Group #37561552 — subgroups

Subgroups — C₅×D₃²×C₇×C₁₉ #37561552

Order 23940.

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₃×C₇×C₁₉	C₂	1	2	yes	maximal, complemented
2	C₅×C₇×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₇×C₁₉	—	3	2	no	maximal
4	C₃²×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃²×C₇×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₇×C₁₉	—	3	2	no	—
7	C₅×D₃×C₇×C₁₉	—	6	1	no	—
8	C₅×D₃×C₇×C₁₉	D₃	1	2	yes	direct product factor
9	C₂×C₃×C₅×C₇×C₁₉	—	3	2	no	—
10	C₅×D₃²×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₅×C₇×C₁₉	—	9	1	no	Hall
12	C₇×C₃⋊D₃×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×D₃×C₇×C₁₉	C₂×C₅	1	2	yes	complemented
14	C₃×C₅×C₇×C₁₉	—	2	1	no	—
15	C₃×C₅×C₇×C₁₉	C₂×D₃	1	2	yes	complemented
16	C₅×C₃⋊D₃×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×C₅×D₃×C₁₉	C₂×C₇	1	2	yes	complemented
18	C₂×D₃×C₇×C₁₉	—	3	2	no	—
19	C₂×C₅×C₇×C₁₉	—	3	2	no	—
20	C₂×C₅×C₇×C₁₉	—	9	1	no	—
21	C₅×D₃²×C₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₃²×C₇×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×D₃×C₁₉	—	3	2	no	—
24	C₃²×C₅×C₁₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₇×C₁₉	—	3	2	no	—
26	D₃×C₇×C₁₉	—	3	2	no	—
27	D₃×C₇×C₁₉	—	6	1	no	—
28	D₃×C₇×C₁₉	C₅×D₃	1	2	yes	direct product factor
29	D₃²×C₁₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
30	C₅×C₇×C₁₉	D₃²	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₇×C₃⋊D₃	C₂×C₁₉	1	1	yes	characteristic, complemented
32	C₃×C₅×D₃×C₇	C₂×C₁₉	1	2	yes	complemented
33	C₂×C₃×C₅×C₁₉	—	3	2	no	—
34	C₅×D₃×C₁₉	—	3	2	no	—
35	C₅×D₃×C₁₉	—	6	1	no	—
36	C₅×D₃×C₁₉	D₃×C₇	1	2	yes	direct product factor
37	C₂²×C₇×C₁₉	—	9	1	no	Hall
38	C₂×C₅×D₃×C₇	—	3	2	no	—
39	C₃×C₇×C₁₉	—	2	1	no	—
40	C₃×C₇×C₁₉	C₂×C₅×D₃	1	2	yes	complemented
41	C₂²×C₅×C₁₉	—	9	1	no	Hall
42	C₃⋊D₃×C₁₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
43	C₃×D₃×C₁₉	C₂×C₅×C₇	1	2	yes	complemented
44	C₃²×C₅×C₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
45	C₃×C₅×C₁₉	—	2	1	no	—
46	C₃×C₅×C₁₉	C₂×D₃×C₇	1	2	yes	complemented
47	C₂×C₇×C₁₉	—	3	2	no	—
48	C₂×C₇×C₁₉	—	9	1	no	—
49	D₃²×C₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
50	C₂×D₃×C₁₉	—	3	2	no	—
51	C₂×C₃×C₅×C₇	—	3	2	no	—
52	C₅×D₃×C₇	—	3	2	no	—
53	C₅×D₃×C₇	—	6	1	no	—
54	C₅×D₃×C₇	D₃×C₁₉	1	2	yes	direct product factor
55	C₂×C₅×C₁₉	—	3	2	no	—
56	C₂×C₅×C₁₉	—	9	1	no	—
