Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 123 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. #10602877 | C2 | semidirect |
| 3. C2×#64787 | C2 | semidirect |
| 4. C2×#64726 | C2 | semidirect |
| 5. C2×C16×Dic5 | C2 | semidirect |
| 9. C2×C5×Q32 | C4 | semidirect |
| 10. C2×C5×SD32 | C4 | semidirect |
| 11. C2×C5×D16 | C4 | semidirect |
| 91. C2×Q32 | Dic5 | semidirect |
| 92. C2×SD32 | Dic5 | semidirect |
| 93. C2×D16 | Dic5 | semidirect |
| 231. C5 | #13241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#508 | 2 |
| #10602877 | 2 |
| C2×#64787 | 2 |
| C2×#64726 | 2 |
| C2×C16×Dic5 | 2 |
| #13241 | 5 |