Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. C5×#500 | C2 | semidirect |
| 3. #65379 | C2 | semidirect |
| 5. #64767 | C2 | semidirect |
| 7. #64676 | C2 | semidirect |
| 52. #500 | D5 | semidirect |
| 72. D20 | Q16 | semidirect |
| 166. C5 | #1649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66061 | 2 |
| C5×#500 | 2 |
| #65379 | 2 |
| #65376 | 2 |
| #64767 | 2 |
| #64679 | 2 |
| #64676 | 2 |
| #1649 | 5 |