mayhem vs crime

mayhem and crime both are nouns.

Word	Noun	Adjective	Verb	Adverb
mayhem	Yes	No	No	No
crime	Yes	No	No	No

As nouns, crime is a hypernym of mayhem; that is, crime is a word with a broader meaning than mayhem:

mayhem: the willful and unlawful crippling or mutilation of another person
crime: (criminal law) an act punishable by law; usually considered an evil act

Other hypernyms of mayhem include criminal offence, criminal offense, law-breaking.

mayhem (noun)	crime (noun)
the willful and unlawful crippling or mutilation of another person	(criminal law) an act punishable by law; usually considered an evil act
violent and needless disturbance	an evil act not necessarily punishable by law