Subgroups — C₂×D₅² #6062

Order 200.

74 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	2	yes	maximal, complemented
3	D₅²	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅²	C₂²	1	1	yes	characteristic, complemented
5	C₅⋊D₅	C₂²	1	2	yes	complemented
6	C₅×D₅	C₂²	1	4	yes	complemented
7	C₂²×D₅	—	5	2	no	maximal
8	C₅²	C₂³	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₅	—	5	2	no	—
10	C₂×D₅	—	5	2	no	—
11	C₂×D₅	—	5	8	no	—
12	C₂×D₅	—	10	2	no	—
13	C₂×D₅	D₅	1	2	yes	direct product factor
14	C₂×C₅	—	2	2	no	—
15	C₂×C₅	—	5	4	no	—
16	C₂×C₅	C₂×D₅	1	2	yes	complemented
17	D₅	—	5	4	no	—
18	D₅	—	10	4	no	—
19	D₅	C₂×D₅	1	4	yes	direct product factor
20	C₂³	—	25	1	no	Sylow
21	C₅	—	2	2	no	—
22	C₅	C₂²×D₅	1	2	yes	complemented
23	C₂²	—	5	2	no	—
24	C₂²	—	25	4	no	—
25	C₂²	—	25	1	no	—
26	C₂	—	5	4	no	—
27	C₂	—	25	2	no	—
28	C₂	D₅²	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅²
commutator, cosocle, hypocenter	C₅²	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₅²	C₂²
LCS	G ▷ 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.