Subgroups — C₂×(C₁₁⋊C₅)⋊D₁₀₁ #36372500

Order 22220.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₁⋊C₅)⋊D₁₀₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁⋊C₅×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊C₅×C₁₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₁×C₁₀₁	C₂×C₅	1	1	yes	characteristic, complemented
6	D₁₁₁₁	C₂×C₅	1	2	yes	complemented
7	C₂×C₅×D₁₀₁	—	11	1	no	maximal, Hall
8	C₁₁×C₁₀₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₁₀₁	—	11	1	no	—
10	C₅×D₁₀₁	—	11	2	no	—
11	C₅×C₁₀₁	—	11	1	no	Hall
12	C₂×D₁₀₁	—	11	1	no	Hall
13	C₂×AGL(1,𝔽₁₁)	—	101	1	no	maximal, Hall
14	C₂×C₁₀₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
15	D₁₀₁	—	55	2	no	—
16	C₂×C₁₁⋊C₅	D₁₀₁	1	1	yes	characteristic, complemented
17	AGL(1,𝔽₁₁)	—	101	2	no	—
18	C₁₀₁	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
19	C₁₁⋊C₅	C₂×D₁₀₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₁	—	101	1	no	Hall
21	C₂×C₁₁	C₅×D₁₀₁	1	1	yes	characteristic, complemented
22	D₁₁	—	101	2	no	—
23	C₂²×C₅	—	1111	1	no	Hall
24	C₁₁	C₂×C₅×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	11	1	no	—
26	C₂×C₅	—	1111	2	no	—
27	C₅	—	11	1	no	Sylow
28	C₂²	—	5555	1	no	Sylow
29	C₂	—	5555	2	no	—
30	C₂	(C₁₁⋊C₅)⋊D₁₀₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₁₁⋊C₅)⋊D₁₀₁
commutator, cosocle, hypocenter	C₁₁×C₁₀₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₀₁	C₂×C₅
LCS	G ▷ C₁₁×C₁₀₁
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.