Let M be a maximal subalgebra of a Lie algebra L and A/B a chief factor of L such that B ⊆ M and A ⊄ M. We call the factor algebra M ∩ A/B a c-section of M. All such c-sections are isomorphic, and this concept is related those of c-ideals and ideal index previously introduced by the author. Properties of c-sections are studied and some new characterizations of solvable Lie algebras are obtained.