Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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×#1571 | C2 | semidirect |
| 5. #10598229 | C2 | semidirect |
| 6. #10598204 | C2 | semidirect |
| 7. #10598198 | C2 | semidirect |
| 53. #1571 | D5 | semidirect |
| 266. C5 | #10638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1571 | 2 |
| #10601550 | 2 |
| #10601320 | 2 |
| #10601273 | 2 |
| #10598229 | 2 |
| #10598204 | 2 |
| #10598198 | 2 |
| #10638 | 5 |