Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
400 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 85 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. C5×#1534 | C2 | semidirect |
| 4. #10602530 | C2 | semidirect |
| 6. #10598250 | C2 | semidirect |
| 7. #10598247 | C2 | semidirect |
| 70. #1534 | D5 | semidirect |
| 281. C5 | #9335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614750 | 2 |
| #10611068 | 2 |
| C5×#1534 | 2 |
| #10602530 | 2 |
| #10601610 | 2 |
| #10598250 | 2 |
| #10598247 | 2 |
| #9335 | 5 |