Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
640 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 120 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×C4⋊C4 | C2 | semidirect |
| 3. C42×C5×A4 | C2 | semidirect |
| 4. C22×C5×#126 | C3 | semidirect |
| 9. A4×#126 | C5 | direct (N × H) |
| 14. C22×C5×C4⋊C4 | C2×C3 | semidirect |
| 16. C22×C42×C5 | C2×C3 | semidirect |
| 24. A4×C4⋊C4 | C2×C5 | semidirect |
| 26. C42×A4 | C2×C5 | semidirect |
| 36. C5×#126 | A4 | direct (N × H) |
| 46. C22×#126 | C3×C5 | semidirect |
| 72. C5×C4⋊C4 | C2×A4 | semidirect |
| 80. C42×C5 | C2×A4 | semidirect |
| 85. C22×C4⋊C4 | C2×C3×C5 | semidirect |
| 87. C22×C42 | C2×C3×C5 | semidirect |
| 90. C5×A4 | #126 | direct (N × H) |
| 133. #126 | C5×A4 | direct (N × H) |
| 160. C22×C5 | C3×#126 | semidirect |
| 182. C4⋊C4 | C2×C5×A4 | semidirect |
| 190. C42 | C2×C5×A4 | semidirect |
| 194. A4 | C5×#126 | direct (N × H) |
| 228. C5 | A4×#126 | direct (N × H) |
| 239. C22 | C3×C5×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×C4⋊C4 | 2 |
| C5×A4×C22⋊C4 | 2 |
| C42×C5×A4 | 2 |
| C22×C5×#126 | 3 |
| C3×C5×#126 | 4 |
| A4×#126 | 5 |