Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
620 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 89 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×#3208 | C2 | semidirect |
| 2. #10615097 | C2 | semidirect |
| 4. #10602614 | C2 | semidirect |
| 5. #10602559 | C2 | semidirect |
| 6. #10601554 | C2 | semidirect |
| 7. #10598234 | C2 | semidirect |
| 79. #3208 | D5 | semidirect |
| 363. C5 | #10105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3208 | 2 |
| #10615097 | 2 |
| #10614894 | 2 |
| #10602614 | 2 |
| #10602559 | 2 |
| #10601554 | 2 |
| #10598234 | 2 |
| #10105 | 5 |