Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 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×C22⋊Dic5 | C2 | semidirect |
| 3. #66132 | C2 | direct (N × H) |
| 4. C2×D4×Dic5 | C2 | semidirect |
| 5. C2×#4072 | C2 | semidirect |
| 7. C22×C5×D4 | C4 | semidirect |
| 11. C23×Dic5 | C22 | semidirect |
| 13. C2×C22⋊Dic5 | C22 | semidirect |
| 14. C2×C22⋊Dic5 | C22 | semidirect |
| 15. D4×Dic5 | C22 | semidirect |
| 16. #4072 | C22 | semidirect |
| 17. C2×C4⋊Dic5 | C22 | semidirect |
| 18. C2×C4×Dic5 | C22 | semidirect |
| 21. C24×C5 | C2×C4 | semidirect |
| 25. C2×C5×D4 | C2×C4 | semidirect |
| 26. C2×C5×D4 | C2×C4 | semidirect |
| 28. C22×C4×C5 | C2×C4 | semidirect |
| 33. C22×Dic5 | C23 | semidirect |
| 35. C22⋊Dic5 | C23 | semidirect |
| 36. C4⋊Dic5 | C23 | semidirect |
| 37. C4×Dic5 | C23 | semidirect |
| 49. C23×C5 | C22×C4 | semidirect |
| 53. C5×D4 | C22×C4 | semidirect |
| 55. C2×C4×C5 | C22×C4 | semidirect |
| 61. C22×D4 | Dic5 | semidirect |
| 86. C24 | C2×Dic5 | semidirect |
| 90. C2×D4 | C2×Dic5 | semidirect |
| 91. C2×D4 | C2×Dic5 | semidirect |
| 96. C22×C4 | C2×Dic5 | semidirect |
| 105. C2×C5 | #518 | semidirect |
| 114. C23 | C22×Dic5 | semidirect |
| 118. D4 | C22×Dic5 | semidirect |
| 123. C2×C4 | C22×Dic5 | semidirect |
| 125. C5 | C2×#518 | semidirect |
| 140. C2 | #66132 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D4 | 2 |
| C22×C22⋊Dic5 | 2 |
| #66132 | 2 |
| C2×D4×Dic5 | 2 |
| C2×#4072 | 2 |
| C2×#518 | 5 |