chord transition

I am new to guitar playing..... I have a song where the chords go from c to F to G
I want, for the break, to change it up a bit and go to a split chord of C/F - the next transition escapes me for the F chord and G chord. Can anyone help me with this? The sound I want if you play just the string goes from High E 3rd fret (which I discovered the chord is called Split C/F) to High E sting 5th fret to High E string 1st Fret. Thank you to anyone who may send me the chords for this

you could maye use a diminished chord? lol or triad or something. im not good with that kind of stuff. try a Bb diminished i guess.