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.

. 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:

• Every pronormal subgroup, and hence, every normal subgroup and every abnormal subgroup, is paranormal.

• Every paranormal subgroup is a polynormal subgroup.

• In finite solvable groups, every polynormal subgroup is paranormal.

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