  A mechanism of radiative generation of realistic neutrino mixing at one-loop
level with $D5\times Z_2$ is presented in this paper. The process is
demonstrated in two set-ups using $D5\times Z_2$ symmetry viz. Model 1 and
Model 2. Two right-handed neutrinos are present in both the models. In both
Model 1 and Model 2, when mixing between these two right-handed neutrinos are
maximal, one can produce the form of the left-handed Majorana neutrino mass
matrix corresponding to $\theta_{13}=0$, $\theta_{23}=\pi/4$ and any value of
$\theta_{12}^0$ associated with Tribimaximal (TBM), Bimaximal (BM), Golden
Ratio (GR) or other mixings. Small shift from maximal mixing between the two
right-handed neutrino states can generate non-zero $\theta_{13}$, deviation of
$\theta_{23}$ from $\pi/4$ and corrections to the solar mixing $\theta_{12}$ in
one step for both Model 1 and Model 2. In both the models, two $Z_2$ odd inert
$SU(2)_L$ doublet scalars are present. The lightest between these two scalars
can be a viable dark matter candidate for both Model 1 and Model 2.
