Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1114 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 351 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 |
|---|---|---|
| 2. C5×#2916 | C2 | semidirect |
| 3. C2×#65429 | C2 | semidirect |
| 4. #10601483 | C2 | semidirect |
| 5. C2×#64717 | C2 | semidirect |
| 15. C2×C5×#108 | C22 | semidirect |
| 17. C2×#3944 | C22 | semidirect |
| 18. C22×#672 | C22 | semidirect |
| 19. #64717 | C22 | semidirect |
| 20. #64717 | C22 | semidirect |
| 52. #2916 | D5 | semidirect |
| 100. C2×#108 | C2×D5 | semidirect |
| 219. C5 | #33385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619064 | 2 |
| C5×#2916 | 2 |
| C2×#65429 | 2 |
| #10601483 | 2 |
| C2×#64717 | 2 |
| #33385 | 5 |