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Starting from the traditional distinction between the minimal and the maximal division, the role of subcategories in Aristotle, as well as that of the highest categories, is discussed. The need for categorial properties which determine categories is pointed out. It is argued that an existent cannot have two such essential properties and that only the lowest subcategories have simple categorial properties. Furthermore, it is emphasised that categories and subcategories must form a tree because they belong to a theory of categories which requires unity. By contrast, it is held that the hierarchy of all concepts need not form a tree. The difficulties Porphyrius and Simplicius find in Aristotle's minimal and maximal division are analysed. Finally, Aristotle's way of avoiding categorial properties by referring to an abstraction is criticised. [ABSTRACT FROM AUTHOR]