Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
166 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 56 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×#170 | C2 | semidirect |
| 4. Q8⋊#170 | C2 | semidirect |
| 6. #64884 | C2 | semidirect |
| 7. #170⋊C8 | C2 | semidirect |
| 51. C5×Q8 | M16 | semidirect |
| 120. Q8 | #704 | semidirect |
| 138. C5 | #1588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#170 | 2 |
| #65774 | 2 |
| SD16×Dic5 | 2 |
| Q8⋊#170 | 2 |
| D4⋊#170 | 2 |
| #64884 | 2 |
| #170⋊C8 | 2 |
| #1588 | 5 |