Subgroups — C₂×Dic₁₀ #706

Order 80.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₅	C₂	1	2	yes	maximal
3	Dic₁₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅	C₂²	1	1	yes	characteristic
5	C₄×C₅	C₂²	1	2	yes	—
6	Dic₅	C₂²	1	4	yes	—
7	C₂×Q₈	—	5	1	no	maximal, Sylow
8	C₂×C₅	Q₈	1	2	yes	complemented
9	C₂×C₅	C₂³	1	1	yes	characteristic
10	Q₈	—	5	4	no	—
11	C₂×C₄	—	5	2	no	—
12	C₂×C₄	D₅	1	1	yes	characteristic
13	C₅	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
14	C₂²	C₂×D₅	1	1	yes	characteristic
15	C₄	—	5	4	no	—
16	C₄	C₂×D₅	1	2	yes	—
17	C₂	Dic₁₀	1	2	yes	direct product factor
18	C₂	C₂²×D₅	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.