Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10604723 | C2 | semidirect |
| 3. D5⋊(C22⋊C16) | C2 | semidirect |
| 4. #10598611 | C2 | semidirect |
| 5. C22×D40 | C4 | semidirect |
| 11. C2×C5×#107 | C4 | semidirect |
| 15. #65172 | C4 | semidirect |
| 18. #64893 | C22 | semidirect |
| 19. #64887 | C22 | semidirect |
| 103. C2×#107 | AGL(1,𝔽5) | semidirect |
| 288. C5 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65172 | 2 |
| #10604723 | 2 |
| D5⋊(C22⋊C16) | 2 |
| #10598611 | 2 |
| #11886 | 5 |