Normal of order two implies central

Statement
Suppose $$G$$ is a group and $$H$$ is a fact about::normal subgroup of $$G$$ that is of order two, i.e., it is isomorphic to fact about::cyclic group:Z2. Then, $$H$$ is a fact about::central subgroup of $$G$$.

Similar facts

 * Normal of order equal to least prime divisor of group order implies central
 * Cyclic normal Sylow subgroup for least prime divisor is central, which leads to cyclic Sylow subgroup for least prime divisor has normal complement
 * Minimal normal implies central in nilpotent, minimal normal implies contained in Omega-1 of center for nilpotent p-group

Dual facts

 * Index two implies normal
 * Subgroup of index equal to least prime divisor of group order is normal

Other normal-to-central facts

 * Totally disconnected and normal in connected implies central
 * Cartan-Brauer-Hua theorem