German cockroach vs cockroach

German cockroach and cockroach both are nouns.

Word	Noun	Adjective	Verb	Adverb
German cockroach	Yes	No	No	No
cockroach	Yes	No	No	No

As nouns, cockroach is a hypernym of German cockroach; that is, cockroach is a word with a broader meaning than German cockroach:

German cockroach: small light-brown cockroach brought to United States from Europe; a common household pest
cockroach: any of numerous chiefly nocturnal insects; some are domestic pests

Other hypernyms of German cockroach include roach.

German cockroach (noun)	cockroach (noun)
small light-brown cockroach brought to United States from Europe; a common household pest	any of numerous chiefly nocturnal insects; some are domestic pests