Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
380 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. C5×#1561 | C2 | semidirect |
| 3. #10602619 | C2 | semidirect |
| 4. #10601311 | C2 | semidirect |
| 7. #10598203 | C2 | semidirect |
| 67. #1561 | D5 | semidirect |
| 304. C5 | #10532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615097 | 2 |
| C5×#1561 | 2 |
| #10602619 | 2 |
| #10601311 | 2 |
| #10601298 | 2 |
| #10601291 | 2 |
| #10598203 | 2 |
| #10532 | 5 |