Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 3. #10601400 | C2 | semidirect |
| 5. C5×#1387 | C2 | semidirect |
| 6. #10598301 | C2 | semidirect |
| 7. #10598223 | C2 | semidirect |
| 61. #1387 | D5 | semidirect |
| 268. C5 | #13485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602232 | 2 |
| #10601489 | 2 |
| #10601400 | 2 |
| #10601391 | 2 |
| C5×#1387 | 2 |
| #10598301 | 2 |
| #10598223 | 2 |
| #13485 | 5 |