Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 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 |
|---|---|---|
| 1. C23×C5×Q8 | C2 | semidirect |
| 3. C22×#689 | C2 | semidirect |
| 4. C2×#4088 | C2 | direct (N × H) |
| 5. C22×#688 | C2 | semidirect |
| 6. C22×#681 | C2 | semidirect |
| 10. C22×C5×Q8 | C22 | semidirect |
| 19. C2×#689 | C22 | semidirect |
| 20. #4088 | C22 | direct (N × H) |
| 21. C2×#688 | C22 | semidirect |
| 22. C2×#681 | C22 | semidirect |
| 31. C2×C5×Q8 | C23 | semidirect |
| 47. #689 | C23 | semidirect |
| 48. #688 | C23 | semidirect |
| 49. #681 | C23 | semidirect |
| 52. C23×Q8 | D5 | semidirect |
| 86. C22×Q8 | C2×D5 | semidirect |
| 98. C22×C5 | #137 | semidirect |
| 118. C2×Q8 | C22×D5 | semidirect |
| 135. C2×C5 | C2×#137 | semidirect |
| 161. C5 | C22×#137 | semidirect |
| 165. C22 | #4088 | direct (N × H) |
| 175. C2 | C2×#4088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×Q8 | 2 |
| C22×#709 | 2 |
| C22×#689 | 2 |
| C2×#4088 | 2 |
| C22×#688 | 2 |
| C22×#681 | 2 |
| C22×#137 | 5 |