It could be socket 478, or socket 423, but it's pretty much guranteed to be a williamette. If there was a 1.5ghz northwood I've never heard of one, but it's possible, especialy if this was an oem computer, like a compaq or HP.
If it's 423, you won't have much of an upgrade path, the fastest williamette wouldn't be worth it. As others have said, the williamette was slower than a P3 in most applications. so if you are limited to a williamette it wouldn't be worth upgrading if you are keeping the motherboard.
If it's 478 it's really hard to say since we have absolutly no details at all. It could be 400mhz FSB, 533mhz FSB, or 800mhz FSB. That gives a range of williamettes, northwoods, or even prescotts that could go on to a socket 478, but it's impossible to tell with no details. You didn't even tell us how old the computer was, what type of memory it uses, nothing, so it's almost impossible to tell you what you can upgrade too. SDRAM, RDRAM, DDR, far too many variables to have even the slightest idea of what the fastest chip that could go on it if it's a 478 board.
If it uses SDRAM, then it's probably a 400mhz FSB board that could support up to a 2.8ghz northwood, but be severely handicapped by the slow memory, if it's RDRAM it could be the 850 chipset or the 850e chipset, so it could support either 400mhz FSB up to a 2.8 northwood, or it could be 533mhz FSB for up to a 3.06ghz northwood. If it's DDR, it could be anything from 400mhz FSB to 800mhz FSB, so it could support anywhere from 2.8 northwoods, to 3.4 northwoods, and possibly prescott up to 3.4ghz as well. So you can see without more info, there is no good guess as to what the board can support..
You might as well be saying I have a car, it has 4 wheels, how fast can it go...
You'll really have to find out at least something about the computer, otherwise you'll most likely end up with something that doesn't work on the motherboard.