A router bit should have some information laser-engraved in its shank. Among these at the very least the shank diameter, maximum speed, and MAN (or not).
Some manufacturers (Trend, notably) have them written on the cardboard in the box, often in a "general" form such as 28,000RPM up to 30mm, 24,000RPM up to 30mm diameter, etc. (presumably they're laser-engraved too, but the writing on Trend bits is too small for me to decipher!).
A bit that doesn't provide such information should go right into the trash can as it is not possible to operate it safely. Seeing how my life depends on that safe operation, that's a must for me.
Shank diameter is not as obvious as you may believe. 12mm and 1/2'' shanks look quite similar, and 6mm and 1/4'' shanks are virtually indistinguishable just from holding them in your hand and looking at them.
However, clamping the respective slightly-too-small shank in the slightly-too-large collet will result in the bit slipping and possibly come hurling through the room. Clamping the respective slightly-too-large shank in the slightly-too-small collet will cause the collet to turn into shrapnels at an unpredictable time later. Neither one is a fun condition.
MAN is important if you intend to use the bit in a plunge router. It means the bit has a certain maximum clearance behind the edge, so it will only bite at most so and so deep into the material with each turn. That limits the amount of locking and kickback and determines whether it is reasonably safe to operate the tool manually (MAN). Lacking the inscription MAN, you may only ever use it in a router table (and forcibly controlled with a guide so the rotating bit won't kick the piece of wood out of your hands and into your genitals).
Regardless of whether a bit is "suitable" for manual operation, I consider diameters greater 20mm a "Meh, if I can't avoid" thing, and diameters greater 35mm a "Dude, you got death wish?" thing. Large bits become steadily more dangerous with increasing diameter, they belong in a router table.
Bits with approx. 140mm diameter like the one in the image probably don't fit into anything that you're likely to own anyway (they sure don't fit into my router, no 20mm collets available, that's an entirely different class of machine). But even if they did fit, I would think twice whether I'd want to use such a thing. 50-55mm is probably the largest diameter (profile cutters) that most people use regularly, though I've used 70mm, which is intimidating enough (and at least 89mm exists with 1/2'' shank, such as the T-C170AX1-2TC -- I've never used such a beast).
Consider that centrifugal force as well as cutting speed goes up with diameter, so quite possibly your router cannot even turn slow enough to operate safely (my router can just about rotate slow enough to satisfy 70mm, possibly 85mm profile cutters which usually allow 11,000 -- the ultra-large diameters often only allow 6,000RPM). Turning slower also means that your motor must be considerably stronger. If you have less than 2kW, you can pretty much forget running large bits at low speeds, it will be not a lot of fun.