Taula de grups per famílies

Grups cíclics
grup	pàg.
$C_{2}$
$C_{3}$
$C_{4}$
$C_{5}$
$C_{6}$
$C_{7}$
$C_{8}$
$C_{9}$
$C_{10}$
$C_{11}$
$C_{12}$
$C_{13}$
$C_{14}$
$C_{15}$
$C_{16}$
$C_{17}$
$C_{18}$
$C_{19}$
$C_{20}$
$C_{21}$
$C_{22}$
$C_{23}$
$C_{24}$
$C_{25}$
$C_{26}$
$C_{27}$
$C_{28}$
$C_{29}$
$C_{30}$
$C_{31}$
$C_{32}$
$\qquad$
Grups simètrics
grup	pàg.
$S_{3}$
$S_{4}$
$\qquad$
Grups alternats
grup	pàg.
$A_{4}$

Grups diedrals
grup	pàg.
$D_{8}$
$D_{10}$
$D_{12}$
$D_{14}$
$D_{16}$
$D_{18}$
$D_{20}$
$D_{22}$
$D_{24}$
$D_{26}$
$D_{28}$
$D_{30}$
$D_{32}$
$\qquad$
Quaternions generalitzats
grup	pàg.
$Q_{8}$
$Q_{16}$
$Q_{32}$
$\qquad$
Grups de Fröbenius
grup	pàg.
$F_{20}$
$F_{21}$
$\qquad$
Grups aïllats
grup	pàg.
$T$
$G_{32,8}$
$G_{32,15}$
$G_{32,32}$
$\qquad$
Productes (abelians)
grup	pàg.
$C_{2} \times C_{2}$
$C_{4} \times C_{2}$
$C_{2} \times C_{2} \times C_{2}$
$C_{3} \times C_{3}$
$C_{6} \times C_{2}$
$C_{4} \times C_{4}$

grup	pàg.
$C_{8} \times C_{2}$
$C_{4} \times C_{2} \times C_{2}$
$C_{2} \times C_{2} \times C_{2} \times C_{2}$
$C_{6} \times C_{3}$
$C_{10} \times C_{2}$
$C_{12} \times C_{2}$
$C_{6} \times C_{2} \times C_{2}$
$C_{5} \times C_{5}$
$C_{9} \times C_{3}$
$C_{3} \times C_{3} \times C_{3}$
$C_{14} \times C_{2}$
$C_{8} \times C_{4}$
$C_{16} \times C_{2}$
$C_{4} \times C_{4} \times C_{2}$
$C_{8} \times C_{2} \times C_{2}$
$C_{4} \times C_{2} \times C_{2} \times C_{2}$
$C_{2} \times C_{2} \times C_{2} \times C_{2} \times C_{2}$
$\qquad$
Productes (no abelians)
grup	pàg.
$(C_{2} \times C_{2}) \rtimes C_{4}$
$C_{4} \rtimes C_{4}$
$C_{8} \rtimes C_{2}$
$C_{8} \rtimes C_{2}$
$C_{2} \times D_{8}$
$C_{2} \times Q_{8}$
$Q_{8} \rtimes C_{2}$
$C_{3} \times S_{3}$
$C_{3} \rtimes S_{3}$
$C_{5} \rtimes C_{4}$
$C_{3} \rtimes C_{8}$
$Q_{8} \rtimes C_{3}$
$C_{3} \rtimes Q_{8}$
$C_{4} \times S_{3}$
$C_{2} \times T$
$(C_{2} \times C_{2}) \rtimes S_{3}$
$C_{3} \times D_{8}$
$C_{3} \times Q_{8}$
$C_{2} \times A_{4}$
$C_{2} \times D_{12}$
$(C_{3} \times C_{3}) \rtimes C_{3}$
$C_{9} \rtimes C_{3}$

grup	pàg.
$C_{7} \rtimes C_{4}$
$C_{5} \times S_{3}$
$C_{3} \times D_{10}$
$(C_{4} \times C_{2}) \rtimes C_{4}$
$C_{8} \rtimes C_{4}$
$(C_{2} \times C_{2}) \rtimes C_{8}$
$(C_{4} \times C_{2}) \rtimes C_{4}$
$(C_{8} \rtimes C_{2}) \rtimes C_{2}$
$D_{8} \rtimes C_{4}$
$Q_{8} \rtimes C_{4}$
$Q_{8} \rtimes C_{4}$
$C_{4} \rtimes C_{8}$
$C_{8} \rtimes C_{4}$
$C_{8} \rtimes C_{4}$
$C_{16} \rtimes C_{2}$
$C_{16} \rtimes C_{2}$
$C_{2} \times ((C_{2} \times C_{2}) \rtimes C_{4})$
$C_{2} \times (C_{4} \rtimes C_{4})$
$(C_{4} \times C_{2}) \rtimes C_{4}$
$C_{4} \times D_{8}$
$C_{4} \times Q_{8}$
$(C_{2} \times C_{2}) \rtimes D_{8}$
$C_{4} \rtimes D_{8}$
$(C_{2} \times C_{2}) \rtimes Q_{8}$
$(C_{4} \rtimes C_{4}) \rtimes C_{2}$
$(C_{2} \times Q_{8}) \rtimes C_{2}$
$(C_{4} \rtimes C_{4}) \rtimes C_{2}$
$C_{4} \rtimes D_{8}$
$C_{4} \rtimes Q_{8}$
$C_{2} \times (C_{8} \rtimes C_{2})$
$(C_{8} \rtimes C_{2}) \rtimes C_{2}$
$C_{2} \times D_{16}$
$C_{2} \times (C_{8} \rtimes C_{2})$
$C_{2} \times Q_{16}$
$Q_{16} \rtimes C_{2}$
$C_{8} \rtimes (C_{2} \times C_{2})$
$Q_{16} \rtimes C_{2}$
$C_{2} \times C_{2} \times D_{8}$
$C_{2} \times C_{2} \times Q_{8}$
$C_{2} \times (Q_{8} \rtimes C_{2})$
$Q_{8} \rtimes (C_{2} \times C_{2})$
$(C_{2} \times Q_{8}) \rtimes C_{2}$