Subgroups — C₃×C₁₉⋊(D₂₉⋊C₇) #37529016

Order 23142.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊(D₂₉⋊C₇)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₂₉⋊C₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₅₅₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₁₉×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₉⋊C₇	—	19	1	no	maximal, Hall
7	D₅₅₁	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×D₁₉	—	29	1	no	maximal, Hall
9	C₃×C₂₉⋊C₇	D₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₉×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	D₂₉⋊C₇	—	19	1	no	Hall
12	C₃×C₇×C₁₉	—	29	1	no	Hall
13	C₇×D₁₉	—	29	1	no	Hall
14	C₂₉⋊C₇	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
15	C₃×D₂₉	—	19	1	no	Hall
16	C₇×C₁₉	—	29	1	no	Hall
17	C₃×D₁₉	—	203	1	no	Hall
18	C₃×C₂₉	C₇×D₁₉	1	1	yes	characteristic, complemented, Hall
19	D₂₉	—	19	1	no	Hall
20	C₃×C₁₉	D₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇	—	551	1	no	Hall
22	D₁₉	—	203	1	no	Hall
23	C₂₉	C₃×C₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	—	29	1	no	Hall
25	C₁₉	C₃×D₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₇	—	551	1	no	Hall
27	C₇	—	29	1	no	Sylow
28	C₂×C₃	—	3857	1	no	Hall
29	C₃	C₁₉⋊(D₂₉⋊C₇)	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3857	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₉⋊(D₂₉⋊C₇)
commutator, cosocle, hypocenter	C₁₉×C₂₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₂₉	C₂×C₇
LCS	G ▷ C₁₉×C₂₉
UCS	C₁ ◁ C₃

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.