Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
452 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 109 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. #10600926 | C2 | semidirect |
| 5. #10600833 | C2 | semidirect |
| 6. C5×#1395 | C2 | semidirect |
| 7. #10598183 | C2 | semidirect |
| 10. C2×#4053 | C4 | semidirect |
| 17. #65407 | C4 | semidirect |
| 18. #65399 | C4 | semidirect |
| 19. C2×#3947 | C4 | semidirect |
| 27. #64698 | C4 | semidirect |
| 28. #64697 | C4 | semidirect |
| 87. #1395 | D5 | semidirect |
| 384. C5 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610389 | 2 |
| #10600941 | 2 |
| #10600926 | 2 |
| #10600853 | 2 |
| #10600833 | 2 |
| C5×#1395 | 2 |
| #10598183 | 2 |
| #12634 | 5 |