Subgroups — D₉×C₁₉×C₁₀₁ #46828804

Order 34542.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₉×C₁₀₁	—	3	1	no	maximal
3	C₃×C₁₉×C₁₀₁	D₃	1	1	yes	characteristic
4	C₂×C₁₉×C₁₀₁	—	9	1	no	Hall
5	C₁₉×C₁₀₁	D₉	1	1	yes	characteristic, direct product factor, Hall
6	D₉×C₁₀₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₁₀₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
8	D₃×C₁₀₁	—	3	1	no	—
9	D₉×C₁₉	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₀₁	D₃×C₁₉	1	1	yes	characteristic
11	C₂×C₁₀₁	—	9	1	no	Hall
12	C₉×C₁₉	C₂×C₁₀₁	1	1	yes	characteristic, complemented, Hall
13	D₃×C₁₉	—	3	1	no	—
14	C₁₀₁	D₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₉	D₃×C₁₀₁	1	1	yes	characteristic
16	C₂×C₁₉	—	9	1	no	Hall
17	C₁₉	D₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
18	D₉	C₁₉×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
19	C₉	C₂×C₁₉×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3	1	no	—
21	C₃	D₃×C₁₉×C₁₀₁	1	1	yes	characteristic
22	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉×C₁₀₁	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₉×C₁₀₁
Frattini	C₃	D₃×C₁₉×C₁₀₁
Fitting	C₉×C₁₉×C₁₀₁	C₂
socle	C₃×C₁₉×C₁₀₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₉×C₁₀₁

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.