Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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. #65371 | C2 | semidirect |
| 4. #65369 | C2 | semidirect |
| 7. #65311 | C2 | semidirect |
| 178. C5 | #3236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#533 | 2 |
| C2×#4016 | 2 |
| #65371 | 2 |
| #65369 | 2 |
| #65333 | 2 |
| #65332 | 2 |
| #65311 | 2 |
| #65215 | 2 |
| #3236 | 5 |