You don’t state what model HP ELITEDESK 800 G1 you have, tower case, Small Form Factor or Ultra Slim Desktop.
If this is the graphics card you’re asking about, its’ dimensions are 145mm x 70mm x ? mm (no width specified but 2 slot spaces required) so it should fit in the TWR and the SFF case with regard to the height of the card but it will not fit into the USDT case as the card is too high.
Here’s a link to the service manual for the HP ELITEDESK 800 G1. Scroll to p.274 onward to view the specifications for all 3 types, including the dimensions.
All 3 models have a PSU >300W which is a requirement for the graphics card.
Hopefully this is of some help.
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