Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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×#1565 | C2 | semidirect |
| 3. #10601542 | C2 | semidirect |
| 6. #10600668 | C2 | semidirect |
| 7. #10598196 | C2 | semidirect |
| 60. #1565 | D5 | semidirect |
| 289. C5 | #10607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1565 | 2 |
| #10601567 | 2 |
| #10601542 | 2 |
| C2×#64705 | 2 |
| #10600669 | 2 |
| #10600668 | 2 |
| #10598196 | 2 |
| #10607 | 5 |