Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
598 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 112 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×#64904 | C2 | semidirect |
| 3. C4×#3994 | C2 | semidirect |
| 4. D5⋊(C4⋊C16) | C2 | semidirect |
| 11. C5×#493 | C4 | semidirect |
| 13. #65440 | C4 | semidirect |
| 15. #64984 | C4 | semidirect |
| 47. #3994 | D4 | semidirect |
| 106. #493 | AGL(1,𝔽5) | semidirect |
| 197. C4×C5 | #357 | semidirect |
| 201. Dic5 | #357 | semidirect |
| 288. C5 | #13252 | semidirect |
| 307. C4 | #64904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#493 | 2 |
| C2×#64904 | 2 |
| C4×#3994 | 2 |
| D5⋊(C4⋊C16) | 2 |
| #13252 | 5 |