The only cards supported with this unit are:
AMD Radeon HD 6350 (512MB) PCIe x16 (includes a DMS-59 to Dual VGA Y Cable)
AMD Radeon HD 7450 (1GB) PCIe x16 (includes a DVI to VGA adapter cable)
NVIDIA NVS 300 (512MB) PCIe x16 (Includes a DMS-59 to Dual VGA Y Cable)
NVIDIA NVS 310 (512MB) PCIe x16
Because it is a microtower, the choices of cards that can been used for 3D gaming are limited to none due to the fact that the GPU's must be low-profile cards to fit into that chassis.
Something like this MAY work, but as you can see, the bracket is still built for a full height PCI slot and would need to be modified. Given the specs of this GPU, its a safe bet that this is Gen 3 PCIe 16 card and you'd need to factor that in too. A Gen 3 card will work in the Gen 2 slot on your unit, but it will suffer from a performance loss. (There is also the power capabilities of this unit - will it be enough to power the card through the PCIe slot? - The nVidia cards qualified for this system are only 2D cards - much lower power consumption.)
Not to mention the unit is 6 years old and may mot be able to work under load you may be planning to throw at it given how intensive new games are - assuming you ware wanting to run modern games.
You need to look got a Gen 2 PCIe card that is low profile with a low profie bracket adn hope it can be powered properly.
This system wasn't built with gaming in mind. 😞
I am an HP Employee
Quality Manager - HP VR / Z Desktops
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“iMaxx” FORMER VOODOO PC / HP LEGACY GAMING SERVICE MANAGER
While I am an HP employee, my comments and suggestions are my own and do not represent HP Inc.