The SSL2-core TFIIH complex when it is part of the general transcription factor TFIIH. It is composed of the tightly associated five subunit core TFIIH subcomplex plus one additional, less tighly associated subunit. The subunits are well conserved from yeast to humans. In S. cerevisiae, the 5-subunit core is composed of Rad3, Tfb1, Tfb2, Ssl1, Tfb4 and the loosely associated subunit is Ssl2p (also called Rad25). In humans, the 5 subunit core is composed of ERCC2, p62, p55, p44, p34 and the loosely associated subunit is XPB.