Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
442 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10604806 | C2 | semidirect |
| 3. D5⋊#361 | C2 | semidirect |
| 4. D5⋊#368 | C2 | semidirect |
| 5. #10604098 | C2 | semidirect |
| 12. C2×C5×D16 | C4 | semidirect |
| 13. C2×#3958 | C4 | semidirect |
| 18. C2×D80 | C4 | semidirect |
| 106. C2×D16 | AGL(1,𝔽5) | semidirect |
| 257. C5 | #13245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D16 | 2 |
| #10604806 | 2 |
| D5⋊#361 | 2 |
| D5⋊#368 | 2 |
| #10604098 | 2 |
| #13245 | 5 |