Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 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. Q8×Dic10 | C2 | semidirect |
| 5. #65309 | C2 | semidirect |
| 7. #65144 | C2 | semidirect |
| 8. #65080 | C2 | semidirect |
| 10. #64969 | C2 | semidirect |
| 11. C8×Dic10 | C2 | semidirect |
| 52. C5×SD16 | Q8 | semidirect |
| 87. C5×Q8 | C2×Q8 | semidirect |
| 106. Dic10 | SD16 | direct (N × H) |
| 108. C5×C8 | C2×Q8 | semidirect |
| 164. SD16 | Dic10 | direct (N × H) |
| 197. Q8 | C2×Dic10 | semidirect |
| 214. C8 | C2×Dic10 | semidirect |
| 215. C5 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic10 | 2 |
| D4×Dic10 | 2 |
| C4×C5×SD16 | 2 |
| SD16×Dic5 | 2 |
| #65309 | 2 |
| #65297 | 2 |
| #65144 | 2 |
| #65080 | 2 |
| #65050 | 2 |
| #64969 | 2 |
| C8×Dic10 | 2 |
| Q8×SD16 | 5 |