If you want to control the 580EX via radio, you need to connect a compatible radio receiver to the hot foot of the flash. The only wireless capability the 580EX has on its own is optical wireless control using Canon's optical wireless protocol.

The Godox X1R-C is the only radio receiver not built into a Godox flash that I'm aware of that is compatible with all of Godox's 2.4GHz transmitters, such as your X2T-C.

For detailed instructions, the Godox X2T-C Instruction Manual can be downloaded from the Godox website here. The Instruction Manual for the Godox X1R-C can be downloaded from the Godox website here.

Basically, you attach the X1R-C to the flash and set the flash as if it is attached to the camera's hot shoe. As far as the flash is concerned, the X1R-C is the camera. Then to fully control it from the X2T-C you need to be sure all of the flash's settings are at default values. (That is, Power at 1:1, FEC at +/-0, zoom setting at 'Auto', etc.) Any settings made on the flash itself that are not at default values will not be changeable by the transmitter.

Beyond making sure the X2T-C transmitter and the X1R-C receiver are on the same channel and group, don't forget to make sure the "Wireless ID" number on both the X2T-C and X1R-C are set to the same value.