In this paper, we study partial words in relation with pcodes, compatibility, and containment. First, we introduce C-subset of(L), the set of all partial words contained by elements of L, and C-superset of(L), the set of all partial words containing elements of L, for a set L of partial words. We discuss the relation between C(L), the set of all partial words compatible with elements of the set L, C-subset of(L), and C-superset of(L). Next, we consider the condition for C(L), C-subset of(L), and C-superset of(L) to be a pcode when L is a pcode. Furthermore, we introduce some classes of pcodes. An infix pcode and a comma-free pcode are defined, and the inclusion relation among these classes is established.
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