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Group divisible designs (GDDs) with block size 4 and at most 30 points are known for all feasible group types except three, namely 2354,3562, and 2255. In this paper we provide solutions for the first two of these three 4‐GDDs without assuming any automorphisms. We also construct several other 4‐GDDs. These include classes of 4‐GDDs of types (3m)4(6m)q(3n)1 for 0≤n≤(q+1)m where q∈{2,3} and solutions for 4‐GDDs of types 3t6s for a wide range of values of s≥2,t≥4 satisfying t≡0 or 1(normalmod0.4em4), including all cases with 4≤t≤s−1. Most of the remaining unknown 4‐GDDs of type 3t6s have (s−1)

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In this paper we provide a 4‐GDD of type 2 2 5 5 ${2}^{2}{5}^{5}$, thereby solving the existence question for the last remaining feasible type for a 4‐GDD with no more than 30 points. We then show that 4‐GDDs of type 2 t 5 s ${2}^{t}{5}^{s}$ exist for all but a finite specified set of feasible pairs ( t , s ) $(t,s)$.