Subgroups — #38760949

Order 25308.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263551	C₂	1	1	yes	maximal, characteristic
2	(C₁₉⋊C₃)⋊Dic₃₇	C₃	1	1	yes	maximal, characteristic
3	#20263551	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	Dic₇₀₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃₇×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic
7	C₂×C₁₉×C₃₇	C₂×C₉	1	1	yes	characteristic
8	#13050607	—	19	1	no	maximal, Hall
9	C₁₉×C₃₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
10	#4296⋊C₄	—	37	1	no	maximal, Hall
11	C₂×#66524	—	19	1	no	—
12	C₃×Dic₃₇	—	19	1	no	—
13	C₂×#4296	—	37	1	no	—
14	#66524	—	19	1	no	Hall
15	(C₁₉⋊C₃)⋊C₄	—	37	1	no	—
16	C₂×C₃×C₃₇	—	19	1	no	—
17	#4296	—	37	1	no	Hall
18	Dic₃₇	—	19	1	no	Hall
19	C₂×C₁₉⋊C₃	D₃₇⋊C₃	1	1	yes	characteristic
20	C₃×C₃₇	—	19	1	no	—
21	Dic₁₉	—	37	1	no	Hall
22	C₂×C₃₇	AGL(1,𝔽₁₉)	1	1	yes	characteristic
23	C₁₉⋊C₃	Dic₃₇⋊C₃	1	1	yes	characteristic
24	C₂×C₁₉	#66524⋊C₂	1	1	yes	characteristic
25	C₃₇	#4296⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₄×C₉	—	703	1	no	Hall
27	C₁₉	#13050607	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	703	1	no	—
29	C₃×C₄	—	703	1	no	—
30	C₉	—	703	1	no	Sylow
31	C₂×C₃	—	19	1	no	—
32	C₄	—	703	1	no	Sylow
33	C₃	—	19	1	no	—
34	C₂	#27162578	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#27162578
commutator, hypocenter	C₁₉×C₃₇	C₄×C₉
Fitting, socle	C₂×C₁₉×C₃₇	C₂×C₉
LCS	G ▷ C₁₉×C₃₇
UCS	C₁ ◁ C₂

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