Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 496 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 |
|---|---|---|
| 3. #10614977 | C2 | semidirect |
| 5. #10602569 | C2 | semidirect |
| 6. #10600656 | C2 | semidirect |
| 7. #10598156 | C2 | semidirect |
| 323. C5 | #10093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3141 | 2 |
| #10615004 | 2 |
| #10614977 | 2 |
| #10602605 | 2 |
| #10602569 | 2 |
| #10600656 | 2 |
| #10598156 | 2 |
| #10093 | 5 |