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Magic: the Gathering is a 25 year old card game where each card can have a 'colour identity'. There are five such identities ([White (W), Blue (U), Black (B), Red (R), Green (G)] ignoring colourless), and when a new collection of cards are released they are often grouped into factions.

Factions often have more than one colour identity (Cards in the 'Blue Red' (UR) faction may be Blue, Red or Blue and Red).

Further, a set is always* colour balanced (meaning that the same number of identities exist across all colours, e.g. you might have one set of factions UBR,WRG,UG,WB wherein all the colours appear twice in each faction).

What are all the ways of constructing the sets of distinct factions, for $n$ factions? Is there a pattern I can use based off of small numbers of factions?

*Exceptions exist outside the scope of this question.