |
| 244. C5 | #10659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1838 | 2 |
| #10601289 | 2 |
| #10601287 | 2 |
| #10601286 | 2 |
| #10600630 | 2 |
| #10598151 | 2 |
| #10659 | 5 |