Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. #10602109 | C2 | semidirect |
| 4. #10602104 | C2 | semidirect |
| 6. #10597959 | C2 | semidirect |
| 7. #10597957 | C2 | semidirect |
| 260. C5 | #12351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611261 | 2 |
| C5×#1689 | 2 |
| #10602109 | 2 |
| #10602104 | 2 |
| #10598252 | 2 |
| #10597959 | 2 |
| #10597957 | 2 |
| #12351 | 5 |