Subgroups — C₂×C₁₆ #109

Order 32.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈	C₂	1	1	yes	maximal, characteristic
2	C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄	C₄	1	1	yes	characteristic
4	C₈	C₄	1	1	yes	characteristic
5	C₈	C₂²	1	1	yes	characteristic
6	C₂²	C₈	1	1	yes	characteristic
7	C₄	C₈	1	1	yes	characteristic
8	C₄	C₂×C₄	1	1	yes	characteristic
9	C₂	C₁₆	1	2	yes	direct product factor
10	C₂	C₂×C₈	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₆	C₂	direct (N × H)
9. C₂	C₁₆	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₈	2
C₁₆	2