  Using vacuum domain structure model, trivial static potentials in various
representations of $F_4$, $E_6$ and $G_2$ exceptional groups are calculated by
means of the unit center element. Due to the absence of the non-trivial center
elements, the potential of every representation is screened at far distances.
However, the linear part is observed at intermediate quark separations which is
investigated by the decomposition of the exceptional group to its maximal
subgroups. Comparing the group factor of the super-group with the corresponding
one obtained from the non-trivial center elements of $SU(3)$ subgroup, shows
that $SU(3)$ is not the direct cause of temporary confinement in any of the
exceptional groups. However, the trivial potential obtained from the group
decomposition to the $SU(3)$ subgroup is the same as the potential of the
super-group itself. In addition, any regular or singular decomposition to the
$SU(2)$ subgroup which produces the Cartan generator with the same elements as
$h_1$, in any exceptional group, leads to the linear intermediate potential of
the exceptional gauge groups. The other $SU(2)$ decompositions with the Cartan
generator different from $h_1$, are still able to describe the linear potential
if the number of $SU(2)$ non-trivial center element which emerge in the
decompositions is the same. As a result, it is the center vortices quantized in
terms of non-trivial center element of the $SU(2)$ subgroup which give rise to
the intermediate confinement in the static potentials.
