Subgroups — C₃⋊(C₁₉⋊#1043) #19152873

Order 5700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#1043	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	5	6	no	maximal
5	C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₃×D₅×C₁₉	—	5	6	no	—
7	C₅²×C₁₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₁₉⋊AGL(1,𝔽₅)	—	15	6	no	—
9	C₃⋊#1043	—	19	1	no	maximal, Hall
10	C₃×C₅×C₁₉	AGL(1,𝔽₅)	1	6	yes	complemented
11	Dic₅₇	—	25	1	no	Hall
12	D₅×C₁₉	—	5	6	no	—
13	C₃×C₅⋊D₅	D₁₉	1	1	yes	characteristic
14	C₂×C₃×C₁₉	—	25	1	no	—
15	#1043	—	57	1	no	Hall
16	C₅×C₁₉	ΓL(1,𝔽₁₆)	1	6	yes	complemented
17	Dic₁₉	—	75	1	no	Hall
18	C₃×C₅²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
19	ΓL(1,𝔽₁₆)	—	95	6	no	—
20	C₃×C₁₉	#1043	1	1	yes	characteristic, complemented, Hall
21	C₅⋊D₅	D₅₇	1	1	yes	characteristic
22	C₂×C₁₉	—	25	1	no	—
23	C₃×D₅	—	5	6	no	—
24	C₅²	Dic₅₇	1	1	yes	characteristic, complemented, Sylow
25	AGL(1,𝔽₅)	—	285	6	no	—
26	C₁₉	C₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₅	C₁₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
28	Dic₃	—	475	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	1	6	yes	complemented
32	C₄	—	1425	1	no	Sylow
33	C₃	C₁₉⋊#1043	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₁₉	C₄
LCS	G ▷ C₃×C₅²×C₁₉
UCS	C₁

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