Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
256 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 16. C5×C4⋊C8 | C4 | semidirect |
| 17. #3946 | C4 | semidirect |
| 18. C4⋊#168 | C4 | semidirect |
| 85. C4⋊C8 | AGL(1,𝔽5) | semidirect |
| 98. C4×C5 | #107 | semidirect |
| 102. Dic5 | #107 | semidirect |
| 161. C5 | #1947 | semidirect |
| 177. C4 | #3994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3994 | 2 |
| #65688 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 2 |
| D5×C4⋊C8 | 2 |
| #64893 | 2 |
| #1947 | 5 |