57	C₅×D₃²	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
58	C₃²×C₁₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₅×C₇	—	9	1	no	Hall
60	C₇×C₁₉	C₅×D₃²	1	1	yes	characteristic, direct product factor, Hall
61	C₇×C₃⋊D₃	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
62	C₃×D₃×C₇	C₂×C₅×C₁₉	1	2	yes	complemented
63	C₂×C₃×C₁₉	—	3	2	no	—
64	D₃×C₁₉	—	3	2	no	—
65	D₃×C₁₉	—	6	1	no	—
66	D₃×C₁₉	C₅×D₃×C₇	1	2	yes	direct product factor
67	C₃×C₅×C₇	—	2	1	no	—
68	C₃×C₅×C₇	C₂×D₃×C₁₉	1	2	yes	complemented
69	C₅×C₁₉	D₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
70	C₅×C₃⋊D₃	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented
71	C₃×C₅×D₃	C₂×C₇×C₁₉	1	2	yes	complemented
72	C₂×D₃×C₇	—	3	2	no	—
73	C₂²×C₁₉	—	9	1	no	Hall
74	C₂×C₅×C₇	—	3	2	no	—
75	C₂×C₅×C₇	—	9	1	no	—
76	C₃²×C₇	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
77	C₂×C₅×D₃	—	3	2	no	—
78	C₃×C₁₉	—	2	1	no	—
79	C₃×C₁₉	C₂×C₅×D₃×C₇	1	2	yes	complemented
80	C₃²×C₅	C₂²×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
81	C₂×C₃×C₇	—	3	2	no	—
82	D₃×C₇	—	3	2	no	—
83	D₃×C₇	—	6	1	no	—
84	D₃×C₇	C₅×D₃×C₁₉	1	2	yes	direct product factor
85	C₂×C₁₉	—	3	2	no	—
86	C₂×C₁₉	—	9	1	no	—
87	D₃²	C₅×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
88	C₅×C₇	D₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
89	C₂×C₃×C₅	—	3	2	no	—
90	C₅×D₃	—	3	2	no	—
91	C₅×D₃	—	6	1	no	—
92	C₅×D₃	D₃×C₇×C₁₉	1	2	yes	direct product factor
93	C₂²×C₇	—	9	1	no	Hall
94	C₃×C₇	—	2	1	no	—
95	C₃×C₇	C₂×C₅×D₃×C₁₉	1	2	yes	complemented
96	C₂²×C₅	—	9	1	no	Hall
97	C₁₉	C₅×D₃²×C₇	1	1	yes	characteristic, direct product factor, Sylow
98	C₃⋊D₃	C₂×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented
99	C₃×D₃	C₂×C₅×C₇×C₁₉	1	2	yes	complemented
100	C₃×C₅	—	2	1	no	—
101	C₃×C₅	C₂×D₃×C₇×C₁₉	1	2	yes	complemented
102	C₂×C₇	—	3	2	no	—
103	C₂×C₇	—	9	1	no	—
104	C₂×D₃	—	3	2	no	—
105	C₂×C₅	—	3	2	no	—
106	C₂×C₅	—	9	1	no	—
107	C₃²	C₂²×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
108	C₇	C₅×D₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
109	C₂×C₃	—	3	2	no	—
110	D₃	—	3	2	no	—
111	D₃	—	6	1	no	—
112	D₃	C₅×D₃×C₇×C₁₉	1	2	yes	direct product factor
113	C₅	D₃²×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²	—	9	1	no	Sylow
115	C₃	—	2	1	no	—
116	C₃	C₂×C₅×D₃×C₇×C₁₉	1	2	yes	complemented
117	C₂	—	3	2	no	—
118	C₂	—	9	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×D₃×C₇×C₁₉

