Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
232 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #65411 | C2 | semidirect |
| 5. #65253 | C2 | semidirect |
| 6. C5×#343 | C2 | semidirect |
| 7. #64778 | C2 | semidirect |
| 15. #3955 | C4 | semidirect |
| 58. #343 | D5 | semidirect |
| 177. C5 | #1931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65420 | 2 |
| C2×#3955 | 2 |
| #65411 | 2 |
| C2×#3941 | 2 |
| #65253 | 2 |
| C5×#343 | 2 |
| #64778 | 2 |
| #1931 | 5 |