Subgroups — C₂×C₃×C₅²×D₁₉ #19152897

Order 5700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	D₁₉
commutator, hypocenter	C₁₉	C₂²×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₅²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×D₁₉	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₉	C₂	semidirect
3. C₂×C₅²×D₁₉	C₃	direct (N × H)
4. C₃×C₅²×C₁₉	C₂²	semidirect
5. C₂×C₃×C₅×D₁₉	C₅	direct (N × H)
6. C₂×C₅²×C₁₉	C₂×C₃	semidirect
7. C₅²×D₁₉	C₂×C₃	direct (N × H)
8. C₂×C₃×C₅×C₁₉	C₂×C₅	semidirect
9. C₃×C₅×D₁₉	C₂×C₅	direct (N × H)
10. C₅²×C₁₉	C₂²×C₃	semidirect
11. C₂×C₅×D₁₉	C₃×C₅	direct (N × H)
13. C₃×C₅×C₁₉	C₂²×C₅	semidirect
14. C₂×C₃×D₁₉	C₅²	direct (N × H)
15. C₂×C₅×C₁₉	C₂×C₃×C₅	semidirect
16. C₅×D₁₉	C₂×C₃×C₅	direct (N × H)
18. C₂×C₃×C₅²	D₁₉	direct (N × H)
19. C₂×C₃×C₁₉	C₂×C₅²	semidirect
20. C₃×D₁₉	C₂×C₅²	direct (N × H)
22. C₅×C₁₉	C₂²×C₃×C₅	semidirect
23. C₂×D₁₉	C₃×C₅²	direct (N × H)
24. C₃×C₅²	C₂×D₁₉	direct (N × H)
26. C₃×C₁₉	C₂²×C₅²	semidirect
28. C₂×C₅²	C₃×D₁₉	direct (N × H)
29. C₂×C₁₉	C₂×C₃×C₅²	semidirect
30. D₁₉	C₂×C₃×C₅²	direct (N × H)
32. C₂×C₃×C₅	C₅×D₁₉	direct (N × H)
33. C₅²	C₂×C₃×D₁₉	direct (N × H)
35. C₁₉	C₂²×C₃×C₅²	semidirect
36. C₃×C₅	C₂×C₅×D₁₉	direct (N × H)
39. C₂×C₅	C₃×C₅×D₁₉	direct (N × H)
41. C₂×C₃	C₅²×D₁₉	direct (N × H)
42. C₅	C₂×C₃×C₅×D₁₉	direct (N × H)
44. C₃	C₂×C₅²×D₁₉	direct (N × H)
46. C₂	C₃×C₅²×D₁₉	direct (N × H)

Subgroups — C2×C3×C52×D19 #19152897

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅²×D₁₉ #19152897