  Quantum anomalous Hall insulator (QAH)/$s$-wave superconductor (SC) hybrid
systems are known to be an ideal platform for realizing two-dimensional
topological superconductors with chiral Majorana edge modes. In this paper we
study QAH/unconventional SC hybrid systems whose pairing symmetry is $p$-wave,
$d$-wave, chiral $p$-wave, or chiral $d$-wave. The hybrid systems are a
generalization of the QAH/$s$-wave SC hybrid system. In view of symmetries of
the QAH and pairings, we introduce three topological numbers to classify
topological phases of the hybrid systems. One is the Chern number that
characterizes chiral Majorana edge modes and the others are topological numbers
associated with crystalline symmetries. We numerically calculate the
topological numbers and associated surface states for three characteristic
regimes that feature an influence of unconventional SCs on QAHs. Our
calculation shows a rich variety of topological phases and unveils the
following topological phases that are no counterpart of the $s$-wave case:
crystalline symmetry-protected helical Majorana edge modes, a line node phase
(crystalline-symmetry-protected Bogoliubov Fermi surface), and multiple chiral
Majorana edge modes. The phenomena result from a nontrivial topological
interplay between the QAH and unconventional SCs. Finally, we discuss tunnel
conductance in a junction between a normal metal and the hybrid systems, and
show that the chiral and helical Majorana edge modes are distinguishable in
terms of the presence/absence of zero-bias conductance peak.
