  It is well-known that any isotopically connected diffeomorphism group $G$ of
a manifold determines uniquely a singular foliation $\F_G$. A one-to-one
correspondence between the class of singular foliations and a subclass of
diffeomorphism groups is established. As an illustration of this correspondence
it is shown that the commutator subgroup $[G,G]$ of an isotopically connected,
factorizable and non-fixing $C^r$-diffeomorphism group $G$ is simple iff the
foliation $\F_{[G,G]}$ defined by $[G,G]$ admits no proper minimal sets. In
particular, the compactly supported $e$-component of the leaf preserving
$C^{\infty}$-diffeomorphism group of a regular foliation $\F$ is simple iff
$\F$ has no proper minimal sets.
