Subgroups — #6038

Order 200.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²	C₂²	1	1	yes	characteristic
5	C₅⋊D₅	—	2	1	no	—
6	C₅×D₅	—	2	1	no	—
7	C₂²⋊D₅	—	5	1	no	maximal
8	D₂₀	—	5	1	no	maximal
9	C₅²	D₄	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₅	—	5	1	no	—
11	C₂×D₅	—	5	1	no	—
12	C₂×D₅	—	5	1	no	—
13	C₂×D₅	—	10	2	no	—
14	C₂×D₅	D₅	1	1	yes	characteristic, complemented
15	C₄×C₅	—	5	1	no	—
16	Dic₅	D₅	1	1	yes	characteristic, complemented
17	C₂×C₅	—	2	2	no	—
18	C₂×C₅	—	10	1	no	—
19	C₂×C₅	C₂×D₅	1	1	yes	characteristic
20	C₂×C₅	C₂×D₅	1	1	yes	characteristic
21	D₅	—	2	1	no	—
22	D₅	—	10	4	no	—
23	D₅	—	10	1	no	—
24	D₅	—	10	1	no	—
25	D₄	—	25	1	no	Sylow
26	C₅	—	2	2	no	—
27	C₅	D₂₀	1	1	yes	characteristic, complemented
28	C₅	C₂²⋊D₅	1	1	yes	characteristic, complemented
29	C₂²	—	5	1	no	—
30	C₂²	—	25	1	no	—
31	C₄	—	5	1	no	—
32	C₂	—	10	1	no	—
33	C₂	—	50	1	no	—
34	C₂	D₅²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅²
commutator, Fitting, socle, cosocle	C₂×C₅²	C₂²
hypocenter	C₅²	D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂

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.