chrysanthemum vs flower

chrysanthemum and flower both are nouns.

Word	Noun	Adjective	Verb	Adverb
chrysanthemum	Yes	No	No	No
flower	Yes	No	Yes	No

As nouns, flower is a hypernym of chrysanthemum; that is, flower is a word with a broader meaning than chrysanthemum:

chrysanthemum: any of numerous perennial Old World herbs having showy brightly colored flower heads of the genera Chrysanthemum, Argyranthemum, Dendranthema, Tanacetum; widely cultivated
flower: a plant cultivated for its blooms or blossoms

As nouns, flower is a hypernym of chrysanthemum; that is, flower is a word with a broader meaning than chrysanthemum:

chrysanthemum: the flower of a chrysanthemum plant
flower: reproductive organ of angiosperm plants especially one having showy or colorful parts

Other hypernyms of chrysanthemum include bloom, blossom.

chrysanthemum (noun)	flower (noun)
any of numerous perennial Old World herbs having showy brightly colored flower heads of the genera Chrysanthemum, Argyranthemum, Dendranthema, Tanacetum; widely cultivated	a plant cultivated for its blooms or blossoms
the flower of a chrysanthemum plant	reproductive organ of angiosperm plants especially one having showy or colorful parts
	the period of greatest prosperity or productivity

chrysanthemum (verb)	flower (verb)
	produce or yield flowers