According to Supported Operating Systems for Intel® Graphics Products your legacy GPU is not supported under Windows 10.
It has even reached "status = end of life" - Intel® Pentium® Processor G620 (3M Cache, 2.60 GHz) Product Specifications
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Thank you for contacting the Intel community.
Stefan3D is right this processor and graphics does not support Windows® 10 and for that reason there is no driver available. This is a 2nd generation processor and Windows® 10 is supported from 3rd generation processor.
I’m sorry this is not the answer you expected and on this case you system should work fine under Windows® 8 and 8.1.