Had crime vs law-breaking

Had crime and law-breaking both are nouns.

Word	Noun	Adjective	Verb	Adverb
Had crime	Yes	No	No	No
law-breaking	Yes	No	No	No

As nouns, law-breaking is a hypernym of Had crime; that is, law-breaking is a word with a broader meaning than Had crime:

Had crime: (Islam) serious crimes committed by Muslims and punishable by punishments established in the Koran
law-breaking: (criminal law) an act punishable by law; usually considered an evil act

Other hypernyms of Had crime include crime, criminal offence, criminal offense.

Had crime (noun)	law-breaking (noun)
(Islam) serious crimes committed by Muslims and punishable by punishments established in the Koran	(criminal law) an act punishable by law; usually considered an evil act