Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
624 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 127 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. #10613935 | C2 | semidirect |
| 3. C5×#1458 | C2 | semidirect |
| 4. #10601567 | C2 | semidirect |
| 5. #10598229 | C2 | semidirect |
| 57. C4⋊#168 | D4 | semidirect |
| 61. #1458 | D5 | semidirect |
| 334. C5 | #9197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614017 | 2 |
| #10613935 | 2 |
| C5×#1458 | 2 |
| #10601567 | 2 |
| #10598229 | 2 |
| #9197 | 5 |