I am 5'6'', a small 34C and 120 lbs. What size would I be if I got 410cc?

Thank you for the question.  There is no accurate/reliable/predictable correlation between size/profile breast implant utilized and cup size achieved. Despite your good description of goals, online consultants will not be able to provide you with specific enough advice to be truly helpful. Ultimately, careful communication of your goals (in my practice I prefer the use of goal pictures, direct examination/communication in front of a full-length mirror, and computer imaging)  will be critical.
Generally speaking, the best online advice I can give to ladies who are considering  breast augmentation surgery ( regarding breast implant size/profile selection) is:
1. Concentrate on choosing your plastic surgeon carefully.  Concentrate on appropriate training, certification, and the ability of the plastic surgeon to achieve the results you are looking for. Ask to see lots of examples of his/her work.
2. Have a full discussion and communication regarding your desired goals  with your plastic surgeon. This communication will be critical in determining  breast implant size/type/profile will most likely help achieve your goals. 
In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. I have found that the use of words such as  “natural” or "C or D cup” etc means different things to different people and therefore prove unhelpful.
 Also, as you know, cup size varies depending on him who makes the bra; therefore, discussing desired cup  size may also be inaccurate.  Again, the use of computer imaging has been very helpful during the communication process, in our practice.
3.  Once you feel you have communicated your goals clearly,  allow your plastic surgeon to use his/her years of experience/judgment to choose the breast implant size/profile that will best meet your goals.  Again, in my practice, this decision is usually made during surgery,  after the use of temporary intraoperative sizers.
I hope this (and the attached link, dedicated to breast  augmentation surgery concerns) helps.

There are several factors that plastic surgeons consider when recommending implant sizes. I consider two factors when selecting implants for my patients:1. Dimensional planning2. Gel Implant Sizing systemDimensional planning – The measurements of your chest wall are taken. Also, the breast dimensions including the height, width, and current dimensions of each breast form the basis of dimensional planning. Based on these measurements, the implant size is recommended. This will give you a unique breast implant that is suited for your body frame. However, there are some limitations of what size we can recommend. For instance, some implants may just be too big for a narrow chest wall. Your surgeon can review this with you during the consultation.Gel Implant Sizing system – During the preliminary breast implant consultation, you will be provided with an option to “try on” a variety of implant shapes and sizes. You can also visualize the possible outcomes of your surgery which helps you to get that perfect size to give you the shape that you longed for. This way your preferences are known and you can then pick a range of implants that will “fit” just right to give a soft natural fuller look. Hope this helps.Dr. BasuHouston, TX