Let $H$ be a normal subgroup of $G$ and assume that $G$ is acting over a set $X$. Let $c$ be some element of $X$, is there any relationship among the size of the orbit of $c$ under the action of $H$ and the size of the orbit of $c$ under the action of $G$?
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Removed the deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)
Martin Sleziak
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Orbit size of an element
user350168
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