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I don't really understand how exactly to FIND subgroups of a given group... Is there any specific process to do so?

## Homework Statement

Find all subgroups of Z

_{6}.

## Homework Equations

## The Attempt at a Solution

How does one find subgroups??

Z

_{6}= Z

_{2}x Z

_{3}

Am I right in saying this?

I think Z

_{6}= {0,1,2,3,4,5}...

Then do I just look at each element or something? I'm really bad at abstract algebra.. Can someone attempt and explain the steps to take to determine a subgroup?

Thanks