Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
386 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 9. C22⋊#674 | C4 | semidirect |
| 13. C5×C22⋊C16 | C4 | semidirect |
| 14. C22⋊#672 | C4 | semidirect |
| 51. C22×AGL(1,𝔽5) | C16 | semidirect |
| 94. C22⋊C16 | AGL(1,𝔽5) | semidirect |
| 265. C5 | #7183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×AGL(1,𝔽5))⋊C8 | 2 |
| D5⋊(C22⋊C16) | 2 |
| D5×C22⋊C16 | 2 |
| #7183 | 5 |