Subgroups — #50310213

Order 38532.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#92788	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#10621725	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×#92788	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₁₃²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#15688282	—	13	14	no	maximal
7	#14523128	—	19	1	no	maximal, Hall
8	C₂×C₁₉×C₁₃⋊C₃	—	13	14	no	—
9	C₂×#92788	D₁₉	1	1	yes	characteristic
10	Dic₂₄₇	—	13	14	no	—
11	C₁₉×C₁₃⋊C₃	—	13	14	no	—
12	#10621725	—	19	1	no	Hall
13	#92788	Dic₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₁₉	D₁₃⋊C₃	1	14	yes	—
15	C₂×C₁₃²	C₃×D₁₉	1	1	yes	characteristic
16	C₁₃×C₁₉	Dic₁₃⋊C₃	1	14	yes	complemented
17	C₃×Dic₁₉	—	169	1	no	Hall
18	C₁₃²	C₃×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
19	Dic₁₃⋊C₃	—	247	14	no	—
20	C₂×C₃×C₁₉	—	169	1	no	—
21	C₂×C₁₃⋊C₃	—	13	14	no	—
22	Dic₁₉	—	169	1	no	Hall
23	C₃×C₁₉	—	169	1	no	Hall
24	Dic₁₃	—	247	14	no	—
25	C₁₃⋊C₃	—	13	14	no	—
26	C₂×C₁₉	#11759815	1	1	yes	characteristic
27	C₂×C₁₃	(C₁₃⋊C₃)⋊D₁₉	1	14	yes	—
28	C₁₉	#14523128	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	#15688282	1	14	yes	complemented
30	C₃×C₄	—	3211	1	no	Hall
31	C₂×C₃	—	169	1	no	—
32	C₄	—	3211	1	no	Sylow
33	C₃	—	169	1	no	Sylow
34	C₂	#34064208	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#34064208
commutator, hypocenter	C₁₃²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₃²×C₁₉	C₂×C₃
prime radical	C₂×C₁₉×#92788	C₂
LCS	G ▷ C₁₃²×C₁₉
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.