Normal subgroups of dihedral groups

[Kurchi]

How many normal subgroups do D₁₅ has?

My teacher says it's 5 because there are total 5 divisors of 30 , which are 1,3,5,15,30. But why? I don't get the logic. Please explain.

 

[Steven G]

What do you think the answer is? What do you think the definition of D₁₅? Please try the problem yourself so that we can help you figure it out. If you do the problem yourself with our help then you will really understand it. Please post back with your work.