  A normal subgroup $E$ of a group $G$ is said to be hypercyclically embedded
in $G$ if either $E=1$ or $E\neq 1$ and every chief factor of $G$ below $E$ is
cyclic. In this article, we present some new characterizations of a normal
subgroup to be hypercyclically embedded. Some recent results in this literature
are generalized and unified.
