  Let $G$ be an affine algebraic group over an algrebraically closed field
$\mathbb K$ of characteristic 0 and $H$ be a subgroup of $G$. The stabilizer of
all the set of all vector-functions of $\mathbb K[G]^H$ with respect to the
right action of $H$ is $\hat H$. $V^H=V^{\hat H}$ for a $G$-module $V$. The
subgroup $H$ is called observable if $H=\hat H$ and epimorphic if $G=\hat H$.
In this work I show that under some natural restrictions $H$ is observable if
and only if some orbit of some group contains 0 in the closure and $H$ is
epimorphic if and only the same orbit is closed.
