Yes it supports Core 2 Quad
https://support.hp.com/us-en/document/c01570344
Intel Core 2 Quad Processors:
Intel Core 2 Quad Q8200 processor 2.33 GHz, 4 MB L2 cache, 1333 MHz FSB
Intel Core 2 Quad Q9400 processor 2.50 GHz, 6 MB L2 cache, 1333 MHz FSB Featuring Core 2 Processor with vPro Technology
Intel Core 2 Quad Q9550 processor 2.66 GHz, 12 MB L2 cache, 1333 MHz FSB Featuring Core 2 Processor with vPro Technology
Intel Core 2 Quad Q9650 processor 2.83 GHz, 12 MB L2 cache, 1333 MHz FSB Featuring Core 2 Processor with vPro Technology
I believe it will even support the other Q8xxx and Q9xxx models not listed, such as Q8400. But whichever is cheapest with highest clock speed would be best.