Subgroups — C₂²×C₅²×C₁₉⋊C₃ #19152890

Order 5700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₉⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₅×C₁₉⋊C₃	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²×C₁₉	C₂×C₃	1	3	yes	complemented
6	C₂×C₅×C₁₉⋊C₃	C₂×C₅	1	18	yes	direct product factor
7	C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₅×C₁₉	C₃×C₅	1	6	yes	complemented
9	C₂²×C₃×C₅²	—	19	1	no	maximal, Hall
10	C₅×C₁₉⋊C₃	C₂²×C₅	1	6	yes	direct product factor
11	C₂²×C₁₉⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₁₉	C₂×C₃×C₅	1	18	yes	complemented
13	C₂×C₃×C₅²	—	19	3	no	—
14	C₂×C₁₉⋊C₃	C₂×C₅²	1	3	yes	direct product factor
15	C₂²×C₅²	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₁₉	C₂²×C₃×C₅	1	6	yes	complemented
17	C₂²×C₁₉	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅²	—	19	1	no	Hall
19	C₂²×C₃×C₅	—	19	6	no	—
20	C₁₉⋊C₃	C₂²×C₅²	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅²	C₂×C₁₉⋊C₃	1	3	yes	direct product factor
22	C₂×C₁₉	C₂×C₃×C₅²	1	3	yes	complemented
23	C₂×C₃×C₅	—	19	18	no	—
24	C₅²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₅	C₅×C₁₉⋊C₃	1	6	yes	direct product factor
26	C₁₉	C₂²×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₅	—	19	6	no	—
28	C₂²×C₃	—	19	1	no	Hall
29	C₂×C₅	C₂×C₅×C₁₉⋊C₃	1	18	yes	direct product factor
30	C₂×C₃	—	19	3	no	—
31	C₅	C₂²×C₅×C₁₉⋊C₃	1	6	yes	direct product factor
32	C₂²	C₅²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	19	1	no	Sylow
34	C₂	C₂×C₅²×C₁₉⋊C₃	1	3	yes	direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂²×C₅²×C₁₉	C₃	semidirect
3. C₅²×C₁₉⋊C₃	C₂²	direct (N × H)
4. C₂²×C₅×C₁₉⋊C₃	C₅	direct (N × H)
5. C₂×C₅²×C₁₉	C₂×C₃	semidirect
6. C₂×C₅×C₁₉⋊C₃	C₂×C₅	direct (N × H)
7. C₅²×C₁₉	C₂²×C₃	semidirect
8. C₂²×C₅×C₁₉	C₃×C₅	semidirect
10. C₅×C₁₉⋊C₃	C₂²×C₅	direct (N × H)
11. C₂²×C₁₉⋊C₃	C₅²	direct (N × H)
12. C₂×C₅×C₁₉	C₂×C₃×C₅	semidirect
14. C₂×C₁₉⋊C₃	C₂×C₅²	direct (N × H)
15. C₂²×C₅²	C₁₉⋊C₃	direct (N × H)
16. C₅×C₁₉	C₂²×C₃×C₅	semidirect
17. C₂²×C₁₉	C₃×C₅²	semidirect
20. C₁₉⋊C₃	C₂²×C₅²	direct (N × H)
21. C₂×C₅²	C₂×C₁₉⋊C₃	direct (N × H)
22. C₂×C₁₉	C₂×C₃×C₅²	semidirect
24. C₅²	C₂²×C₁₉⋊C₃	direct (N × H)
25. C₂²×C₅	C₅×C₁₉⋊C₃	direct (N × H)
26. C₁₉	C₂²×C₃×C₅²	semidirect
29. C₂×C₅	C₂×C₅×C₁₉⋊C₃	direct (N × H)
31. C₅	C₂²×C₅×C₁₉⋊C₃	direct (N × H)
32. C₂²	C₅²×C₁₉⋊C₃	direct (N × H)
34. C₂	C₂×C₅²×C₁₉⋊C₃	direct (N × H)

Subgroups — C22×C52×C19⋊C3 #19152890

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₅²×C₁₉⋊C₃ #19152890