Subgroups — C₂×D₁₉×C₅²⋊C₃ #19152850

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	D₁₉×C₅²⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅²×D₁₉	C₂×C₃	1	2	yes	complemented
7	C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×D₁₉	—	3	2	no	—
9	C₂²×C₅²⋊C₃	—	19	1	no	maximal, Hall
10	C₂×C₃×D₁₉	—	25	1	no	maximal, Hall
11	C₂×C₅×C₁₉	—	3	2	no	—
12	C₅×D₁₉	—	3	4	no	—
13	C₂×C₅²⋊C₃	—	19	2	no	—
14	C₂×C₅²⋊C₃	D₁₉	1	1	yes	characteristic, direct product factor
15	C₂×C₃×C₁₉	—	25	1	no	—
16	C₃×D₁₉	—	25	2	no	—
17	C₂²×C₅²	—	19	1	no	Hall
18	C₅×C₁₉	—	3	2	no	—
19	C₂×D₁₉	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅²⋊C₃	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₉	—	25	1	no	Hall
22	C₂×C₅²	—	19	2	no	—
23	C₂×C₅²	C₃×D₁₉	1	1	yes	characteristic, complemented
24	C₂×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
25	D₁₉	C₂×C₅²⋊C₃	1	2	yes	direct product factor
26	C₅²	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₅	—	57	2	no	—
28	C₁₉	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₃	—	475	1	no	Hall
30	C₂×C₅	—	3	2	no	—
31	C₂×C₅	—	57	4	no	—
32	C₂×C₃	—	25	1	no	—
33	C₂×C₃	—	475	2	no	—
34	C₅	—	3	2	no	—
35	C₂²	—	19	1	no	Sylow
36	C₃	—	25	1	no	Sylow
37	C₂	—	19	2	no	—
38	C₂	D₁₉×C₅²⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₉×C₅²⋊C₃
commutator, hypocenter	C₅²×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₉
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. D₁₉×C₅²⋊C₃	C₂	direct (N × H)
3. C₂×C₅²×D₁₉	C₃	semidirect
4. C₁₉×C₅²⋊C₃	C₂²	semidirect
5. C₂×C₅²×C₁₉	C₂×C₃	semidirect
6. C₅²×D₁₉	C₂×C₃	semidirect
7. C₅²×C₁₉	C₂²×C₃	semidirect
14. C₂×C₅²⋊C₃	D₁₉	direct (N × H)
19. C₂×D₁₉	C₅²⋊C₃	direct (N × H)
20. C₅²⋊C₃	C₂×D₁₉	direct (N × H)
23. C₂×C₅²	C₃×D₁₉	semidirect
24. C₂×C₁₉	C₂×C₅²⋊C₃	semidirect
25. D₁₉	C₂×C₅²⋊C₃	direct (N × H)
26. C₅²	C₂×C₃×D₁₉	semidirect
28. C₁₉	C₂²×C₅²⋊C₃	semidirect
38. C₂	D₁₉×C₅²⋊C₃	direct (N × H)

Subgroups — C2×D19×C52⋊C3 #19152850

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₁₉×C₅²⋊C₃ #19152850