  We investigate the instabilities and associated bifurcation structure near
the onset of rotating magnetoconvection of low Prandtl number fluids by
performing three dimensional direct numerical simulations. Previous studies
considered zero magnetic Prandtl number ($\mathrm{Pm}$) limit for the
investigation of bifurcation structure near the onset of convection. Here we
numerically investigate the effect of $\mathrm{Pm}$ on the bifurcation
structure. The classical Rayleigh-B\'{e}nard convection setup in the presence
of horizontal magnetic field and rotation about the vertical axis are
considered for the study. The control parameters, including the Taylor number
($\mathrm{Ta}$), Chandrasekhar number ($\mathrm{Q}$), reduced Rayleigh number
($\mathrm{r}$), and magnetic Prandtl number ($\mathrm{Pm}$) are varied in the
ranges $0 < \mathrm{Ta}\leq 500$, $0 < \mathrm{Q}\leq 1000$, $0.8\leq
\mathrm{r} \leq 2$ and $0 < \mathrm{Pm} < 1$ by considering Prandtl numbers
$\mathrm{Pr}= 0.025$ and $0.1$. The investigation reveals the presence of
supercritical, subcritical and hybrid transitions to convection. These
transitions leads to infinitesimal and finite amplitude fluid patterns at the
onset of convection. The finite amplitude solutions can be both stationary and
time dependent. The bifurcation structures associated with these flow patterns
at the onset are studied in detail. For very small $\mathrm{Pm}$, the
bifurcation structure is found to be qualitatively similar to the ones observed
in the $\mathrm{Pm}\rightarrow 0$ limit. However, as $\mathrm{Pm}$ is
increased, several new solutions appear at the onset and the resulting
bifurcation structures are greatly modified.
