Subgroups — C₂²×Dic₁₃ #6132

Order 208.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₁₃	C₄	1	4	yes	complemented
4	C₂²×C₁₃	C₂²	1	3	yes	—
5	Dic₁₃	C₂²	1	4	yes	direct product factor
6	C₂×C₁₃	C₂×C₄	1	6	yes	complemented
7	C₂×C₁₃	C₂³	1	1	yes	characteristic
8	C₂²×C₄	—	13	1	no	maximal, Sylow
9	C₁₃	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
10	C₂³	D₁₃	1	1	yes	characteristic
11	C₂×C₄	—	13	6	no	—
12	C₂²	Dic₁₃	1	4	yes	direct product factor
13	C₂²	C₂×D₁₃	1	3	yes	—
14	C₄	—	13	4	no	—
15	C₂	C₂×Dic₁₃	1	6	yes	direct product factor
16	C₂	C₂²×D₁₃	1	1	yes	characteristic

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

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