Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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. #65126 | C2 | semidirect |
| 3. #64974 | C2 | semidirect |
| 4. C5×D4⋊C8 | C2 | semidirect |
| 5. D4⋊#168 | C2 | semidirect |
| 6. #64704 | C2 | semidirect |
| 7. #64676 | C2 | semidirect |
| 62. D4⋊C8 | D5 | semidirect |
| 187. C5 | #1495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65891 | 2 |
| #65126 | 2 |
| #64974 | 2 |
| C5×D4⋊C8 | 2 |
| D4⋊#168 | 2 |
| #64704 | 2 |
| #64676 | 2 |
| #1495 | 5 |