I am conducting a rearch project.  There is 1,380 possibe subjects to
be considered on one survey and 160 on the other survey.  Because of
the number of possible participants I want a random sample for each
group.  My quesiton is what would be a reasonalbe number of surveys to
be sent out to achieve my goal.

More information please.  How are you planning on sending out the
survey, how many responses would you like, what sort of demographics
are in the area and are you planning on capturing?  Also, be aware
that a mathematical answer is very unlikely.  In strict probability
study you can calculate the number of responses based on requested
margin of error.  In surveying it is much more difficult because of
the possibility of survey error as well as an unknown response rate.

Looking for your answer I found an amazing site:
http://www.surveysystem.com/sscalc.htm

I used their calculator to determine some sampling sizes using:
95% confidence level
4 confidence interval

population: 1380 --> sample size: 419
population: 160  --> sample size: 126

95% confidence level
8 confidence interval

population: 1380 --> sample size: 135
population: 160  --> sample size: 78

If you want to use a 99% confidence level or other confidence
intervals (the site explains confidence interval if you need more
info) then go to the site and plug in the numbers, it's fun :)

Best of luck in your researching endeavours!