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×#1497 | C2 | semidirect |
| 4. #10602615 | C2 | semidirect |
| 6. #10598248 | C2 | semidirect |
| 7. #10598231 | C2 | semidirect |
| 76. #1497 | 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 |
| #10611021 | 2 |
| C5×#1497 | 2 |
| #10602615 | 2 |
| #10601599 | 2 |
| #10598248 | 2 |
| #10598231 | 2 |
| #9285 | 5 |