Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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. C5×#1531 | C2 | semidirect |
| 4. #10602620 | C2 | semidirect |
| 6. #10598247 | C2 | semidirect |
| 7. #10598151 | C2 | semidirect |
| 74. #1531 | D5 | semidirect |
| 312. C5 | #9285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615087 | 2 |
| #10611069 | 2 |
| C5×#1531 | 2 |
| #10602620 | 2 |
| #10600591 | 2 |
| #10598247 | 2 |
| #10598151 | 2 |
| #9285 | 5 |