Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
328 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 71 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×#3393 | C2 | semidirect |
| 2. #10602106 | C2 | semidirect |
| 3. #10601732 | C2 | semidirect |
| 5. #10598284 | C2 | semidirect |
| 6. Q8⋊#672 | C2 | semidirect |
| 7. #10598254 | C2 | semidirect |
| 55. #3393 | D5 | semidirect |
| 253. C5 | #12331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3393 | 2 |
| #10602106 | 2 |
| #10601732 | 2 |
| #10601682 | 2 |
| #10598284 | 2 |
| Q8⋊#672 | 2 |
| #10598254 | 2 |
| #12331 | 5 |