Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#4097 | C2 | semidirect |
| 3. D4×Dic10 | C2 | semidirect |
| 4. #65528 | C2 | semidirect |
| 5. #65365 | C2 | semidirect |
| 6. #65364 | C2 | semidirect |
| 7. #65331 | C2 | semidirect |
| 8. #65329 | C2 | semidirect |
| 9. #65320 | C2 | semidirect |
| 10. C4×#689 | C2 | semidirect |
| 11. #65301 | C2 | semidirect |
| 69. #689 | D4 | semidirect |
| 167. C4×C5 | #137 | semidirect |
| 250. C5 | #3278 | semidirect |
| 265. C4 | #4097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#550 | 2 |
| C2×#4097 | 2 |
| D4×Dic10 | 2 |
| #65528 | 2 |
| #65365 | 2 |
| #65364 | 2 |
| #65331 | 2 |
| #65329 | 2 |
| #65320 | 2 |
| C4×#689 | 2 |
| #65301 | 2 |
| #3278 | 5 |