  Normal subgroups and there properties for finite and infinite iterated wreath
products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded.
The special classes of normal subgroups and there orders are investigated.
Special classes of normal subgroups are investigated and their generators are
found and presented in the form of Kaloujnine tables. Inverse limit of wreath
product of permutation groups is found.
