allow vs countenance

allow is not a noun while countenance is a noun.

Word	Noun	Adjective	Verb	Adverb
allow	No	No	Yes	No
countenance	Yes	No	Yes	No

As verbs, allow and countenance are synonyms defined as:

Other synonyms of allow include let, permit.

As verbs, countenance is a hypernym of allow; that is, countenance is a word with a broader meaning than allow:

allow: allow the presence of or allow (an activity) without opposing or prohibiting
countenance: consent to, give permission; permit

Other hypernyms of allow include allow, let, permit.

allow (noun)	countenance (noun)
	the appearance conveyed by a person's face
	the human face (`kisser' and `smiler' and `mug' are informal terms for `face' and `phiz' is British)
	formal and explicit approval

allow (verb)	countenance (verb)
allow or plan for a certain possibility; concede the truth or validity of something	consent to, give permission; permit
give or assign a resource to a particular person or cause
consent to, give permission; permit
allow the presence of or allow (an activity) without opposing or prohibiting
let have
grant as a discount or in exchange
make it possible through a specific action or lack of action for something to happen
allow the other (baseball) team to score
make a possibility or provide opportunity for; permit to be attainable or cause to remain
afford possibility