In finite $p$-groups, the number of subgroups of order $p^k$ is congruent to $1 \mod p$.
Is it true that the number of normal subgroups of order $p^k$ is congruent to $1 \mod p$?
In finite $p$-groups, the number of subgroups of order $p^k$ is congruent to $1 \mod p$.
Is it true that the number of normal subgroups of order $p^k$ is congruent to $1 \mod p$?