Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 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. C5×#2213 | C2 | semidirect |
| 2. #10602083 | C2 | semidirect |
| 3. #10601719 | C2 | semidirect |
| 4. #10601716 | C2 | semidirect |
| 5. #10598282 | C2 | semidirect |
| 6. #10598062 | C2 | semidirect |
| 7. #10598057 | C2 | semidirect |
| 51. #2213 | D5 | semidirect |
| 205. C5 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2213 | 2 |
| #10602083 | 2 |
| #10601719 | 2 |
| #10601716 | 2 |
| #10598282 | 2 |
| #10598062 | 2 |
| #10598057 | 2 |
| #12436 | 5 |