I once heard that each of the 613 mitzvos can be categorized as being one of the 10 commandments, and was under the impression one of the early commentators did this categorization. I thought it was Rav Saadiah Gaon, but I can only find the statement attributed to him (although I don't know where he writes it), but not that he actually did this categorization. Did anyone?
Azharot – אזהרות are liturgical poetical compositions dealing with the 613 precepts (see Jewish Encyclopedia. There are many authors of these compositions.
According to p127 of An Introduction to Judaic Thought and Rabbinic Literature, by Martin Sicker. Saadia Gaon composed two forms of Azharot (in his Siddur) for recitation on Shavuos. Sicker says that either each statement of the 10 Commandments relates to a group of precepts or each letter of the 10 Commandments to a precept.
Jewish Encyclopedia reports that Saadia Gaon ..
.. adduces the precepts according to their derivation from the Decalogue, an idea often imitated; by Saadia himself again in his Yeẓirah Commentary, and then, not only by later poets, but by writers on jurisprudence.
So Saadia Gaon did categorise the mitzvos in relation to the 10 commandments. This is printed in his Siddur starting, thanks to @robev, on p 250. To see an example later in the ten commandments, (לא תענה) see page 271.