Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #10615064 | C2 | semidirect |
| 3. C5×#1554 | C2 | semidirect |
| 6. #10598250 | C2 | semidirect |
| 7. #10598238 | C2 | semidirect |
| 69. #1554 | D5 | semidirect |
| 284. C5 | #9334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615088 | 2 |
| #10615064 | 2 |
| C5×#1554 | 2 |
| #10601601 | 2 |
| #10601577 | 2 |
| #10598250 | 2 |
| #10598238 | 2 |
| #9334 | 5 |