Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 121 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. #10601532 | C2 | semidirect |
| 5. M16×#168 | C2 | semidirect |
| 6. C5×#1299 | C2 | semidirect |
| 7. #10598201 | C2 | semidirect |
| 70. #1299 | D5 | semidirect |
| 274. C5 | #8241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610772 | 2 |
| #10601566 | 2 |
| #10601532 | 2 |
| #10600652 | 2 |
| M16×#168 | 2 |
| C5×#1299 | 2 |
| #10598201 | 2 |
| #8241 | 5 |