Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
726 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10615793 | C2 | semidirect |
| 3. #10602926 | C2 | semidirect |
| 5. #10598107 | C2 | semidirect |
| 7. C2×C5×#124 | C4 | semidirect |
| 11. C5×#391 | C4 | semidirect |
| 104. C2×#124 | Dic5 | semidirect |
| 111. #391 | Dic5 | semidirect |
| 305. C5 | #9466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2436 | 2 |
| #10615793 | 2 |
| #10602926 | 2 |
| #10602467 | 2 |
| #10598107 | 2 |
| #9466 | 5 |