Here is the list of all the English words containing letters E, I, L and X grouped by number of letters: elix, ilex, Lexi, axile, dixel, exfil, exile, Felix, helix, ixtle, lexia, lexic.
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Please note: the Wiktionary contains many more words - in particular proper nouns and inflected forms: plurals of nouns and past tense of verbs - than other English language dictionaries such as the Official Scrabble Players Dictionary (OSPD) from Merriam-Webster, the Official Tournament and Club Word List (OTCWL / OWL / TWL) from the National Scrabble Association, and the Collins Scrabble Words used in the UK (about 180,000 words each). LotsOfWords knows 480,000 words.