Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 8. C22×C5×C8 | C4 | semidirect |
| 9. C22×#168 | C4 | semidirect |
| 10. C22⋊#170 | C4 | semidirect |
| 27. C22⋊AGL(1,𝔽5) | C8 | semidirect |
| 69. C22×C8 | AGL(1,𝔽5) | semidirect |
| 150. C5 | #1282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊AGL(1,𝔽5) | 2 |
| D5⋊(C22⋊C8) | 2 |
| C2×#3952 | 2 |
| #1282 | 5 |