Theorem 17.2:

(i) The group action defined in theorem (17.1) is transitive.

(ii) For $x_0 \in X$ and each ${\tilde x}\in p^{-1}(x_0)$, the stabilizer of ${\tilde x}$ is the subgroup $p_*(\pi_1({\tilde X}, {\tilde x}))$.

(iii) The family $\{p_*(\pi_1({\tilde X}, {\tilde x}))/ {\tilde x}\in p^{-1}(x_0)\}$ forms a complete conjugacy class of subgroups of $\pi_1(X, x_0)$.

(iv) $\vert p^{-1}(x_0)\vert = [\pi_1(X, x_0) : p_*(\pi_1({\tilde X}, {\tilde x}_0))]$