If you want [as in your image] to use all such subdividing locations [not just snap to one of them], and do with them something like placing a Line like that at each one, without the intermediate step of using the regular DIVIDE command to place Points at each location [and therefore without needing to get rid of them afterwards], you can use my DivideMeasurePlus.lsp routine, available here. Its DIV+ command has a lot of enhancements over regular DIVIDE, including not limiting you to Points or Blocks [you can select any object(s) under the Selection option]. This image was done with it, starting with Selecting the vertical green Line and giving its top end as the reference location on it, accepting the Aligned orientation option, and picking the white Polyline to DIV+ into 5 segments. Read the comments at the top of the file, and follow the prompts -- there are many other choices you can make that improve on the capabilities of regular DIVIDE though they may not be needed for your particular example. [And similarly with MEA+ improving on regular MEASURE.]

[It also has an option to draw Lines, in which case you would not need to have one drawn first to Select, but so far they are only centered on the path object. I have had in mind for some time to add an option for the positioning -- left/centered/right -- and maybe this will stir me to make that adjustment.]
It would also be possible to make a routine that would let you snap to one such location -- for instance to snap to only the one spot that's 3/10 of the way along a path. The code would be similar to FromEnd.lsp with its (fe) function [available here], and it shouldn't be too hard to adjust that routine, if that's the kind of thing you're after.
Kent Cooper, AIA