Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 82 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×C5×C16 | C4 | semidirect |
| 10. C22×#672 | C4 | semidirect |
| 11. C22⋊#674 | C4 | semidirect |
| 55. C22⋊AGL(1,𝔽5) | C16 | semidirect |
| 80. C22×C16 | AGL(1,𝔽5) | semidirect |
| 230. C5 | #7199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C22⋊AGL(1,𝔽5) | 2 |
| D5⋊(C22⋊C16) | 2 |
| C2×#64727 | 2 |
| #7199 | 5 |