Modify page layout using titleps

Question

I defined 3 different page styles with titleps. I also used titlesec to define a new sectioning level namely \subpart.

Now I can't use this new level's title with titleps as header in odd pages. I don't know how to introduce it to titleps. I include the code I used, it delivers what I intend(apart from the above mentioned problem), but I'd really appreciate if you could refine it.

I marked the problem in the comment to the main page-style definition.

Note: Upon @cfr's remark I removed vide page-style definition.

\documentclass[b5paper,twoside]{book}
\usepackage{geometry}
\usepackage{titletoc}
\usepackage[rm,small,center,compact,newparttoc,clearempty]{titlesec}
\titleclass{\subpart}{page}[\part]
%
%\titleformat{\chapter}{\thechapter .,. \chaptertitlename}
\newcounter{subpart}

\renewcommand{\thesubpart}{\Alph{subpart}}
\newcommand{\subpartname}{Subpart}
%
\titleformat{\subpart}[display]{\centering\normalfont\Large\bfseries}%
{\subpartname~\thesubpart}{1pc}{\Huge\bfseries}
%
\titlespacing{\subpart}{0pt}{0pt}{0pt}

\titlecontents{subpart}[0pt]{\addvspace{1pc}\normalfont\bfseries}%
{\thecontentslabel\enspace ---\enspace\large}%
{\normalfont\large\bfseries}{\hspace{2em plus 1fill}\large\contentspage}
\setcounter{secnumdepth}{-2}

\usepackage{titleps}
\newpagestyle{main}{
    \sethead[][\chaptertitle][] % even
    {}{\subparttitle}{} % Problem: Here I want to have subpart title. 
    \setfoot[][\thepage][]
    {}{\thepage}{}}
\pagestyle{main}


\newpagestyle{preface}{
    \sethead[][\chaptertitle][] % even
    {}{\chaptertitle}{} % odd
    \setfoot[][\thepage][]
    {}{\thepage}{}}
\pagestyle{preface}
\assignpagestyle{\part}{empty}%it is a titlesec pkg command which suppresses page number only on the first page of the relevant sectioning command
\assignpagestyle{\subpart}{empty}
\assignpagestyle{\chapter}{empty}
\begin{document}

\frontmatter
\pagestyle{empty}
.
.
.
\chapter[Preface]{PREFACE}
\pagestyle{preface}
.
.
.
\mainmatter
\part{History}
\subpart{Primitive Historians}
\pagestyle{main}
\chapter{The Formation of the Concept of History}

\end{document}

Answer 1

You need to tell titleps which titlemarks are defined using the \settitlemarks macro. As cfr noted in the comments, you also need to load titlesec with the pagestyles option rather than loading the package separately.

So you need:

\usepackage[rm,small,center,compact,newparttoc,clearempty,pagestyles]{titlesec}

and then after you've made your new pagestyles:

\settitlemarks{part,subpart,chapter}

Here's a complete document. I haven't looked at the rest of your code. I've also added the lipsum package to show some pages.

\documentclass[b5paper,twoside]{book}
\usepackage{geometry}
\usepackage{titletoc}
\usepackage[rm,small,center,compact,newparttoc,clearempty,pagestyles]{titlesec}
\usepackage{kantlipsum}
\titleclass{\subpart}{page}[\part]
%
%\titleformat{\chapter}{\thechapter .,. \chaptertitlename}
\newcounter{subpart}

\renewcommand{\thesubpart}{\Alph{subpart}}
\newcommand{\subpartname}{Subpart}
%
\titleformat{\subpart}[display]{\centering\normalfont\Large\bfseries}%
{\subpartname~\thesubpart}{1pc}{\Huge\bfseries}
%
\titlespacing{\subpart}{0pt}{0pt}{0pt}

\titlecontents{subpart}[0pt]{\addvspace{1pc}\normalfont\bfseries}%
{\thecontentslabel\enspace ---\enspace\large}%
{\normalfont\large\bfseries}{\hspace{2em plus 1fill}\large\contentspage}
\setcounter{secnumdepth}{-2}

\newpagestyle{main}{
    \sethead[][\chaptertitle][] % even
    {}{\subparttitle}{} % Problem: Here I want to have subpart title. 
    \setfoot[][\thepage][]
    {}{\thepage}{}}
\pagestyle{main}


\newpagestyle{preface}{
    \sethead[][\chaptertitle][] % even
    {}{\chaptertitle}{} % odd
    \setfoot[][\thepage][]
    {}{\thepage}{}}
\pagestyle{empty}
\assignpagestyle{\part}{empty}%it is a titlesec pkg command which suppresses page number only on the first page of the relevant sectioning command
\assignpagestyle{\subpart}{empty}
\assignpagestyle{\chapter}{empty}
\settitlemarks{subpart,chapter}
\begin{document}

\frontmatter
\pagestyle{empty}
.
.
.
\chapter[Preface]{PREFACE}
\pagestyle{preface}
.
.
.
\part{History}
\subpart{Primitive Historians}
\pagestyle{main}
\chapter{The Formation of the Concept of History}
\kant[1-20]
\end{document}