Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. D4×Dic10 | C2 | semidirect |
| 4. #65296 | C2 | semidirect |
| 5. #65163 | C2 | semidirect |
| 6. #65048 | C2 | semidirect |
| 7. #64971 | C2 | semidirect |
| 8. C8×Dic10 | C2 | semidirect |
| 36. C5×D8 | Q8 | semidirect |
| 60. C5×D4 | C2×Q8 | semidirect |
| 72. Dic10 | D8 | direct (N × H) |
| 74. C5×C8 | C2×Q8 | semidirect |
| 114. D8 | Dic10 | direct (N × H) |
| 137. D4 | C2×Dic10 | semidirect |
| 149. C8 | C2×Dic10 | semidirect |
| 150. C5 | Q8×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic10 | 2 |
| C4×C5×D8 | 2 |
| D8×Dic5 | 2 |
| #65296 | 2 |
| #65163 | 2 |
| #65048 | 2 |
| #64971 | 2 |
| C8×Dic10 | 2 |
| Q8×D8 | 5 |