Theorem 25, which he credits to Issai Schur, proves the existence of a complement, and theorem 27 proves that all complements are conjugate under the assumption that   or  is solvable. It is not easy to find an explicit statement of the existence of a complement in Schur's published works, though the results of  on the Schur multiplier imply the existence of a complement in the special case when the normal subgroup is in the center.
Theorem 25 asserts the existence of a complement and Theorem 27 confirms that all complements are conjugate under the condition   or  being solvable. While an explicit statement of the existence of a complement may not be found in Schur's published works, his results on the Schur multiplier indicate the existence of a complement when the normal subgroup is in the center.