Remark 1

Let H be an integral subgroup of G. Let Y be the left foliation of G associated with L(H). If $g \in G$, let $gH$ be given the manifold structure derived from that on H by $\gamma(g)$. By Differentiable and Analytic Manifolds, R, 9.3.2, the canonical injection of $gH$ into Y is a morphism. This morphism is étale. Hence the maximal connected leaves of Y are the left cosets modulo H.