Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
570 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C5×#3227 | C2 | semidirect |
| 3. #10614944 | C2 | semidirect |
| 4. #10602607 | C2 | semidirect |
| 5. #10602581 | C2 | semidirect |
| 6. #10601583 | C2 | semidirect |
| 7. #10598232 | C2 | semidirect |
| 78. #3227 | D5 | semidirect |
| 135. C2×#168 | SD16 | semidirect |
| 362. C5 | #10221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3227 | 2 |
| #10615017 | 2 |
| #10614944 | 2 |
| #10602607 | 2 |
| #10602581 | 2 |
| #10601583 | 2 |
| #10598232 | 2 |
| #10221 | 5 |