Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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. C22×Q8×D5 | C2 | semidirect |
| 3. C22×C5×Q16 | C2 | semidirect |
| 4. C22×#689 | C2 | semidirect |
| 5. C22×#688 | C2 | semidirect |
| 6. C2×#4064 | C2 | direct (N × H) |
| 7. C22×#677 | C2 | semidirect |
| 8. C22×#676 | C2 | semidirect |
| 14. C2×Q8×D5 | C22 | semidirect |
| 22. C2×C5×Q16 | C22 | semidirect |
| 24. C2×#689 | C22 | semidirect |
| 25. C2×#688 | C22 | semidirect |
| 27. #4064 | C22 | direct (N × H) |
| 28. C2×#677 | C22 | semidirect |
| 29. C2×#676 | C22 | semidirect |
| 45. Q8×D5 | C23 | semidirect |
| 56. C5×Q16 | C23 | semidirect |
| 58. #689 | C23 | semidirect |
| 59. #688 | C23 | semidirect |
| 61. #677 | C23 | semidirect |
| 62. #676 | C23 | semidirect |
| 67. C22×Q16 | D5 | semidirect |
| 113. C2×Q16 | C2×D5 | semidirect |
| 119. C22×C5 | #137 | semidirect |
| 157. Q16 | C22×D5 | semidirect |
| 163. C2×C5 | C2×#137 | semidirect |
| 194. C5 | C22×#137 | semidirect |
| 199. C22 | #4064 | direct (N × H) |
| 209. C2 | C2×#4064 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#713 | 2 |
| C22×Q8×D5 | 2 |
| C22×C5×Q16 | 2 |
| C22×#689 | 2 |
| C22×#688 | 2 |
| C2×#4064 | 2 |
| C22×#677 | 2 |
| C22×#676 | 2 |
| C22×#137 | 5 |