JNU SSS 2013 Question 12: Logic and proof techniques

An exclusive club is trying very hard to pick its members from the social elite. An exact election mechanism has been agreed upon that will ensure the entrance of only the most suave members from the group $A$, $B$, $C$, $D$, $E$, $F$, $G$ and $H$. Being ‘in’ or ‘out’ of the club is determined by the following rules : If $A$ is in, then $G$ is out. If $H$ is out, then $B$ is in. If $D$ is out, then $E$ is out. If $H$ is in, then $C$ is in. If $B$ is out, then $G$ and $D$ are out.

If $E$ and $G$ are in the club, then what other two people must also be in the club?