Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10601538 | C2 | semidirect |
| 4. #10600340 | C2 | semidirect |
| 6. C5×#1286 | C2 | semidirect |
| 7. #10598204 | C2 | semidirect |
| 18. #65127 | C4 | semidirect |
| 20. #65123 | C4 | semidirect |
| 70. #1286 | D5 | semidirect |
| 311. C5 | #8680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610772 | 2 |
| #10601583 | 2 |
| #10601538 | 2 |
| #10600340 | 2 |
| #10600338 | 2 |
| C5×#1286 | 2 |
| #10598204 | 2 |
| #8680 | 5 |