Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 9. C3×C5×Q32 | C4 | semidirect |
| 15. Dic3×Q32 | C5 | direct (N × H) |
| 39. C5×Q32 | Dic3 | direct (N × H) |
| 58. C3×Q32 | C4×C5 | semidirect |
| 86. C5×Dic3 | Q32 | direct (N × H) |
| 110. Q32 | C5×Dic3 | direct (N × H) |
| 147. C3×C5 | C4×Q32 | semidirect |
| 154. Dic3 | C5×Q32 | direct (N × H) |
| 171. C5 | Dic3×Q32 | direct (N × H) |
| 179. C3 | C4×C5×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q32 | 2 |
| C5×Dic3×Q16 | 2 |
| C5×#4564 | 2 |
| C5×#4504 | 2 |
| C5×Dic3×C16 | 2 |
| C4×C5×Q32 | 3 |
| Dic3×Q32 | 5 |