Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 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. C22×C4⋊Dic5 | C2 | semidirect |
| 5. C22×#683 | C2 | semidirect |
| 6. C22×#683 | C2 | semidirect |
| 7. C22×C4×Dic5 | C2 | semidirect |
| 8. C2×#4025 | C2 | direct (N × H) |
| 19. C2×C4⋊Dic5 | C22 | semidirect |
| 20. C2×#683 | C22 | semidirect |
| 21. C2×#683 | C22 | semidirect |
| 22. C2×C4×Dic5 | C22 | semidirect |
| 23. #4025 | C22 | direct (N × H) |
| 45. C4⋊Dic5 | C23 | semidirect |
| 46. #683 | C23 | semidirect |
| 47. #683 | C23 | semidirect |
| 48. C4×Dic5 | C23 | semidirect |
| 97. C22×C5 | #126 | semidirect |
| 133. C2×C5 | C2×#126 | semidirect |
| 158. C5 | C22×#126 | semidirect |
| 163. C22 | #4025 | direct (N × H) |
| 175. C2 | C2×#4025 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C22⋊C4 | 2 |
| C22×C22⋊Dic5 | 2 |
| C22×C4⋊Dic5 | 2 |
| C22×#683 | 2 |
| C22×C4×Dic5 | 2 |
| C2×#4025 | 2 |
| C22×#126 | 5 |