Subgroups — C₅×D₂₀ #6042

Order 200.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₅	C₂	1	2	yes	maximal, complemented
2	C₄×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²	C₂²	1	1	yes	characteristic
4	C₅×D₅	—	2	2	no	—
5	C₅×D₄	—	5	1	no	maximal
6	D₂₀	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅²	D₄	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₅	—	5	2	no	—
9	C₂×D₅	C₂×C₅	1	2	yes	complemented
10	C₄×C₅	—	2	2	no	—
11	C₄×C₅	D₅	1	1	yes	characteristic, complemented
12	C₄×C₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₅	—	2	2	no	—
14	C₂×C₅	—	10	2	no	—
15	C₂×C₅	C₂×D₅	1	1	yes	characteristic
16	C₂×C₅	C₂²×C₅	1	1	yes	characteristic
17	D₅	—	2	2	no	—
18	D₄	—	5	1	no	Sylow
19	C₅	—	2	2	no	—
20	C₅	D₂₀	1	1	yes	characteristic, direct product factor
21	C₅	C₅×D₄	1	1	yes	characteristic, complemented
22	C₂²	—	5	2	no	—
23	C₄	C₅×D₅	1	1	yes	characteristic, complemented
24	C₂	—	10	2	no	—
25	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.