  We investigate finite-$N$ corrections to the superconformal indices of the
theories realized on M2- and M5-branes. For three-dimensional theories realized
on a stack of $N$ M2-branes we calculate the finite-$N$ corrections as the
contribution of extended M5-branes in the dual geometry $AdS_4\times
\boldsymbol{S}^7$. We take only M5-brane configurations with a single wrapping
into account, and neglect multiple-wrapping configurations. We compare the
results with the indices calculated from the ABJM theory, and find agreement up
to expected errors due to the multiple wrapping. For six-dimensional theories
on $N$ M5-branes we calculate the indices by analyzing extended M2-branes in
$AdS_7\times \boldsymbol{S}^4$. Again, we include only configurations with
single wrapping. We first compare the result for $N=1$ with the index of the
free tensor multiplet to estimate the order of the error due to multiple
wrapping. We calculate first few terms of the index of $A_{N-1}$ theories
explicitly, and confirm that they can be expanded by superconformal
representations. We also discuss multiple-wrapping contributions to the
six-dimensional Schur-like index.
