Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
816 conjugacy classes of subgroups; only the 516 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 516 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 |
|---|---|---|
| 3. C42×#170 | C3 | direct (N × H) |
| 8. C3×C4×#170 | C4 | direct (N × H) |
| 16. C3×C42×C5 | C8 | semidirect |
| 17. C3×C4×Dic5 | C8 | semidirect |
| 25. C4×#170 | C3×C4 | direct (N × H) |
| 34. C3×#170 | C42 | direct (N × H) |
| 44. C42×C5 | C3×C8 | semidirect |
| 45. C4×Dic5 | C3×C8 | semidirect |
| 52. C3×C4×C5 | C4×C8 | semidirect |
| 53. C3×Dic5 | C4×C8 | semidirect |
| 61. C3×C42 | #170 | direct (N × H) |
| 69. #170 | C3×C42 | direct (N × H) |
| 89. C4×C5 | C3×C4×C8 | semidirect |
| 90. Dic5 | C3×C4×C8 | semidirect |
| 98. C42 | C3×#170 | direct (N × H) |
| 99. C3×C5 | C42×C8 | semidirect |
| 105. C3×C4 | C4×#170 | direct (N × H) |
| 120. C5 | C3×C42×C8 | semidirect |
| 126. C4 | C3×C4×#170 | direct (N × H) |
| 127. C3 | C42×#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×#170 | 2 |
| C3×C42×Dic5 | 2 |
| C42×#170 | 3 |
| C3×C42×C8 | 5 |