Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#4050 | C2 | semidirect |
| 2. C22×D40 | C2 | semidirect |
| 3. C2×C5×M32 | C2 | semidirect |
| 4. #65197 | C2 | direct (N × H) |
| 5. C2×#3932 | C2 | semidirect |
| 6. C2×D80 | C2 | semidirect |
| 10. C2×Dic20 | C22 | semidirect |
| 12. #4050 | C22 | semidirect |
| 16. C2×D40 | C22 | semidirect |
| 17. C2×D40 | C22 | semidirect |
| 19. C5×M32 | C22 | semidirect |
| 20. C2×C5×C16 | C22 | semidirect |
| 21. #3932 | C22 | semidirect |
| 22. D80 | C22 | semidirect |
| 41. Dic20 | C23 | semidirect |
| 46. D40 | C23 | semidirect |
| 48. C5×C16 | C23 | semidirect |
| 54. C2×M32 | D5 | semidirect |
| 91. M32 | C2×D5 | semidirect |
| 92. C2×C16 | C2×D5 | semidirect |
| 129. C16 | C22×D5 | semidirect |
| 131. C2×C5 | #509 | semidirect |
| 157. C5 | C2×#509 | semidirect |
| 173. C2 | #65197 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4050 | 2 |
| C22×D40 | 2 |
| C2×C5×M32 | 2 |
| #65197 | 2 |
| C2×#3932 | 2 |
| C2×D80 | 2 |
| C2×#509 | 5 |