Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#689 | C2 | semidirect |
| 4. #65517 | C2 | semidirect |
| 5. #65381 | C2 | semidirect |
| 6. #65379 | C2 | semidirect |
| 7. #65340 | C2 | semidirect |
| 8. #65339 | C2 | semidirect |
| 9. #65320 | C2 | semidirect |
| 10. C4×#689 | C2 | semidirect |
| 72. #689 | D4 | direct (N × H) |
| 100. C5×D4 | Q16 | semidirect |
| 155. C22×C5 | C2×Q16 | semidirect |
| 162. C4×C5 | C2×Q16 | semidirect |
| 223. D4 | #689 | direct (N × H) |
| 241. C5 | D4×Q16 | semidirect |
| 244. C22 | C2×#689 | semidirect |
| 254. C4 | C2×#689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Q8 | 2 |
| C22×#689 | 2 |
| D4×Dic10 | 2 |
| #65517 | 2 |
| #65381 | 2 |
| #65379 | 2 |
| #65340 | 2 |
| #65339 | 2 |
| #65320 | 2 |
| C4×#689 | 2 |
| D4×#168 | 2 |
| D4×Q16 | 5 |