Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
484 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 72 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×M16 | C2 | semidirect |
| 3. C22×C5×#100 | C3 | semidirect |
| 9. A4×#100 | C5 | direct (N × H) |
| 11. C22×C5×M16 | C2×C3 | semidirect |
| 22. A4×M16 | C2×C5 | semidirect |
| 37. C5×#100 | A4 | direct (N × H) |
| 38. C22×#100 | C3×C5 | semidirect |
| 75. C5×M16 | C2×A4 | semidirect |
| 79. C22×M16 | C2×C3×C5 | semidirect |
| 86. C5×A4 | #100 | direct (N × H) |
| 139. #100 | C5×A4 | direct (N × H) |
| 167. C22×C5 | C3×#100 | semidirect |
| 195. M16 | C2×C5×A4 | semidirect |
| 202. A4 | C5×#100 | direct (N × H) |
| 245. C5 | A4×#100 | direct (N × H) |
| 263. C22 | C3×C5×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×A4 | 2 |
| C5×A4×M16 | 2 |
| C22×C5×#100 | 3 |
| C3×C5×#100 | 4 |
| A4×#100 | 5 |