While the standard invasive ductal carcinoma (IDC) is the most common form of invasive breast cancer, there are four additional types of invasive carcinoma that are much less common; however, that does not reduce the seriousness of these diseases.

Papillary Ductal Carcinoma: Although this is considered an invasive cancer because of its finger-like appearance under a microscope, it is only in rare cases that it truly becomes an invasive cancer. This form of cancer is most common in women over the age of 50, and it is treated like ductal carcinoma in situ (DCIS). 

Tubular Ductal Carcinoma: The rarest form of IDC, tubular ductal carcinoma makes up only two percent of all diagnoses of breast cancer. More commonly seen in women over 50 years of age, tubular ductal carcinoma is usually seen as smaller, estrogen-receptor positive cancers. This means they respond to the hormone estrogen, which feeds the cancer cells and enables them to grow. The name for this particular form of IDC comes from the way the cancer looks like hundreds of tiny tubes when viewed under a microscope.

Medullary Ductal Carcinoma: This is the second rarest form of IDC, as it makes up only 3 to 5 percent of all breast cancer diagnoses. This form of cancer usually feels more like a spongy change in the breast tissue as opposed to the traditional hard lump, and is most commonly found through mammogram imaging. 

Mucinous Ductal Carcinoma: This form of cancer occurs when the cancer cells inside the breast produce mucous, and this mucous also contains more breast cancer cells. When the cancer cells and the mucous come together to form a tumor, it is then diagnosed as mucinous ductal carcinoma. Cases of pure mucinous ductal carcinoma usually carries a better prognosis than the more common types of IDC.