Subgroups of order 2 in groups of order 16

This article contains summary information about all subgroups of order 2 inside groups of order 16. See also groups of order 16 | groups of order 2 | subgroup structure of groups of order 16 | supergroups of groups of order 2

Numerical information on counts of subgroups

Group	Second part of GAP ID	Hall-Senior number	Hall-Senior symbol	Nilpotency class	Minimum size of generating set	Number of subgroups of order 2	Number of normal subgroups of order 2	Number of 2-core-automorphism-invariant subgroups of order 2 (must be odd)	Number of 2-automorphism-invariant subgroups of order 2	Number of characteristic subgroups of order 2
cyclic group:Z16	1	5	$(4)$	1	1	1	1	1	1	1
direct product of Z4 and Z4	2	3	$(2^{2})$	1	2	3	3		0	0
SmallGroup(16,3)	3	9	$16\Gamma _{3}c_{1}$	2	2	7	3	1	1	1
nontrivial semidirect product of Z4 and Z4	4	10	$16\Gamma _{3}c_{2}$	2	2	3	3	3	3	3
direct product of Z8 and Z2	5	4	$(31)$	3	3	1	1	1
M16	6	11	$16\Gamma _{3}d$