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. C5×#1009 | C2 | semidirect |
| 3. C5×#950 | C2 | semidirect |
| 4. C5×#949 | C2 | semidirect |
| 5. C5×#948 | C2 | semidirect |
| 6. C5×#942 | C2 | semidirect |
| 7. C2×C5×#215 | C2 | semidirect |
| 11. C3×C5×#41 | C22 | semidirect |
| 13. C2×C3×C5×Q8 | C22 | semidirect |
| 18. C5×#216 | C22 | semidirect |
| 19. C5×#215 | C22 | semidirect |
| 20. C5×#215 | C22 | semidirect |
| 21. C5×#214 | C22 | semidirect |
| 22. C5×#213 | C22 | semidirect |
| 23. C5×#208 | C22 | semidirect |
| 24. C2×C5×C3⋊C8 | C22 | semidirect |
| 25. #5837 | C5 | direct (N × H) |
| 26. C5×2−1+4 | D3 | semidirect |
| 50. C3×2−1+4 | C2×C5 | semidirect |
| 51. #1009 | C2×C5 | semidirect |
| 52. #950 | C2×C5 | semidirect |
| 53. #949 | C2×C5 | semidirect |
| 54. #948 | C2×C5 | semidirect |
| 55. #942 | C2×C5 | semidirect |
| 56. C2×#215 | C2×C5 | semidirect |
| 61. C5×#41 | C2×D3 | semidirect |
| 63. C2×C5×Q8 | C2×D3 | semidirect |
| 84. C3×#41 | C22×C5 | semidirect |
| 86. C2×C3×Q8 | C22×C5 | semidirect |
| 91. #216 | C22×C5 | semidirect |
| 92. #215 | C22×C5 | semidirect |
| 93. #215 | C22×C5 | semidirect |
| 94. #214 | C22×C5 | semidirect |
| 95. #213 | C22×C5 | semidirect |
| 96. #208 | C22×C5 | semidirect |
| 97. C2×C3⋊C8 | C22×C5 | semidirect |
| 115. 2−1+4 | C5×D3 | semidirect |
| 155. #41 | C2×C5×D3 | semidirect |
| 157. C2×Q8 | C2×C5×D3 | semidirect |
| 167. C3×C5 | #577 | semidirect |
| 201. C5 | #5837 | 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 |
|---|---|
| C3×C5×2−1+4 | 2 |
| C5×#1009 | 2 |
| C5×#950 | 2 |
| C5×#949 | 2 |
| C5×#948 | 2 |
| C5×#942 | 2 |
| C2×C5×#215 | 2 |
| C5×#577 | 3 |
| #5837 | 5 |