Are there infinite positive $n \in \Bbb N$ such that ($D^+_n$, |) is isomorphic to ($D^+_{4100}$, |)?

Question

Are there infinite positive $n \in \Bbb N$ such that ($D^+_n$, |) is isomorphic to ($D^+_{4100}$, |)?

I'm guessing no because I can't relate every element of ($D^+_{4100}$, |) to ($D^+_n$, |) because ($D^+_{4100}$, |) has finite elements. I don't know how to prove it.

Thanks

Answer 1

Hint: Note that $4100=2^2\cdot 5^2\cdot 41$. Let $n=p^2 q^2 r$, where $p$, $q$, and $r$ are distinct primes.