Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
426 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 426 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. #10604843 | C2 | semidirect |
| 3. C2×#64909 | C2 | semidirect |
| 4. #10604797 | C2 | semidirect |
| 5. C2×#64905 | C2 | semidirect |
| 6. C2×#64852 | C2 | semidirect |
| 7. C2×C16×AGL(1,𝔽5) | C2 | semidirect |
| 18. C2×C5×SD32 | C4 | semidirect |
| 19. C2×#3961 | C4 | semidirect |
| 20. C2×#3958 | C4 | semidirect |
| 23. C2×#3932 | C4 | semidirect |
| 135. C2×SD32 | AGL(1,𝔽5) | semidirect |
| 335. C5 | #13241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65205 | 2 |
| #10604843 | 2 |
| C2×#64909 | 2 |
| #10604797 | 2 |
| C2×#64905 | 2 |
| C2×#64852 | 2 |
| C2×C16×AGL(1,𝔽5) | 2 |
| #13241 | 5 |