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We study probe M5-branes in N=1 AdS5 solutions of M-theory that arise fromM5-branes wrapped on a Riemann surface. Using the BPS condition fromkappa-symmetry, we classify supersymmetric probe M5-branes that extend alongall of AdS5 and intersect the Riemann surface at points. These can be viewed aspunctures in the dual N=1 superconformal field theories. We find M5-branes thatcorrespond to the two types of simple punctures previously studied in fieldtheory. In addition, when the central charge is rational, we find a new classof M5-branes with a moduli space that includes two internal dimensions inaddition to the Riemann surface. These new M5-branes have the essentialcharacteristic of fractional branes, in that a single one at a generic point ofits moduli space becomes multiple M5-branes at special points.

Punctures from Probe M5-Branes and N=1 Superconformal Field Theories