Subgroups — C₂²⋊(C₁₉⋊(C₅²⋊C₃)) #19152896

Order 5700.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊(C₅²⋊C₃)	—	4	1	no	maximal, Hall
3	C₂×C₅²×C₁₉	—	3	1	no	—
4	C₅²×C₁₉	A₄	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₅×C₁₉	—	3	2	no	—
6	C₂²⋊(C₅²⋊C₃)	—	19	1	no	maximal, Hall
7	C₂²⋊(C₁₉⋊C₃)	—	25	1	no	maximal, Hall
8	C₂×C₅×C₁₉	—	3	6	no	—
9	C₂²×C₅²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
10	C₅×C₁₉	—	3	2	no	—
11	C₂²×C₁₉	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₅²⋊C₃	—	76	1	no	Hall
13	C₁₉⋊C₃	—	100	1	no	Hall
14	C₂×C₅²	—	3	1	no	—
15	C₂×C₁₉	—	3	1	no	—
16	C₅²	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₅	—	3	2	no	—
18	C₁₉	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
19	A₄	—	475	1	no	Hall
20	C₂×C₅	—	3	6	no	—
21	C₅	—	3	2	no	—
22	C₂²	C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
23	C₃	—	1900	1	no	Sylow
24	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂²×C₅²×C₁₉	C₃
LCS	G ▷ C₂²×C₅²×C₁₉
UCS	C₁

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