Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
566 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #10615004 | C2 | semidirect |
| 3. #10614114 | C2 | semidirect |
| 4. #10602611 | C2 | semidirect |
| 5. #10602392 | C2 | semidirect |
| 6. #10601605 | C2 | semidirect |
| 7. #10598240 | C2 | semidirect |
| 399. C5 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3109 | 2 |
| #10615004 | 2 |
| #10614114 | 2 |
| #10602611 | 2 |
| #10602392 | 2 |
| #10601605 | 2 |
| #10598240 | 2 |
| #10005 | 5 |