I am currently working on number theory and I have come across a question asking for non-trivial subgroups of a given group. the question states that G = Z\*73, I know this is equal to all values of 73 which are inversable so that is 1..72.

I understand that a subgroup must satisfy closure, identity, inverses and be associative. 

i know that trivial subgroups are the ones that any group can have, when the subset is equal to the identity element or G itself.

but when trying to work out non-trivial ones, as it is a large number 73, I don't know how I would go about working out subgroups of it?

any infomration would be appreciated!