Subgroups — C₁₉×C₃⋊(C₅⋊D₃₅) #34093104

Order 19950.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₅⋊D₃₅	—	3	1	no	maximal, Hall
3	C₁₉×D₁₀₅	—	5	6	no	maximal
4	C₅²×C₇×C₁₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₁₉×C₃⋊(C₅⋊D₅)	—	7	1	no	maximal, Hall
6	C₃×C₅×C₇×C₁₉	D₅	1	6	yes	complemented
7	C₃×C₅²×C₁₉	D₇	1	1	yes	characteristic, complemented, Hall
8	C₁₉×D₃₅	—	15	6	no	—
9	C₃⋊(C₅⋊D₃₅)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₉×C₅⋊D₅	—	21	1	no	Hall
11	C₁₉×D₂₁	—	25	1	no	Hall
12	C₅×C₇×C₁₉	D₁₅	1	6	yes	complemented
13	C₁₉×D₁₅	—	35	6	no	—
14	C₃×C₅²×C₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
15	C₅²×C₁₉	D₂₁	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×C₁₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
17	C₅⋊D₃₅	—	3	1	no	Hall
18	C₃×C₅×C₁₉	D₃₅	1	6	yes	complemented
19	D₇×C₁₉	—	75	1	no	Hall
20	D₁₀₅	—	5	6	no	—
21	D₅×C₁₉	—	105	6	no	—
22	C₅²×C₇	D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
23	C₃⋊(C₅⋊D₅)	—	7	1	no	Hall
24	C₇×C₁₉	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Hall
25	D₃×C₁₉	—	175	1	no	Hall
26	C₃×C₅×C₇	D₅×C₁₉	1	6	yes	complemented
27	C₅×C₁₉	D₁₀₅	1	6	yes	complemented
28	C₃×C₅²	D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
29	D₃₅	—	15	6	no	—
30	C₃×C₁₉	C₅⋊D₃₅	1	1	yes	characteristic, complemented, Hall
31	C₅⋊D₅	—	21	1	no	Hall
32	D₂₁	—	25	1	no	Hall
33	C₂×C₁₉	—	525	1	no	Hall
34	C₅×C₇	C₁₉×D₁₅	1	6	yes	complemented
35	D₁₅	—	35	6	no	—
36	C₅²	C₁₉×D₂₁	1	1	yes	characteristic, complemented, Sylow
37	C₃×C₇	C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
38	C₁₉	C₃⋊(C₅⋊D₃₅)	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	C₁₉×D₃₅	1	6	yes	complemented
40	D₇	—	75	1	no	Hall
41	D₅	—	105	6	no	—
42	C₇	C₁₉×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	175	1	no	Hall
44	C₅	C₁₉×D₁₀₅	1	6	yes	complemented
45	C₃	C₁₉×C₅⋊D₃₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	525	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊(C₅⋊D₃₅)
commutator, cosocle, hypocenter	C₃×C₅²×C₇	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₉	C₂
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇×C₁₉	C₂	semidirect
4. C₅²×C₇×C₁₉	D₃	semidirect
6. C₃×C₅×C₇×C₁₉	D₅	semidirect
7. C₃×C₅²×C₁₉	D₇	semidirect
9. C₃⋊(C₅⋊D₃₅)	C₁₉	direct (N × H)
12. C₅×C₇×C₁₉	D₁₅	semidirect
14. C₃×C₅²×C₇	C₂×C₁₉	semidirect
15. C₅²×C₁₉	D₂₁	semidirect
16. C₃×C₇×C₁₉	C₅⋊D₅	semidirect
18. C₃×C₅×C₁₉	D₃₅	semidirect
22. C₅²×C₇	D₃×C₁₉	semidirect
24. C₇×C₁₉	C₃⋊(C₅⋊D₅)	semidirect
26. C₃×C₅×C₇	D₅×C₁₉	semidirect
27. C₅×C₁₉	D₁₀₅	semidirect
28. C₃×C₅²	D₇×C₁₉	semidirect
30. C₃×C₁₉	C₅⋊D₃₅	semidirect
34. C₅×C₇	C₁₉×D₁₅	semidirect
36. C₅²	C₁₉×D₂₁	semidirect
37. C₃×C₇	C₁₉×C₅⋊D₅	semidirect
38. C₁₉	C₃⋊(C₅⋊D₃₅)	direct (N × H)
39. C₃×C₅	C₁₉×D₃₅	semidirect
42. C₇	C₁₉×C₃⋊(C₅⋊D₅)	semidirect
44. C₅	C₁₉×D₁₀₅	semidirect
45. C₃	C₁₉×C₅⋊D₃₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅²×C₇×C₁₉	2
C₁₉×C₅⋊D₃₅	3
C₁₉×D₁₀₅	5
C₁₉×C₃⋊(C₅⋊D₅)	7
C₃⋊(C₅⋊D₃₅)	19

Subgroups — C19×C3⋊(C5⋊D35) #34093104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊(C₅⋊D₃₅) #34093104