Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10601546 | C2 | semidirect |
| 4. #10601541 | C2 | semidirect |
| 6. C5×#1276 | C2 | semidirect |
| 7. #10598102 | C2 | semidirect |
| 21. #64705 | C4 | semidirect |
| 22. #64705 | C4 | semidirect |
| 23. #64701 | C4 | semidirect |
| 24. #64701 | C4 | semidirect |
| 72. #1276 | D5 | semidirect |
| 301. C5 | #8934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611020 | 2 |
| #10601566 | 2 |
| #10601546 | 2 |
| #10601541 | 2 |
| #10600188 | 2 |
| C5×#1276 | 2 |
| #10598102 | 2 |
| #8934 | 5 |