Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
880 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 247 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. C22×D120 | C2 | semidirect |
| 2. C22×C3×C5×C16 | C2 | semidirect |
| 3. C2×D240 | C2 | direct (N × H) |
| 8. C2×D120 | C22 | semidirect |
| 9. C2×C3×C5×C16 | C22 | semidirect |
| 10. D240 | C22 | direct (N × H) |
| 13. C22×C5×C16 | D3 | semidirect |
| 22. D120 | C23 | semidirect |
| 23. C3×C5×C16 | C23 | semidirect |
| 25. C22×C3×C16 | D5 | semidirect |
| 31. C2×C5×C16 | C2×D3 | semidirect |
| 47. C2×C3×C16 | C2×D5 | semidirect |
| 57. C5×C16 | C22×D3 | semidirect |
| 60. C22×C16 | D15 | semidirect |
| 61. C22×C3×C5 | D16 | semidirect |
| 75. C3×C16 | C22×D5 | semidirect |
| 90. C2×C16 | C2×D15 | semidirect |
| 91. C2×C3×C5 | C2×D16 | semidirect |
| 103. C22×C5 | D48 | semidirect |
| 117. C16 | C22×D15 | semidirect |
| 118. C3×C5 | C22×D16 | semidirect |
| 119. C22×C3 | D80 | semidirect |
| 125. C2×C5 | C2×D48 | semidirect |
| 137. C2×C3 | C2×D80 | semidirect |
| 140. C5 | C22×D48 | semidirect |
| 143. C22 | D240 | direct (N × H) |
| 147. C3 | C22×D80 | semidirect |
| 149. C2 | C2×D240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D120 | 2 |
| C22×C3×C5×C16 | 2 |
| C2×D240 | 2 |
| C22×D80 | 3 |
| C22×D48 | 5 |