Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 21. C5×C4⋊C8 | C4 | semidirect |
| 22. #3946 | C4 | semidirect |
| 23. #3946 | C4 | semidirect |
| 24. C4⋊#168 | C4 | semidirect |
| 105. C4⋊C8 | AGL(1,𝔽5) | semidirect |
| 194. C5 | #1949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3994 | 2 |
| C2×#3993 | 2 |
| #65689 | 2 |
| C4×C4⋊AGL(1,𝔽5) | 2 |
| D5×C4⋊C8 | 2 |
| #64893 | 2 |
| #1949 | 5 |