Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #10602222 | C2 | semidirect |
| 5. #10598312 | C2 | semidirect |
| 6. #10598307 | C2 | semidirect |
| 7. #10598307 | C2 | semidirect |
| 247. C5 | #13497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2117 | 2 |
| #10602808 | 2 |
| #10602807 | 2 |
| #10602222 | 2 |
| #10598312 | 2 |
| #10598307 | 2 |
| #13497 | 5 |