  We study the structural, magnetic, transport and electronic properties of
LaCoO$_3$ with Sr/Nb co-substitution, i.e.,
La$_{(1-2x)}$Sr$_{2x}$Co$_{(1-x)}$Nb$_{x}$O$_3$ using x-ray and neutron
diffraction, dc and ac-magnetization, neutron depolarization, dc-resistivity
and photoemission measurements. The powder x-ray and neutron diffraction data
were fitted well with the rhombohedral crystal symmetry (space group
\textit{R$\bar{3}$c}) in Rietveld refinement analysis. The calculated effective
magnetic moment ($\approx$3.85~$\mu_B$) and average spin ($\approx$1.5) of Co
ions from the analysis of magnetic susceptibility data are consistent with 3+
state of Co ions in intermediate-spin (IS) and high-spin (HS) states in the
ratio of $\approx$50:50, i.e., spin-state of Co$^{3+}$ is preserved at least up
to $x=$ 0.1 sample. Interestingly, the magnetization values were significantly
increased with respect to the $x=$ 0 sample, and the M-H curves show
non-saturated behavior up to an applied maximum magnetic field of $\pm$70 kOe.
The ac-susceptibility data show a shift in the freezing temperature with
excitation frequency and the detailed analysis confirm the slower dynamics and
a non-zero value of the Vogel-Fulcher temperature T$_0$, which suggests for the
cluster spin glass. The unusual magnetic behavior indicates the presence of
complex magnetic interactions at low temperatures. The dc-resistivity
measurements show the insulating nature in all the samples. However, relatively
large density of states $\approx$10$^{22}$ eV$^{-1}$cm$^{-3}$ and low
activation energy $\approx$130~meV are found in $x=$ 0.05 sample. Using x-ray
photoemission spectroscopy, we study the core-level spectra of La 3$d$, Co
2$p$, Sr 3$d$, and Nb 3$d$ to confirm the valence state.
