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In mathematics, in the field of group theory, a paranormal subgroup is a subgroup such that the subgroup generated by it and any conjugate of it, is also generated by it and a conjugate of it within that subgroup.

In symbols, H {\displaystyle H} is paranormal in G {\displaystyle G} if given any g {\displaystyle g} in G {\displaystyle G} , the subgroup K {\displaystyle K} generated by H {\displaystyle H} and H g {\displaystyle H^{g}} is also equal to H K {\displaystyle H^{K}}. Equivalently, a subgroup is paranormal if its weak closure and normal closure coincide in all intermediate subgroups.

Here are some facts relating paranormality to other subgroup properties:

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