Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
278 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10613746 | C2 | semidirect |
| 2. C5×#2221 | C2 | semidirect |
| 3. C2×#64740 | C2 | semidirect |
| 4. #10602251 | C2 | semidirect |
| 5. #10598314 | C2 | semidirect |
| 6. #10598076 | C2 | semidirect |
| 7. #10598075 | C2 | semidirect |
| 56. #2221 | D5 | semidirect |
| 221. C5 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613746 | 2 |
| C5×#2221 | 2 |
| C2×#64740 | 2 |
| #10602251 | 2 |
| #10598314 | 2 |
| #10598076 | 2 |
| #10598075 | 2 |
| #13670 | 5 |