Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 4. C2×#3947 | C2 | semidirect |
| 5. C2×C8×Dic5 | C2 | semidirect |
| 6. #64770 | C2 | semidirect |
| 7. #64770 | C2 | semidirect |
| 11. C2×C5×M16 | C4 | semidirect |
| 20. C22⋊#168 | C4 | semidirect |
| 84. C2×Dic5 | M16 | semidirect |
| 86. C5×C8 | C22⋊C4 | semidirect |
| 92. C2×M16 | Dic5 | semidirect |
| 184. C8 | C22⋊Dic5 | semidirect |
| 185. C5 | #1753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×M16 | 2 |
| C4×C22⋊Dic5 | 2 |
| C2×C22⋊#168 | 2 |
| C2×#3947 | 2 |
| C2×C8×Dic5 | 2 |
| #64770 | 2 |
| #1753 | 5 |