Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 90 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. C5×#948 | C2 | semidirect |
| 3. C5×#907 | C2 | semidirect |
| 4. C3×C5×#104 | C2 | semidirect |
| 5. C5×#822 | C2 | semidirect |
| 6. C5×#805 | C2 | semidirect |
| 7. C4×C5×C3⋊C8 | C2 | semidirect |
| 13. C5×#216 | C4 | semidirect |
| 14. C5×#215 | C4 | semidirect |
| 15. C5×#214 | C4 | semidirect |
| 16. C5×#213 | C4 | semidirect |
| 24. #4824 | C5 | direct (N × H) |
| 30. C5×#104 | D3 | semidirect |
| 49. #948 | C2×C5 | semidirect |
| 50. #907 | C2×C5 | semidirect |
| 51. C3×#104 | C2×C5 | semidirect |
| 52. #822 | C2×C5 | semidirect |
| 53. #805 | C2×C5 | semidirect |
| 54. C4×C3⋊C8 | C2×C5 | semidirect |
| 83. #216 | C4×C5 | semidirect |
| 84. #215 | C4×C5 | semidirect |
| 85. #214 | C4×C5 | semidirect |
| 86. #213 | C4×C5 | semidirect |
| 115. #104 | C5×D3 | semidirect |
| 160. C3×C5 | #443 | semidirect |
| 193. C5 | #4824 | direct (N × H) |
| 202. C3 | C5×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#950 | 2 |
| C5×#948 | 2 |
| C5×#907 | 2 |
| C3×C5×#104 | 2 |
| C5×#822 | 2 |
| C5×#805 | 2 |
| C4×C5×C3⋊C8 | 2 |
| C5×#443 | 3 |
| #4824 | 5 |