Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
856 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 856 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×#64868 | C2 | semidirect |
| 3. C4×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 4. #10604182 | C2 | semidirect |
| 9. C2×#4020 | C4 | semidirect |
| 15. C5×#384 | C4 | semidirect |
| 18. #65277 | C4 | semidirect |
| 53. (C2×AGL(1,𝔽5))⋊C4 | D4 | semidirect |
| 126. #384 | AGL(1,𝔽5) | semidirect |
| 249. C4×C5 | #327 | semidirect |
| 375. C5 | #9712 | semidirect |
| 408. C4 | #64868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10606106 | 2 |
| C2×#64868 | 2 |
| C4×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| #10604182 | 2 |
| #9712 | 5 |