Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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×#1568 | C2 | semidirect |
| 4. C4×#3949 | C2 | semidirect |
| 5. #10598240 | C2 | semidirect |
| 16. #64977 | C4 | semidirect |
| 17. C8×D20 | C4 | semidirect |
| 18. #64968 | C4 | semidirect |
| 19. C8×Dic10 | C4 | semidirect |
| 64. #1568 | D5 | semidirect |
| 281. C5 | #8694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610179 | 2 |
| C5×#1568 | 2 |
| #10601626 | 2 |
| C4×#3949 | 2 |
| #10598240 | 2 |
| #8694 | 5 |