Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 84 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×A4×C16 | C2 | direct (N × H) |
| 3. C23×C5×C16 | C3 | semidirect |
| 8. C2×A4×C16 | C5 | direct (N × H) |
| 13. C22×C5×C16 | C2×C3 | semidirect |
| 20. A4×C16 | C2×C5 | direct (N × H) |
| 33. C2×C5×C16 | A4 | direct (N × H) |
| 34. C23×C16 | C3×C5 | semidirect |
| 35. C2×C5×A4 | C16 | direct (N × H) |
| 61. C5×C16 | C2×A4 | direct (N × H) |
| 66. C22×C16 | C2×C3×C5 | semidirect |
| 68. C5×A4 | C2×C16 | direct (N × H) |
| 79. C23×C5 | C3×C16 | semidirect |
| 106. C2×C16 | C5×A4 | direct (N × H) |
| 109. C2×A4 | C5×C16 | direct (N × H) |
| 121. C22×C5 | C2×C3×C16 | semidirect |
| 144. C16 | C2×C5×A4 | direct (N × H) |
| 147. A4 | C2×C5×C16 | direct (N × H) |
| 153. C2×C5 | A4×C16 | direct (N × H) |
| 158. C23 | C3×C5×C16 | semidirect |
| 175. C5 | C2×A4×C16 | direct (N × H) |
| 183. C22 | C2×C3×C5×C16 | semidirect |
| 193. C2 | C5×A4×C16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×A4 | 2 |
| C5×A4×C16 | 2 |
| C23×C5×C16 | 3 |
| C2×C3×C5×C16 | 4 |
| C2×A4×C16 | 5 |