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. C3×C5×2−1+4 | C2 | semidirect |
| 2. C3×#4149 | C2 | semidirect |
| 3. C3×#4096 | C2 | semidirect |
| 4. C3×#4095 | C2 | semidirect |
| 5. C3×#4094 | C2 | semidirect |
| 6. C3×#4088 | C2 | semidirect |
| 7. C2×C3×#688 | C2 | semidirect |
| 8. #66171 | C3 | direct (N × H) |
| 11. C3×C5×#41 | C22 | semidirect |
| 13. C2×C3×C5×Q8 | C22 | semidirect |
| 18. C3×#689 | C22 | semidirect |
| 19. C3×#688 | C22 | semidirect |
| 20. C3×#688 | C22 | semidirect |
| 21. C3×#687 | C22 | semidirect |
| 22. C3×#686 | C22 | semidirect |
| 23. C3×#681 | C22 | semidirect |
| 24. C2×C3×#168 | C22 | semidirect |
| 26. C5×2−1+4 | C2×C3 | semidirect |
| 27. #4149 | C2×C3 | semidirect |
| 28. #4096 | C2×C3 | semidirect |
| 29. #4095 | C2×C3 | semidirect |
| 30. #4094 | C2×C3 | semidirect |
| 31. #4088 | C2×C3 | semidirect |
| 32. C2×#688 | C2×C3 | semidirect |
| 50. C3×2−1+4 | D5 | semidirect |
| 59. C5×#41 | C22×C3 | semidirect |
| 61. C2×C5×Q8 | C22×C3 | semidirect |
| 66. #689 | C22×C3 | semidirect |
| 67. #688 | C22×C3 | semidirect |
| 68. #688 | C22×C3 | semidirect |
| 69. #687 | C22×C3 | semidirect |
| 70. #686 | C22×C3 | semidirect |
| 71. #681 | C22×C3 | semidirect |
| 72. C2×#168 | C22×C3 | semidirect |
| 86. C3×#41 | C2×D5 | semidirect |
| 88. C2×C3×Q8 | C2×D5 | semidirect |
| 115. 2−1+4 | C3×D5 | semidirect |
| 155. #41 | C2×C3×D5 | semidirect |
| 157. C2×Q8 | C2×C3×D5 | semidirect |
| 167. C3×C5 | #577 | semidirect |
| 201. C5 | C3×#577 | semidirect |
| 210. C3 | #66171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×2−1+4 | 2 |
| C3×#4149 | 2 |
| C3×#4096 | 2 |
| C3×#4095 | 2 |
| C3×#4094 | 2 |
| C3×#4088 | 2 |
| C2×C3×#688 | 2 |
| #66171 | 3 |
| C3×#577 | 5 |