Subgroups — C₃×C₁₉⋊C₃×D₃₅ #26046180

Order 11970.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊C₃×D₃₅	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₉×D₃₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×C₁₉⋊C₃	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₇×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
7	C₃×D₅×C₁₉⋊C₃	—	7	1	no	maximal, Hall
8	C₁₉×D₃₅	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₁₉⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
11	C₃×D₇×C₁₉	—	5	1	no	—
12	D₇×C₁₉⋊C₃	—	5	3	no	—
13	C₅×C₇×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃²×D₃₅	—	19	1	no	maximal, Hall
15	C₃×D₅×C₁₉	—	7	1	no	—
16	D₅×C₁₉⋊C₃	—	7	3	no	—
17	C₃×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
18	C₇×C₁₉⋊C₃	C₃×D₅	1	3	yes	complemented
19	C₂×C₃×C₁₉⋊C₃	—	35	1	no	Hall
20	C₃²×C₅×C₇	—	19	1	no	Hall
21	C₃×C₅×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
22	C₅×C₁₉⋊C₃	C₃×D₇	1	3	yes	complemented
23	D₇×C₁₉	—	5	1	no	Hall
24	C₃×D₃₅	—	19	3	no	—
25	C₃×D₃₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
26	D₅×C₁₉	—	7	1	no	Hall
27	C₃×C₁₉⋊C₃	D₃₅	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₁₉	C₃²×D₅	1	1	yes	characteristic, complemented, Hall
29	C₃²×D₇	—	95	1	no	Hall
30	C₂×C₃×C₁₉	—	35	1	no	—
31	C₂×C₁₉⋊C₃	—	35	3	no	—
32	C₃×C₅×C₇	—	19	3	no	—
33	C₃×C₅×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
34	C₅×C₁₉	C₃²×D₇	1	1	yes	characteristic, complemented, Hall
35	C₃²×D₅	—	133	1	no	Hall
36	D₃₅	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
37	C₃²×C₇	—	19	1	no	Hall
38	C₃×C₁₉	C₃×D₃₅	1	1	yes	characteristic, complemented
39	C₁₉⋊C₃	C₃×D₃₅	1	3	yes	direct product factor
40	C₃²×C₅	—	19	1	no	Hall
41	C₃×D₇	—	5	1	no	—
42	C₃×D₇	—	95	3	no	—
43	C₂×C₁₉	—	35	1	no	Hall
44	C₅×C₇	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
45	C₃×D₅	—	7	1	no	—
46	C₃×D₅	—	133	3	no	—
47	C₃×C₇	—	19	3	no	—
48	C₃×C₇	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
49	C₁₉	C₃²×D₃₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃²	—	665	1	no	Hall
51	C₃×C₅	—	19	3	no	—
52	C₃×C₅	D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
53	D₇	—	5	1	no	Hall
54	D₅	—	7	1	no	Hall
55	C₃²	—	19	1	no	Sylow
56	C₇	C₃×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	35	1	no	—
58	C₂×C₃	—	665	3	no	—
59	C₅	C₃×D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₃	—	19	3	no	—
61	C₃	C₁₉⋊C₃×D₃₅	1	1	yes	characteristic, direct product factor
62	C₂	—	35	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₉⋊C₃×D₃₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₉⋊C₃	C₂	semidirect
2. C₁₉⋊C₃×D₃₅	C₃	direct (N × H)
3. C₃×C₁₉×D₃₅	C₃	semidirect
5. C₃×C₅×C₇×C₁₉	C₂×C₃	semidirect
6. C₅×C₇×C₁₉⋊C₃	C₂×C₃	semidirect
8. C₁₉×D₃₅	C₃²	semidirect
9. C₃×C₇×C₁₉⋊C₃	D₅	semidirect
10. C₃×C₅×C₁₉⋊C₃	D₇	semidirect
13. C₅×C₇×C₁₉	C₂×C₃²	semidirect
17. C₃×C₇×C₁₉	C₃×D₅	semidirect
18. C₇×C₁₉⋊C₃	C₃×D₅	semidirect
21. C₃×C₅×C₁₉	C₃×D₇	semidirect
22. C₅×C₁₉⋊C₃	C₃×D₇	semidirect
25. C₃×D₃₅	C₁₉⋊C₃	direct (N × H)
27. C₃×C₁₉⋊C₃	D₃₅	direct (N × H)
28. C₇×C₁₉	C₃²×D₅	semidirect
33. C₃×C₅×C₇	C₂×C₁₉⋊C₃	semidirect
34. C₅×C₁₉	C₃²×D₇	semidirect
36. D₃₅	C₃×C₁₉⋊C₃	direct (N × H)
38. C₃×C₁₉	C₃×D₃₅	semidirect
39. C₁₉⋊C₃	C₃×D₃₅	direct (N × H)
44. C₅×C₇	C₂×C₃×C₁₉⋊C₃	semidirect
48. C₃×C₇	D₅×C₁₉⋊C₃	semidirect
49. C₁₉	C₃²×D₃₅	semidirect
52. C₃×C₅	D₇×C₁₉⋊C₃	semidirect
56. C₇	C₃×D₅×C₁₉⋊C₃	semidirect
59. C₅	C₃×D₇×C₁₉⋊C₃	semidirect
61. C₃	C₁₉⋊C₃×D₃₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₁₉⋊C₃	2
C₁₉⋊C₃×D₃₅	3
C₃×C₁₉×D₃₅	3
C₃×D₇×C₁₉⋊C₃	5
C₃×D₅×C₁₉⋊C₃	7
C₃²×D₃₅	19

Subgroups — C3×C19⋊C3×D35 #26046180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉⋊C₃×D₃₅ #26046180