I am asked the find the possible orders of subgroups of a group of order 60.
By Lagrange's theorem: $\left | H \right | | \left | G \right |$ Any positive integer n that is a divisor of $\left | G \right |=60$ is a possible order of a subgroup of a group of order 60.
The possible orders are 1,2,3,4,5,6,10,12,15,20,30,60.
Question: Find a group of order 60 that has subgroup of all possible orders.
Is there a quick way to determine this?