# Notation for proper normal subgroup

Is there any easy way to put not-equal sign to any binary operation symbol like \triangleright etc.

For example, I want to use it for a proper normal subgroup.

If found one solution for \lhd but it is not so simple (symbol for proper ideal (\unlhd + \lneq))

You may choose between the amssymbversion and a variant borrowed from mathabx:

\documentclass{article}
\usepackage{amssymb}

\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{ <-6> matha5 <6-7> matha6 <7-8>
matha7 <8-9> matha8 <9-10> matha9 <10-12> matha10 <12-> matha12 }{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}
%
\DeclareMathSymbol{\nvartrianglelefteq}{\mathrel}{matha}{"9E}
\DeclareMathSymbol{\vartrianglelefteq}{\mathrel}{matha}{"9C}

\begin{document}

$H \nvartrianglelefteq G \qquad H \vartrianglelefteq G$

$H \ntrianglelefteq G \qquad H \trianglelefteq G$

\end{document}


The general easy way to do this is to use \underset from the amsmath package,

\underset{\neq}{\triangleleft}


however it will give you a rather bulky symbol, that you would not want to use in running text.

\documentclass{article}

\usepackage{amsmath,amssymb}

\begin{document}

\begin{equation*}
In text we say $$H \triangleleft G$$ and $$H\ne G$$.