Viscosity index improver and lubricating oil composition

A viscosity index improver comprising:

• a copolymer (A) whose essential constituent monomer is a monomer (a) having a number average molecular weight of 800 to 4,000 represented by the following formula (1), the copolymer (A) having a solubility parameter in the range of 9.00 to 9.40:
• wherein R1 is a hydrogen atom or a methyl group;
• —X1— is a group represented by —O—, —O(AO)m—, or —NH—, AO is a C2-C4 alkyleneoxy group, m is an integer of 1 to 10, each AO may be the same or different when m is 2 or more, and the (AO)m moieties may be randomly bonded or block-bonded;
• R2 is a residue after removal of one hydrogen atom from a hydrocarbon polymer whose essential constituent monomer is butadiene in which the butadiene is present in a proportion of 50% by weight or more based on the weight of R2, or after removal of one hydrogen atom from a polymer formed by partial hydrogenation of the hydrocarbon polymer;
• and p represents a number of 0 or 1, and
• wherein in the formula (1), a structure derived from the butadiene constituting a part or all of R2 has a 1,2-adduct/1,4-adduct molar ratio of 40/60 to 70/30.