Subgroups — C₁₉×D₂₆₁ #23755342

Order 9918.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₈₇	—	3	1	no	maximal
3	C₃×C₁₉×C₂₉	D₃	1	1	yes	characteristic
4	C₁₉×D₂₉	—	9	1	no	Hall
5	C₁₉×C₂₉	D₉	1	1	yes	characteristic, complemented, Hall
6	D₂₆₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₉×C₁₉	—	29	1	no	maximal, Hall
8	C₉×C₂₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
9	D₈₇	—	3	1	no	—
10	C₉×C₁₉	D₂₉	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₉	—	87	1	no	—
12	C₃×C₂₉	D₃×C₁₉	1	1	yes	characteristic
13	D₂₉	—	9	1	no	Hall
14	C₃×C₁₉	D₈₇	1	1	yes	characteristic
15	C₂×C₁₉	—	261	1	no	Hall
16	C₂₉	D₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
17	C₁₉	D₂₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	D₉	—	29	1	no	Hall
19	C₉	C₁₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	87	1	no	—
21	C₃	C₁₉×D₈₇	1	1	yes	characteristic
22	C₂	—	261	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₂₆₁
commutator, cosocle, hypocenter	C₉×C₂₉	C₂×C₁₉
Frattini	C₃	C₁₉×D₈₇
Fitting	C₉×C₁₉×C₂₉	C₂
socle	C₃×C₁₉×C₂₉	D₃
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₁₉

Splittings G = N ⋊ H with N normal; H ≅ G/N.