Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
232 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#3993 | C2 | semidirect |
| 3. C2×#3990 | C2 | semidirect |
| 4. #64903 | C2 | direct (N × H) |
| 7. C2×C5×D8 | C4 | semidirect |
| 11. #4058 | C4 | semidirect |
| 13. C2×Dic20 | C4 | semidirect |
| 17. #3993 | C22 | semidirect |
| 19. #3990 | C22 | semidirect |
| 34. C5×D8 | C2×C4 | semidirect |
| 40. Dic20 | C2×C4 | semidirect |
| 80. C2×D8 | AGL(1,𝔽5) | semidirect |
| 115. D8 | C2×AGL(1,𝔽5) | semidirect |
| 126. C2×C5 | #360 | semidirect |
| 153. C5 | C2×#360 | semidirect |
| 169. C2 | #64903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4058 | 2 |
| C2×#3993 | 2 |
| C2×#3990 | 2 |
| #64903 | 2 |
| C2×#360 | 5 |