  Let $X$ be any $\mathbb{Q}$-Fano variety and $\mathrm{Aut}(X)_0$ be the
identity component of the automorphism group of $X$. Let $\mathbb{G}$ be a
connected reductive subgroup of $\mathrm{Aut}(X)_0$ that contains a maximal
torus of $\mathrm{Aut}(X)_0$. We prove that $X$ admits a K\"{a}hler-Einstein
metric if and only if $X$ is $\mathbb{G}$-uniformly K-stable. This proves a
version of Yau-Tian-Donaldson conjecture for arbitrary singular Fano varieties.
A key new ingredient is a valuative criterion for $\mathbb{G}$-uniform
K-stability.
