Like with anything in that era "there be dragons".
The i815E was Intel's low budget crap that was designed to replace the aging 440BX, but it was new enough that it was also competing with the Pentium 4, so Intel purposefully knee-capped it. It has an artificial memory limit of 512 MB, on 3 slot RAM boards, it will drop the memory speed from 133 to 100 MHz, on 66 or 100 MHz FSB CPUs, it will also drop the memory speed. AGP texturing memory limits, etc.
As to what the chipset supports, it entirely is dependent on what revision of the i815E it is, and motherboard BIOS support.
What it will most definitely support are all Celerons and Pentium IIIs with a 66, 100 and 133 MHz FSB, up to the Coppermine core, So 1.13 GHz. That final speed is exceedingly rare because Intel pushed the chip too far, which caused the chip to be very unstable. They issued a recall on it and not many exist today. The 1000 MHz part was the most common and is the fastest you can get for a reasonable cost. There's also a 1100 MHz model, but that drops the FSB to 100 MHz.
What it *might* support are Coppermine-T chips, which were an in between of the Coppermine and the Tualatin cores. They were designed to be backwards compatible with the older AGTL bus protocol of the Coppermine. They have no benefit over a Coppermine and are rare today.
What it *probably doesn't* support are Tualatin Celerons and Pentium IIIs. These use a smaller lithography process, a newer lower voltage AGTL bus, and the -S models have 512k of cache, vs 256k. Only the "B" stepping of the i815E supports Tualatins, and it's hard to know what version you have. There's probably a guide floating around on the dusty corners of the internet to tell you what you have, but you only need to worry about this if you want to use a Tualatin processor.
