Consider $n\cdot m$ independent draws from cdf $F(x)$, which is defined over 0-1, where $n$ and $m$ are integers. Arbitrarily group the draws into $n$ groups with m values in each group. Look at the minimum value in each group. Take the group that has the greatest of these minima. Now, what is the distribution that defines the maximum value in that group? More generally, what is the distribution for the $j$-th order statistic of $m$ draws of $F(x)$, where the kth order of those m draws is also the pth order of the n draws of that kth order statistic?
All of that is at the most abstract, so here is a more concrete example. Consider 8 draws of $F(x)$. Group them into 4 pairs of 2. Compare the minimum value in each pair. Select the pair with the highest of these 4 minima. Label that draw "a". Label the other value in that same pair as "b". What is the distribution $F_b(b)$? We know $b>a$. We know a is the maximum of 4 minimums of $F(x)$, of $F_a(a) = (1-(1-F(x))^2)^4$. What is $F_b(b)$?