Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Give all possible ways to partition a set into a given number of subsets, ignoring order of blocks and within blocks
ResourceFunction["KSetPartitions"][set,k] returns the list of set partitions of set with k blocks. 

ResourceFunction["KSetPartitions"][n,k] returns the list of set partitions of {1,2,…, n} with k blocks. 
There are 15 set partitions of a fiveelement set into two subsets:
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The number of such set partitions is given by a Stirling number of the second kind:
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Here is a compact way to see the blocks:
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Wolfram Language 11.3 (March 2018) or above
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