Subgroups — C₃×D₅×C₁₉×D₁₇ #34084355

Order 19380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₉×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₉×D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₉×D₁₇	—	5	1	no	maximal, Hall
7	C₁₉×D₈₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₉×D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₁₇×C₁₉	—	5	1	no	—
11	C₃×C₁₉×D₁₇	—	5	1	no	—
12	C₃×C₁₉×D₁₇	D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₁₇×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₉×D₁₇	—	5	1	no	Hall
15	C₂×C₃×D₅×C₁₉	—	17	1	no	maximal, Hall
16	C₃×D₅×D₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₁₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₇×C₁₉	—	5	1	no	—
19	C₁₉×D₁₇	—	5	1	no	—
20	C₁₉×D₁₇	C₃×D₅	1	1	yes	characteristic, direct product factor
21	C₂×C₃×C₅×C₁₉	—	17	1	no	—
22	C₃×D₅×C₁₉	—	17	1	no	—
23	C₃×D₅×C₁₉	D₁₇	1	1	yes	characteristic, direct product factor
24	C₃×D₈₅	C₂×C₁₉	1	1	yes	characteristic, complemented
25	C₃×D₅×C₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented
26	C₃×C₅×D₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented
27	C₂×D₅×C₁₉	—	17	1	no	Hall
28	D₅×D₁₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₁₇×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₁₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₁₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₃×C₁₉	—	85	1	no	Hall
33	C₂×C₃×D₁₇	—	5	1	no	Hall
34	C₂×C₅×C₁₉	—	17	1	no	—
35	D₅×C₁₉	—	17	1	no	—
36	D₅×C₁₉	C₃×D₁₇	1	1	yes	characteristic, direct product factor
37	D₈₅	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
38	C₅×D₁₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
39	D₅×C₁₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
40	C₂×C₃×C₁₉	—	5	1	no	—
41	C₂×C₃×C₁₉	—	17	1	no	—
42	C₂×C₃×C₁₉	—	85	1	no	—
43	C₂×C₃×C₁₇	—	5	1	no	—
44	C₃×D₁₇	—	5	1	no	—
45	C₃×D₁₇	D₅×C₁₉	1	1	yes	characteristic, direct product factor
46	C₅×C₁₉	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
47	C₅×C₁₇	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₁₉	—	85	1	no	Hall
49	C₂×D₁₇	—	5	1	no	Hall
50	C₂×C₃×D₅	—	17	1	no	Hall
51	C₃×C₁₉	D₅×D₁₇	1	1	yes	characteristic, direct product factor, Hall
52	C₃×C₁₇	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
53	C₂×C₁₉	—	5	1	no	—
54	C₂×C₁₉	—	17	1	no	—
55	C₂×C₁₉	—	85	1	no	—
56	C₂×C₁₇	—	5	1	no	—
57	D₁₇	—	5	1	no	—
58	D₁₇	C₃×D₅×C₁₉	1	1	yes	characteristic, direct product factor
59	C₂×C₃×C₅	—	17	1	no	—
60	C₃×D₅	—	17	1	no	—
61	C₃×D₅	C₁₉×D₁₇	1	1	yes	characteristic, direct product factor
62	C₂×D₅	—	17	1	no	Hall
63	C₁₉	C₃×D₅×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
64	C₁₇	C₂×C₃×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	C₂×C₁₉×D₁₇	1	1	yes	characteristic, complemented, Hall
66	C₂²×C₃	—	85	1	no	Hall
67	C₂×C₅	—	17	1	no	—
68	D₅	—	17	1	no	—
69	D₅	C₃×C₁₉×D₁₇	1	1	yes	characteristic, direct product factor
70	C₂×C₃	—	5	1	no	—
71	C₂×C₃	—	17	1	no	—
72	C₂×C₃	—	85	1	no	—
73	C₅	C₂×C₃×C₁₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	85	1	no	Sylow
75	C₃	D₅×C₁₉×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	5	1	no	—
77	C₂	—	17	1	no	—
78	C₂	—	85	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₅×D₁₇
commutator, cosocle, hypocenter	C₅×C₁₇	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₁₉	C₂²
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×D₈₅	C₂	semidirect
2. C₃×D₅×C₁₇×C₁₉	C₂	semidirect
3. C₃×C₅×C₁₉×D₁₇	C₂	semidirect
4. D₅×C₁₉×D₁₇	C₃	direct (N × H)
5. C₃×C₅×C₁₇×C₁₉	C₂²	semidirect
7. C₁₉×D₈₅	C₂×C₃	semidirect
8. D₅×C₁₇×C₁₉	C₂×C₃	semidirect
9. C₅×C₁₉×D₁₇	C₂×C₃	semidirect
12. C₃×C₁₉×D₁₇	D₅	direct (N × H)
13. C₅×C₁₇×C₁₉	C₂²×C₃	semidirect
16. C₃×D₅×D₁₇	C₁₉	direct (N × H)
17. C₃×C₁₇×C₁₉	C₂×D₅	semidirect
20. C₁₉×D₁₇	C₃×D₅	direct (N × H)
23. C₃×D₅×C₁₉	D₁₇	direct (N × H)
24. C₃×D₈₅	C₂×C₁₉	semidirect
25. C₃×D₅×C₁₇	C₂×C₁₉	semidirect
26. C₃×C₅×D₁₇	C₂×C₁₉	semidirect
28. D₅×D₁₇	C₃×C₁₉	direct (N × H)
29. C₁₇×C₁₉	C₂×C₃×D₅	semidirect
30. C₃×C₅×C₁₉	C₂×D₁₇	semidirect
31. C₃×C₅×C₁₇	C₂²×C₁₉	semidirect
36. D₅×C₁₉	C₃×D₁₇	direct (N × H)
37. D₈₅	C₂×C₃×C₁₉	semidirect
38. C₅×D₁₇	C₂×C₃×C₁₉	semidirect
39. D₅×C₁₇	C₂×C₃×C₁₉	semidirect
45. C₃×D₁₇	D₅×C₁₉	direct (N × H)
46. C₅×C₁₉	C₂×C₃×D₁₇	semidirect
47. C₅×C₁₇	C₂²×C₃×C₁₉	semidirect
51. C₃×C₁₉	D₅×D₁₇	direct (N × H)
52. C₃×C₁₇	C₂×D₅×C₁₉	semidirect
58. D₁₇	C₃×D₅×C₁₉	direct (N × H)
61. C₃×D₅	C₁₉×D₁₇	direct (N × H)
63. C₁₉	C₃×D₅×D₁₇	direct (N × H)
64. C₁₇	C₂×C₃×D₅×C₁₉	semidirect
65. C₃×C₅	C₂×C₁₉×D₁₇	semidirect
69. D₅	C₃×C₁₉×D₁₇	direct (N × H)
73. C₅	C₂×C₃×C₁₉×D₁₇	semidirect
75. C₃	D₅×C₁₉×D₁₇	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×C₁₉×D₈₅	2
C₃×D₅×C₁₇×C₁₉	2
C₃×C₅×C₁₉×D₁₇	2
D₅×C₁₉×D₁₇	3
C₂×C₃×C₁₉×D₁₇	5
C₂×C₃×D₅×C₁₉	17
C₃×D₅×D₁₇	19

Subgroups — C3×D5×C19×D17 #34084355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₁₉×D₁₇ #34084355