20 Let the set $M=\{1,2,3, \cdots, 50\}$, and the set $S \subseteq M$, for any $x, y \in S, x \neq y$, we have $x+y \neq 7 k(k \in \mathbf{N})$. Among all such sets $S$, the set $S_{0}$ is the one that contains the most elements, then the number of elements in $S_{0}$ is $\qquad$.
20 23. Classify the numbers in $M$ according to the remainder obtained when divided by 7. The class with a remainder of 0 can only take 1 number. The class with a remainder of 1 and the class with a remainder of 6 can only take numbers from one of these classes. The same applies to the classes with remainders of 2 and 5, and remainders of 3 and 4. Each class has 7 numbers, except for the class with a remainder of 1, which has $7+1$ numbers, so
$$
\left|S_{0}\right|=1+7 \times 3+1=23
$$