Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 510 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×#3216 | C2 | semidirect |
| 2. #10615082 | C2 | semidirect |
| 4. #10602616 | C2 | semidirect |
| 5. #10602596 | C2 | semidirect |
| 6. #10601620 | C2 | semidirect |
| 7. #10598248 | C2 | semidirect |
| 83. #3216 | D5 | semidirect |
| 368. C5 | #10039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3216 | 2 |
| #10615082 | 2 |
| #10615031 | 2 |
| #10602616 | 2 |
| #10602596 | 2 |
| #10601620 | 2 |
| #10598248 | 2 |
| #10039 | 5 |