Subgroups — #50310344

Order 38532.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34064207	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#10621728	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#23751431	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#15688301	—	13	14	no	maximal
7	#14523144	—	19	1	no	maximal, Hall
8	#13093365	—	13	14	no	—
9	#11759815	—	19	1	no	—
10	C₁₉⋊#261	—	13	14	no	—
11	#10625203	—	13	14	no	—
12	#10621728	—	19	1	no	Hall
13	#92788	—	19	1	no	Hall
14	C₁₉×D₁₃	—	13	14	no	—
15	C₁₃⋊D₁₃	D₁₉⋊C₃	1	1	yes	characteristic
16	C₁₃×C₁₉	AGL(1,𝔽₁₃)	1	14	yes	complemented
17	(C₁₉⋊C₃)⋊C₄	—	169	1	no	Hall
18	C₁₃²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	AGL(1,𝔽₁₃)	—	247	14	no	—
20	C₂×C₁₉⋊C₃	—	169	1	no	—
21	D₁₃⋊C₃	—	247	14	no	—
22	Dic₁₉	—	169	1	no	Hall
23	C₁₉⋊C₃	—	169	1	no	Hall
24	#261	—	247	14	no	—
25	C₁₃⋊C₃	—	247	14	no	—
26	C₂×C₁₉	—	169	1	no	—
27	D₁₃	—	13	14	no	—
28	C₁₉	#14523144	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	#15688301	1	14	yes	complemented
30	C₃×C₄	—	3211	1	no	Hall
31	C₂×C₃	—	3211	1	no	—
32	C₄	—	3211	1	no	Sylow
33	C₃	—	3211	1	no	Sylow
34	C₂	—	169	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃²×C₁₉	C₃×C₄
prime radical	#34064207	C₂
cosocle	C₁₉×C₁₃⋊D₁₃	C₂×C₃
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁

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.