Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
340 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 87 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×#1712 | C2 | semidirect |
| 2. #10602083 | C2 | semidirect |
| 3. #10602081 | C2 | semidirect |
| 4. #10598851 | C2 | semidirect |
| 5. #10597929 | C2 | semidirect |
| 36. #1712 | D5 | semidirect |
| 85. C5×C8 | D16 | semidirect |
| 154. C8 | #3958 | semidirect |
| 156. C5 | #12525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1712 | 2 |
| #10602083 | 2 |
| #10602081 | 2 |
| #10598851 | 2 |
| #10597929 | 2 |
| #12525 | 5 |