Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
410 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10604847 | C2 | semidirect |
| 3. #10604830 | C2 | semidirect |
| 4. #10604107 | C2 | semidirect |
| 5. #10604098 | C2 | semidirect |
| 12. C2×C5×Q32 | C4 | semidirect |
| 13. C2×#3960 | C4 | semidirect |
| 18. C2×D80 | C4 | semidirect |
| 104. C2×Q32 | AGL(1,𝔽5) | semidirect |
| 252. C5 | #13243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65208 | 2 |
| #10604847 | 2 |
| #10604830 | 2 |
| #10604107 | 2 |
| #10604098 | 2 |
| #13243 | 5 |