Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
220 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 220 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×Q16 | C2 | semidirect |
| 3. C5×A4×C16 | C2 | semidirect |
| 4. C22×C5×SD32 | C3 | semidirect |
| 9. A4×SD32 | C5 | direct (N × H) |
| 10. C22×C5×Q16 | C2×C3 | semidirect |
| 16. C22×C5×C16 | C2×C3 | semidirect |
| 23. A4×Q16 | C2×C5 | semidirect |
| 25. A4×C16 | C2×C5 | semidirect |
| 39. C5×SD32 | A4 | direct (N × H) |
| 42. C22×SD32 | C3×C5 | semidirect |
| 64. C5×Q16 | C2×A4 | semidirect |
| 72. C5×C16 | C2×A4 | semidirect |
| 73. C22×Q16 | C2×C3×C5 | semidirect |
| 79. C22×C16 | C2×C3×C5 | semidirect |
| 81. C5×A4 | SD32 | direct (N × H) |
| 122. SD32 | C5×A4 | direct (N × H) |
| 140. C22×C5 | C3×SD32 | semidirect |
| 157. Q16 | C2×C5×A4 | semidirect |
| 165. C16 | C2×C5×A4 | semidirect |
| 168. A4 | C5×SD32 | direct (N × H) |
| 197. C5 | A4×SD32 | direct (N × H) |
| 206. C22 | C3×C5×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×A4×Q16 | 2 |
| C5×A4×D8 | 2 |
| C5×A4×C16 | 2 |
| C22×C5×SD32 | 3 |
| C3×C5×SD32 | 4 |
| A4×SD32 | 5 |