Yes CD1 is the name of an outbred strain. Both C57 and CD1 showed great difference after injection of a stimulator of the immune response. but I can't find information to explain that. For instance if they differ by the intensity of cell-mediated immune responses.
You have to keep in mind that inbred strains are literally genetically identical while you have broader genetic diversity in outbred mice. So the response that you observe in one experiment might not be exactly reproducible in a second experiment using the same strain. I think outbred strains are far less used in immunological research than inbred strains so I am not even sure it such data on immunological response in your strain of interest exist somewhere. Anyway, you did not mention what was readout for the response, but I would try to analyze a panel of cell surface markers to quantify the number and frequency of immune cells in spleen and lymph node of each strain by flow cytometry. e.g. a panel of CD3, CD19, CD4, CD25, FOXP3, CD11c, CD11b, Gr-1 might give you an idea.
I have compared different strains for their cellular immune response proclivities. I elucidated and named macrophages M1 and M2. C57Bl/6 mice have a strong macrophage killer responses called M1 macrophages, and Balb/c have an M2-dominant response that aids in healing. I did not examine outbred strains, but one might predict they fail in the middle between these 2 strains. Publications attached. The 2000 paper describes different strains, and the 2014 paper provides a review. Good luck. Charlie
There is also a great difference in expression in subpopulations of dendritic cells.
For example, Balb / C strongly express the Langerin (immature DC) and very little DC LAMP (mature DCs), unlike the mouse C57B / 6 mainly express DC LAMP and almost no Langerin under their shape axenic.
This directly impacts their ability to present antigen and activate the immune response.
There are many other markers of DCs that are differential and can play a role in vaccination (if not all markers of DCs)