Hm, I'm also not seeing an index. I'm a bit confused because the thing called "State Street Equty 500 Idx Adm" sounds promising and like it ought to be an S&P500 index fund, but when I look up the ticker "FINX", it is some sort of tech fund. It might be worth confirming that is the ticker and/or getting a copy of that fund's prospectus.
If that does not turn out to be an index fund, I'd go with the appropriate lifecycle fund. The expense ratio isn't stunning, but it isn't awful and you're still pretty early on, so it's probably still worth doing for the tax break and tax free growth.
It might also be worth dropping a note to HR/the finance department/whatever and politely ask why they aren't offering an S&P500 or total market index fund. There are some assorted resources around for how to get the conversation started about getting better investment options.