Is it normal to pay more to social security than to federal income taxes?

I claimed 0, my employer does not issue pay stubs, merely gives a check weekly. Pay was $8378.00 federal withheld was $252.80, social security wethheld was $519.39.

Public Comments

Depends on what you put into your W-4. medicare rate 1.45% FICA 6.20% Fed and state withholding depend on your stated exemptions
I'm not going to say normal, but it is very possible. Social security is a flat rate of 6.2% on income up to like $97,400. So depending on what tax bracket you fall in then your social security tax may very well be larger than the federal tax withheld. I am going to tell you the truth though. If you claimed zero on your W4 then your federal withholding should have been ~$2507.49. So I don't think that your employer is withholding enough.
Your employer is required by law to give you a paystub outlining exactly where withholding is going with each check. I'm guessing your $8378 figure is for the entire year, in which case the total Federal Withholding for the year should be about $838 for single "0" or $ 0 for married "0". If your pay varies widely from week to week, your witholding may be correct. Smaller checks have less or $0 withholding. SS witholding is correct at $519. The amount of Federal Withholding does not affect the amount of tax you pay, it only affects WHEN you pay it. If you withhold more each paycheck you get a bigger refund (or owe less) at tax time.
For people at the lower end of the income scale it is very normal. You will get a relatively larger benefit when you retire too.