Subgroups — C₂×C₁₉⋊#3874 #19152844

Order 5700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉⋊#3874	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₉₅	—	3	1	no	maximal, Hall
4	C₁₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₁₉	D₃	1	1	yes	characteristic, complemented
6	C₅×D₉₅	—	3	2	no	—
7	C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₉₅	—	3	1	no	—
9	C₂×C₅×D₁₉	—	15	1	no	—
10	C₂×#3874	—	19	1	no	maximal, Hall
11	C₂×D₅₇	—	25	1	no	maximal, Hall
12	C₂×C₅×C₁₉	—	3	1	no	—
13	C₂×C₅×C₁₉	—	3	1	no	—
14	D₉₅	—	3	2	no	—
15	C₅×D₁₉	—	15	2	no	—
16	C₂×C₅²⋊C₃	D₁₉	1	1	yes	characteristic, complemented
17	#3874	—	19	2	no	—
18	C₂×C₃×C₁₉	—	25	1	no	—
19	D₅₇	—	25	2	no	—
20	C₂×C₅×D₅	—	57	1	no	Hall
21	C₅×C₁₉	—	3	1	no	—
22	C₅×C₁₉	—	3	1	no	—
23	C₂×D₁₉	—	15	1	no	Hall
24	C₅²⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₉	—	25	1	no	Hall
26	C₂×C₅²	D₅₇	1	1	yes	characteristic, complemented
27	C₅×D₅	—	57	2	no	—
28	C₂×C₁₉	#3874	1	1	yes	characteristic, complemented
29	D₁₉	—	15	2	no	—
30	C₅²	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₅	—	285	1	no	—
32	C₂×D₅	—	57	1	no	—
33	C₁₉	C₂×#3874	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₃	—	475	1	no	Hall
35	C₂×C₅	—	3	1	no	—
36	C₂×C₅	—	3	1	no	—
37	C₂×C₅	—	285	2	no	—
38	D₅	—	57	2	no	—
39	C₂×C₃	—	25	1	no	—
40	D₃	—	475	2	no	—
41	C₅	—	3	1	no	—
42	C₅	—	3	1	no	—
43	C₂²	—	285	1	no	Sylow
44	C₃	—	25	1	no	Sylow
45	C₂	—	285	2	no	—
46	C₂	C₁₉⋊#3874	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₉⋊#3874
commutator, hypocenter	C₁₉×C₅²⋊C₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₉	D₃
LCS	G ▷ C₁₉×C₅²⋊C₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×C₅²⋊C₃	C₂	semidirect
2. C₁₉⋊#3874	C₂	direct (N × H)
4. C₁₉×C₅²⋊C₃	C₂²	semidirect
5. C₂×C₅²×C₁₉	D₃	semidirect
7. C₅²×C₁₉	C₂×D₃	semidirect
16. C₂×C₅²⋊C₃	D₁₉	semidirect
24. C₅²⋊C₃	C₂×D₁₉	semidirect
26. C₂×C₅²	D₅₇	semidirect
28. C₂×C₁₉	#3874	semidirect
30. C₅²	C₂×D₅₇	semidirect
33. C₁₉	C₂×#3874	semidirect
46. C₂	C₁₉⋊#3874	direct (N × H)

Subgroups — C2×C19⋊#3874 #19152844

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₉⋊#3874 #19152844