Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
338 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C4×C5×A4 | C2 | semidirect |
| 3. C22×C5×C22⋊C4 | C3 | semidirect |
| 5. C22×C5×A4 | C4 | semidirect |
| 9. A4×C22⋊C4 | C5 | direct (N × H) |
| 11. C23×C4×C5 | C2×C3 | semidirect |
| 21. C2×C4×A4 | C2×C5 | semidirect |
| 27. C24×C5 | C3×C4 | semidirect |
| 36. C5×C22⋊C4 | A4 | direct (N × H) |
| 37. C22×C22⋊C4 | C3×C5 | semidirect |
| 41. C5×A4 | C22⋊C4 | direct (N × H) |
| 44. C22×A4 | C4×C5 | semidirect |
| 72. C2×C4×C5 | C2×A4 | semidirect |
| 74. C23×C4 | C2×C3×C5 | semidirect |
| 102. C22×C5 | C3×C22⋊C4 | semidirect |
| 103. C22×C5 | C4×A4 | semidirect |
| 112. C24 | C3×C4×C5 | semidirect |
| 121. C22⋊C4 | C5×A4 | direct (N × H) |
| 126. A4 | C5×C22⋊C4 | direct (N × H) |
| 159. C2×C4 | C2×C5×A4 | semidirect |
| 163. C5 | A4×C22⋊C4 | direct (N × H) |
| 180. C22 | C3×C5×C22⋊C4 | semidirect |
| 181. C22 | C4×C5×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×A4 | 2 |
| C2×C4×C5×A4 | 2 |
| C22×C5×C22⋊C4 | 3 |
| C3×C5×C22⋊C4 | 4 |
| A4×C22⋊C4 | 5 |