When one considers the hyperovals in PG(2, q), qeven, q>2, then the hyperoval in PG(2, 4) and the Lunelli-Sce hyperoval in PG(2, 16) are the only hyperovals stabilized by a transitive projective group [10]. In both cases, this group is an irreducible group fixing no triangle in the plane of the hyperoval, nor in a cubic extension of that plane. Using Hartley's classification of subgroups of PGL 3( q), qeven [6], all k-arcs in PG(2, q) fixed by a transitive irreducible group, fixing no triangle in PG(2, q) or in PG(2, q 3), are determined. This leads to new 18-, 36- and 72-arcs in PG(2, q), q=2 2 h . The projective equivalences among the arcs are investigated and each section ends with a detailed study of the collineation groups of these arcs.