grammar - Proper form of なさる - なさります or なさいます

In Genki II (second ed.), page 168 we are given polite forms of some verbs, among them する with なさる. They have also written that some of them have irregular conjugations in long forms, among them なさる, which becomes なさいます. However, in tangorin.com the conjugation table says なさります while Jisho.org recognizes both as forms of なさる. At the same when I type なさります or なさいます into google.com I get about 900 000 or 600 000 results respectively. Are both forms correct? Or is one of them just a common mistake?

Answer

There are five honorific (subsidiary) verbs of almost r-consonant (type I) conjugation that have very peculiar style of irregularity, ending in い in 命令形 (command form) and before ます.

plain form　　　regular masu-stem　　 masu(-only)-stem　　command form
いらっしゃる　　いらっしゃり-たい　　いらっしゃい-ます　　いらっしゃい
おっしゃる　　　　おっしゃり-たい　　　おっしゃい-ます　　　おっしゃい
くださる　　　　　　くださり-たい　　　　ください-ます　　　　ください

ござる　　　　　　　　ござり-たい　　　　　ござい-ます　　　　ござれ／ござい†
なさる　　　　　　　　なさり-たい　　　　　なさい-ます　　　　　なさい
--------
なる (regular)　　　　　なり-たい　　　　　　なり-ます　　　　　　なれ

^{† so rare that I can't decide which is more natural...
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These verbs are used predominantly in this irregular style, and using regular conjugation would have various extra effects depending on the verb, from just sounding a bit old-fashioned to making you into a ninja...

PS "なさります" and "なさいます" have 26,800 and 430,000 hits in Google.co.jp, respectively.