Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
310 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. C5×#1364 | C2 | semidirect |
| 5. #10598292 | C2 | semidirect |
| 6. #10598056 | C2 | semidirect |
| 7. #10597967 | C2 | semidirect |
| 60. #1364 | D5 | semidirect |
| 230. C5 | #11942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613669 | 2 |
| #10600077 | 2 |
| D5×#335 | 2 |
| C5×#1364 | 2 |
| #10598292 | 2 |
| #10598056 | 2 |
| #10597967 | 2 |
| #11942 | 5 |