Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1156 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1156 conjugacy classes of subgroups — too many to draw. Only its 130 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. C2×#64920 | C2 | semidirect |
| 3. #10604197 | C2 | semidirect |
| 4. #10604184 | C2 | semidirect |
| 6. C2×C5×#127 | C4 | semidirect |
| 11. C2×D4×Dic5 | C4 | semidirect |
| 14. C2×#4015 | C4 | semidirect |
| 127. C2×#127 | AGL(1,𝔽5) | semidirect |
| 394. C5 | #8332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66050 | 2 |
| C2×#64920 | 2 |
| #10604197 | 2 |
| #10604184 | 2 |
| #8332 | 5 |