Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10601629 | C2 | semidirect |
| 5. #10601596 | C2 | semidirect |
| 6. C5×#1287 | C2 | semidirect |
| 7. #10598228 | C2 | semidirect |
| 21. #64983 | C4 | semidirect |
| 22. #64983 | C4 | semidirect |
| 23. #64971 | C4 | semidirect |
| 24. #64969 | C4 | semidirect |
| 77. #1287 | D5 | semidirect |
| 313. C5 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611069 | 2 |
| #10611001 | 2 |
| #10601629 | 2 |
| #10601625 | 2 |
| #10601596 | 2 |
| C5×#1287 | 2 |
| #10598228 | 2 |
| #9279 | 5 |