\input amstex

$$\multline
\Bigl|\bigl(\bigcup_{H\in S_3}H\bigr)\cup\bigl(\bigcup_{K\in S_5}K\bigr)\cup\bigl(\bigcup_{L\in S_{11}}L\bigr)\Bigr|=\\
=55\cdot(9-3)+(3-1)+11\cdot(5-1)+45\cdot(11-1)+1=\\
=332+44+450+1=827>495=|G|
\endmultline$$
\bye