Subgroups — C₅×Dic₁₀ #6040

Order 200.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅	C₂	1	2	yes	maximal
3	C₂×C₅²	C₂²	1	1	yes	characteristic
4	C₅×Q₈	—	5	1	no	maximal
5	Dic₁₀	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅²	Q₈	1	1	yes	characteristic, complemented, Sylow
7	C₄×C₅	—	2	2	no	—
8	C₄×C₅	—	5	2	no	—
9	C₄×C₅	D₅	1	1	yes	characteristic
10	C₄×C₅	C₂×C₅	1	1	yes	characteristic
11	Dic₅	C₂×C₅	1	2	yes	—
12	C₂×C₅	—	2	2	no	—
13	C₂×C₅	C₂×D₅	1	1	yes	characteristic
14	C₂×C₅	C₂²×C₅	1	1	yes	characteristic
15	Q₈	—	5	1	no	Sylow
16	C₅	—	2	2	no	—
17	C₅	Dic₁₀	1	1	yes	characteristic, direct product factor
18	C₅	C₅×Q₈	1	1	yes	characteristic, complemented
19	C₄	—	5	2	no	—
20	C₄	C₅×D₅	1	1	yes	characteristic
21	C₂	C₂×C₅×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.