Arc-transitive pentavalent graphs of order 4pq

This paper determines all arc-transitive pentavalent graphs of order 4pq, where q > p >= 5 are primes. The cases p = 1,2,3 and p = q is a prime have been treated previously by Hua et al. [Pentavalent symmetric graphs of order 2pq, Discrete Math. 311 (2011), 2259-2267], Hua and Feng [Pentavalent symmetric graphs of order 8p, J. Beijing Jiaotong University 35 (2011), 132-135], Guo et al. [Pentavalent symmetric graphs of order 12p, Electronic J. Combin. 18 (2011), #P233] and Huang et al. [Pentavalent symmetric graphs of order four time a prime power, submitted for publication], respectively.