Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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. #64988 | C2 | semidirect |
| 5. #64970 | C2 | semidirect |
| 6. #64969 | C2 | semidirect |
| 7. C5×#322 | C2 | semidirect |
| 45. #322 | D5 | semidirect |
| 122. C5 | #1720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64988 | 2 |
| #64983 | 2 |
| #64970 | 2 |
| #64969 | 2 |
| C5×#322 | 2 |
| #1720 | 5 |