Find all subgroups of S3 the symmetric group of degree 3Solu

Find all subgroups of S₃, the symmetric group of degree 3.

Solution

As per theorem order of any subgroup must divide the order of S3. Now, the order of S3 is just 3! = 6

S3 has order 6, so subgroups have order 1, 2, 3, or 6

S3={id,(12),(13),(23),(123),(132)}