Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. C2×C5×#107 | C2 | semidirect |
| 4. C4⋊C4×Dic5 | C2 | semidirect |
| 6. #64770 | C2 | semidirect |
| 7. #64749 | C2 | semidirect |
| 20. #3953 | C4 | semidirect |
| 53. C2×#107 | D5 | semidirect |
| 205. C5 | #1925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#107 | 2 |
| C2×#3953 | 2 |
| #65277 | 2 |
| C4⋊C4×Dic5 | 2 |
| C2×#3941 | 2 |
| #64770 | 2 |
| #64749 | 2 |
| #1925 | 5 |