We consider the class Sn(1324) of permutations of size n that avoid the pattern 1324 and examine the subset Sa≺nn(1324) of elements for which a≺n≺[a−1], a≥1. This notation means that, when written in one line notation, such a permutation must have a to the left of n, and the elements of {1,…,a−1} must all be to the right of n. For n≥2, we establish a connection between the subset of permutations in S1≺nn(1324) having the 1 adjacent to the n (called primitives), and the set of 1324-avoiding dominoes with n−2 points. For a∈{1,2}, we introduce constructive algorithms and give formulas for the enumeration of Sa≺nn(1324) by the position of a relative to the position of n. For a≥3, we formulate some conjectures for the corresponding generating functions.