Given a simple compact Lie group, SU($n$) group, for $n=2,3,4,...$,
Can we determine what are the allowed dihedral groups D$_k$ (of order $k$) realized as a subgroup embedded into SU($n$)?
What is the restriction of $k$ for given SU($n$) of
$n=2?$
$n=3?$
$n=4?$
$n=5?$
(BONUS but not necessary: Are there some general rules one can use to determine any $n$ what is the allowed $k$?)
