on the contrary vs contrarily

on the contrary and contrarily both are adverbs.

Word	Noun	Adjective	Verb	Adverb
on the contrary	No	No	No	Yes
contrarily	No	No	No	Yes

As adverbs, on the contrary and contrarily are synonyms defined as:

Other synonyms of on the contrary include contrariwise, to the contrary.

on the contrary (adverb)	contrarily (adverb)
contrary to expectations	contrary to expectations
	in a contrary disobedient manner