Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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×#477 | C2 | semidirect |
| 3. #65381 | C2 | semidirect |
| 5. Q8⋊#168 | C2 | semidirect |
| 7. #64701 | C2 | semidirect |
| 51. #477 | D5 | semidirect |
| 69. D20 | Q16 | semidirect |
| 156. C5 | #1632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65913 | 2 |
| C5×#477 | 2 |
| #65381 | 2 |
| #65373 | 2 |
| Q8⋊#168 | 2 |
| #64703 | 2 |
| #64701 | 2 |
| #1632 | 5 |