Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
642 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 140 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. #10604674 | C2 | semidirect |
| 4. #10603847 | C2 | semidirect |
| 5. C8×D5⋊C8 | C2 | semidirect |
| 13. C5×#492 | C4 | semidirect |
| 15. #65374 | C4 | semidirect |
| 16. #65365 | C4 | semidirect |
| 17. #64982 | C4 | semidirect |
| 83. D5⋊C8 | SD16 | semidirect |
| 105. #492 | AGL(1,𝔽5) | semidirect |
| 145. C5×C8 | #102 | semidirect |
| 146. #168 | #102 | semidirect |
| 277. C8 | #4007 | semidirect |
| 278. C5 | #9820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#492 | 2 |
| #10604674 | 2 |
| #10604616 | 2 |
| #10603847 | 2 |
| C8×D5⋊C8 | 2 |
| #9820 | 5 |