Subgroups — C₂²×C₅×D₅ #6063

Order 200.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₅	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₅²	C₂²	1	3	yes	complemented
4	C₅×D₅	C₂²	1	4	yes	direct product factor
5	C₂³×C₅	—	5	1	no	maximal
6	C₂²×D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅²	C₂³	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₅	—	2	2	no	—
9	C₂²×C₅	—	5	6	no	—
10	C₂²×C₅	D₅	1	1	yes	characteristic, direct product factor
11	C₂²×C₅	C₂×C₅	1	1	yes	characteristic, complemented
12	C₂×D₅	C₂×C₅	1	6	yes	direct product factor
13	C₂×C₅	—	2	6	no	—
14	C₂×C₅	—	5	4	no	—
15	C₂×C₅	C₂×D₅	1	3	yes	direct product factor
16	C₂×C₅	C₂²×C₅	1	3	yes	complemented
17	D₅	C₂²×C₅	1	4	yes	direct product factor
18	C₂³	—	5	1	no	Sylow
19	C₅	—	2	2	no	—
20	C₅	C₂²×D₅	1	1	yes	characteristic, direct product factor
21	C₅	C₂³×C₅	1	1	yes	characteristic, complemented
22	C₂²	—	5	6	no	—
23	C₂²	C₅×D₅	1	1	yes	characteristic, direct product factor
24	C₂	—	5	4	no	—
25	C₂	C₂×C₅×D₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅	D₅
commutator, cosocle, hypocenter	C₅	C₂³×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅²	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂²×C₅

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.