Java - In which cases , moving methods to utility class could be useful

 It could be worthy to move a method to util class if the method needs to be shared, doesn't require polymorphic behavior and need not be overridden in special cases.

Don't belong to one group through is-a relationship ( You can share through parent class method )

Don't implement a specific interface ( java 8 default methods )

Doesn't involve complex computing as you will be loosing the benefit of object state with just static method.

Doesn't require polymorphic behavior as static methods don't participate in runtime polymorphism.