Tags in the Apertium stream format and dictionaries are ordered. Language pairs more or less stick to the same ordering conventions, with the main part-of-speech being first (after the lemma). The main rule-of-thumb is that tags that don't change within this lemma, go first. Nouns with gender typically have gender right after <n> (a different gender might make the word refer to something completely different), while tags like number follow gender (changing number doesn't change the meaning of the lemma).
Examples of typical tag order for some parts-of-speech:
<vblex><past><p3><m><sg> <n><f><pl><def> <adj><posi><mf><sg><ind>
For noun with case, it's typically