Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 48 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. C5×A4×D8 | C2 | semidirect |
| 2. C5×A4×C16 | C2 | semidirect |
| 3. C22×C5×D16 | C3 | semidirect |
| 7. A4×D16 | C5 | direct (N × H) |
| 8. C22×C5×D8 | C2×C3 | semidirect |
| 12. C22×C5×C16 | C2×C3 | semidirect |
| 17. A4×D8 | C2×C5 | semidirect |
| 18. A4×C16 | C2×C5 | semidirect |
| 27. C5×D16 | A4 | direct (N × H) |
| 30. C22×D16 | C3×C5 | semidirect |
| 46. C5×D8 | C2×A4 | semidirect |
| 50. C5×C16 | C2×A4 | semidirect |
| 51. C22×D8 | C2×C3×C5 | semidirect |
| 55. C22×C16 | C2×C3×C5 | semidirect |
| 57. C5×A4 | D16 | direct (N × H) |
| 84. D16 | C5×A4 | direct (N × H) |
| 101. C22×C5 | C3×D16 | semidirect |
| 112. D8 | C2×C5×A4 | semidirect |
| 116. C16 | C2×C5×A4 | semidirect |
| 119. A4 | C5×D16 | direct (N × H) |
| 141. C5 | A4×D16 | direct (N × H) |
| 150. C22 | C3×C5×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×D8 | 2 |
| C5×A4×C16 | 2 |
| C22×C5×D16 | 3 |
| C3×C5×D16 | 4 |
| A4×D16 | 5 |