Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 408 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. #10600928 | C2 | semidirect |
| 5. #10600794 | C2 | semidirect |
| 6. C5×#1395 | C2 | semidirect |
| 7. #10598188 | C2 | semidirect |
| 27. #64698 | C4 | semidirect |
| 28. #64697 | C4 | semidirect |
| 79. #1395 | D5 | semidirect |
| 349. C5 | #12974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610399 | 2 |
| #10600941 | 2 |
| #10600928 | 2 |
| #10600838 | 2 |
| #10600794 | 2 |
| C5×#1395 | 2 |
| #10598188 | 2 |
| #12974 | 5 |