Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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×#1706 | C2 | semidirect |
| 2. #10602175 | C2 | semidirect |
| 3. #10602174 | C2 | semidirect |
| 4. #10602084 | C2 | semidirect |
| 6. #10598853 | C2 | semidirect |
| 7. #10597929 | C2 | semidirect |
| 52. #1706 | D5 | semidirect |
| 206. C5 | #12527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1706 | 2 |
| #10602175 | 2 |
| #10602174 | 2 |
| #10602084 | 2 |
| #10602083 | 2 |
| #10598853 | 2 |
| #10597929 | 2 |
| #12527 | 5 |