HP2311x resolution not accepted

Problem: There is notification "set resolution 1920x1080" however you can't select it in display settings screen resolution

Problem was old graphics card - it was onboard card. Shows messages as "Input signal out of range" and "change settings to 1920x1080". However, the only resolution that was possible for HP2311x monitor to show on this old video card was 1280x1024. Otherwise it was either black screen or stretched screen.
Resolution is to buy a new video card -
for example for AGP slot - Ati Radeon HD 3450
or PCIe - Asus GT4400.