Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
300 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 3. #10601738 | C2 | semidirect |
| 4. #10601704 | C2 | semidirect |
| 6. Q8⋊#672 | C2 | semidirect |
| 7. #10598256 | C2 | semidirect |
| 234. C5 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3396 | 2 |
| #10602081 | 2 |
| #10601738 | 2 |
| #10601704 | 2 |
| #10598281 | 2 |
| Q8⋊#672 | 2 |
| #10598256 | 2 |
| #12385 | 5 |