  Let $X$ be a smooth, separated, geometrically connected scheme defined over a
number field $K$ and $\{\rho_\lambda\}_\lambda$ a system of n-dimensional
semisimple $\lambda$-adic representations of the \'etale fundamental group of
$X$ such that for each closed point $x$ of $X$, the specialization
$\{\rho_{\lambda,x}\}_\lambda$ is a compatible system of Galois representations
under mild local conditions. For almost all $\lambda$, we prove that any type A
irreducible subrepresentation of $\rho_\lambda\otimes \bar{\mathbb{Q}}_\ell$ is
residually irreducible. When $K$ is totally real or CM, $n\leq 6$, and
$\{\rho_\lambda\}_\lambda$ is the compatible system of Galois representations
of $K$ attached to a regular algebraic, polarized, cuspidal automorphic
representation of $\mathrm{GL}_n(\mathbb{A}_K)$, for almost all $\lambda$ we
prove that $\rho_\lambda\otimes\bar{\mathbb{Q}}_\ell$ is (i) irreducible and
(ii) residually irreducible if in addition $K=\mathbb{Q}$.
