Greedy Bin Packing

Finitely many positive integers satisfy condition $T$: each is at most $7$ and their total sum is $S = 430$. They are divided into $M$ groups, each with sum at most $21$, by the following greedy rule: group $1$ picks numbers so that its sum $S_1$ is as large as possible; group $2$ then picks from the remaining numbers so that its sum $S_2$ is as large as possible; and so on, with $S_i$ the sum of group $i$ for $i \in \{1, 2, \ldots, M\}$. Over all collections satisfying condition $T$, find the maximum possible value of $M$.