  We consider three-loop radiative corrections to the Lamb shift and hyperfine
splitting. Corrections of order $\alpha^3(Z\alpha)^5m$ are the largest still
unknown contributions to the Lamb shift in hydrogen. We calculated radiative
corrections to the Lamb shift and hyperfine splitting generated by the diagrams
with insertions of one radiative photon and electron polarization loops in the
graphs with two external photons. We also obtained corrections generated by the
gauge invariant sets of diagrams with two reducible radiative photon insertions
in the electron line and polarization operator insertion in one of the
radiative photons, and diagrams with two reducible radiative photon insertions
in the electron line and polarization operator insertion in one the external
photons. Corrections to the Lamb shift and hyperfine splitting generated by the
diagrams with insertions of the three-loop one-particle reducible diagrams with
radiative photons in the electron line are calculated in the Yennie gauge.
