Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
574 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 101 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×#3226 | C2 | semidirect |
| 3. #10614946 | C2 | semidirect |
| 4. #10602607 | C2 | semidirect |
| 5. #10602579 | C2 | semidirect |
| 6. #10601583 | C2 | semidirect |
| 7. #10598232 | C2 | semidirect |
| 80. #3226 | D5 | semidirect |
| 366. C5 | #10225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3226 | 2 |
| #10615017 | 2 |
| #10614946 | 2 |
| #10602607 | 2 |
| #10602579 | 2 |
| #10601583 | 2 |
| #10598232 | 2 |
| #10225 | 5 |