Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 214 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. C5×#1010 | C2 | semidirect |
| 2. C5×#1009 | C2 | semidirect |
| 3. C3×C5×#131 | C2 | semidirect |
| 4. C5×#909 | C2 | semidirect |
| 5. C5×#908 | C2 | semidirect |
| 6. C5×#904 | C2 | semidirect |
| 7. C2×C5×#204 | C2 | semidirect |
| 15. C5×#235 | C22 | semidirect |
| 17. C2×C5×Dic6 | C22 | semidirect |
| 18. C3×C5×M16 | C22 | semidirect |
| 19. C2×C3×C5×C8 | C22 | semidirect |
| 20. C5×Dic12 | C22 | semidirect |
| 21. C5×D24 | C22 | semidirect |
| 22. C5×#204 | C22 | semidirect |
| 23. C5×#204 | C22 | semidirect |
| 24. C5×#204 | C22 | semidirect |
| 25. #5751 | C5 | direct (N × H) |
| 32. C5×#131 | D3 | semidirect |
| 50. #1010 | C2×C5 | semidirect |
| 51. #1009 | C2×C5 | semidirect |
| 52. C3×#131 | C2×C5 | semidirect |
| 53. #909 | C2×C5 | semidirect |
| 54. #908 | C2×C5 | semidirect |
| 55. #904 | C2×C5 | semidirect |
| 56. C2×#204 | C2×C5 | semidirect |
| 71. C5×M16 | C2×D3 | semidirect |
| 72. C2×C5×C8 | C2×D3 | semidirect |
| 88. #235 | C22×C5 | semidirect |
| 90. C2×Dic6 | C22×C5 | semidirect |
| 91. C3×M16 | C22×C5 | semidirect |
| 92. C2×C3×C8 | C22×C5 | semidirect |
| 93. Dic12 | C22×C5 | semidirect |
| 94. D24 | C22×C5 | semidirect |
| 95. #204 | C22×C5 | semidirect |
| 96. #204 | C22×C5 | semidirect |
| 97. #204 | C22×C5 | semidirect |
| 121. #131 | C5×D3 | semidirect |
| 165. M16 | C2×C5×D3 | semidirect |
| 166. C2×C8 | C2×C5×D3 | semidirect |
| 167. C3×C5 | #577 | semidirect |
| 201. C5 | #5751 | direct (N × H) |
| 210. C3 | C5×#577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1010 | 2 |
| C5×#1009 | 2 |
| C3×C5×#131 | 2 |
| C5×#909 | 2 |
| C5×#908 | 2 |
| C5×#904 | 2 |
| C2×C5×#204 | 2 |
| C5×#577 | 3 |
| #5751 | 5 |