Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
498 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 81 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×#3110 | C2 | semidirect |
| 2. #10615092 | C2 | semidirect |
| 4. #10602620 | C2 | semidirect |
| 5. #10602396 | C2 | semidirect |
| 6. #10601604 | C2 | semidirect |
| 7. #10598247 | C2 | semidirect |
| 84. #3110 | D5 | semidirect |
| 362. C5 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3110 | 2 |
| #10615092 | 2 |
| #10614039 | 2 |
| #10602620 | 2 |
| #10602396 | 2 |
| #10601604 | 2 |
| #10598247 | 2 |
| #10042 | 5 |