C₂

yes

maximal, complemented

C₅×C₇×C₃⋊D₃×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₅×D₃×C₇×C₁₉

—

maximal

C₃²×C₅×C₇×C₁₉

C₂²

yes

characteristic, complemented, Hall

D₃²×C₇×C₁₉

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×D₃×C₇×C₁₉

—

C₅×D₃×C₇×C₁₉

—

C₅×D₃×C₇×C₁₉

D₃

yes

direct product factor

C₂×C₃×C₅×C₇×C₁₉

—

C₅×D₃²×C₁₉

C₇

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₅×C₇×C₁₉

—

Hall

C₇×C₃⋊D₃×C₁₉

C₂×C₅

yes

characteristic, complemented

C₃×D₃×C₇×C₁₉

C₂×C₅

yes

complemented

C₃×C₅×C₇×C₁₉

—

C₃×C₅×C₇×C₁₉

C₂×D₃

yes

complemented

C₅×C₃⋊D₃×C₁₉

C₂×C₇

yes

characteristic, complemented

C₃×C₅×D₃×C₁₉

C₂×C₇

yes

complemented

C₂×D₃×C₇×C₁₉

—

C₂×C₅×C₇×C₁₉

—

C₂×C₅×C₇×C₁₉

—

C₅×D₃²×C₇

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₇×C₁₉

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₁₉

—

C₃²×C₅×C₁₉

C₂²×C₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₉

—

D₃×C₇×C₁₉

—

D₃×C₇×C₁₉

—

D₃×C₇×C₁₉

C₅×D₃

yes

direct product factor

D₃²×C₁₉

C₅×C₇

yes

characteristic, direct product factor, Hall

C₅×C₇×C₁₉

D₃²

yes

characteristic, direct product factor, Hall

C₅×C₇×C₃⋊D₃

C₂×C₁₉

yes

characteristic, complemented

C₃×C₅×D₃×C₇

C₂×C₁₉

yes

complemented

C₂×C₃×C₅×C₁₉

—

C₅×D₃×C₁₉

—

C₅×D₃×C₁₉

—

C₅×D₃×C₁₉

D₃×C₇

yes

direct product factor

C₂²×C₇×C₁₉

—

Hall

C₂×C₅×D₃×C₇

—

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

C₂×C₅×D₃

yes

complemented

C₂²×C₅×C₁₉

—

Hall

C₃⋊D₃×C₁₉

C₂×C₅×C₇

yes

characteristic, complemented

C₃×D₃×C₁₉

C₂×C₅×C₇

yes

complemented

C₃²×C₅×C₇

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×D₃×C₇

yes

complemented

C₂×C₇×C₁₉

—

C₂×C₇×C₁₉

—

D₃²×C₇

C₅×C₁₉

yes

characteristic, direct product factor, Hall

C₂×D₃×C₁₉

—

C₂×C₃×C₅×C₇

—

C₅×D₃×C₇

—

C₅×D₃×C₇

—

C₅×D₃×C₇

D₃×C₁₉

yes

direct product factor

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

—

C₅×D₃²

C₇×C₁₉

yes

characteristic, direct product factor, Hall

C₃²×C₁₉

C₂²×C₅×C₇

yes

characteristic, complemented, Hall

C₂²×C₅×C₇

—

Hall

C₇×C₁₉

C₅×D₃²

yes

characteristic, direct product factor, Hall

C₇×C₃⋊D₃

C₂×C₅×C₁₉

yes

characteristic, complemented

C₃×D₃×C₇

C₂×C₅×C₁₉

yes

complemented

C₂×C₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

C₅×D₃×C₇

yes

direct product factor

C₃×C₅×C₇

—

C₃×C₅×C₇

C₂×D₃×C₁₉

yes

complemented

C₅×C₁₉

D₃²×C₇

yes

characteristic, direct product factor, Hall

C₅×C₃⋊D₃

C₂×C₇×C₁₉

yes

characteristic, complemented

C₃×C₅×D₃

C₂×C₇×C₁₉

yes

complemented

C₂×D₃×C₇

—

C₂²×C₁₉

—

Hall

C₂×C₅×C₇

—

C₂×C₅×C₇

—

C₃²×C₇

C₂²×C₅×C₁₉

yes

characteristic, complemented, Hall

C₂×C₅×D₃

—

C₃×C₁₉

—

C₃×C₁₉

C₂×C₅×D₃×C₇

yes

complemented

C₃²×C₅

C₂²×C₇×C₁₉

yes

characteristic, complemented, Hall

C₂×C₃×C₇

—

D₃×C₇

—

D₃×C₇

—

D₃×C₇

C₅×D₃×C₁₉

yes

direct product factor

C₂×C₁₉

—

C₂×C₁₉

—

D₃²

C₅×C₇×C₁₉

yes

characteristic, direct product factor, Hall

C₅×C₇

D₃²×C₁₉

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅

—

C₅×D₃

—

C₅×D₃

—

C₅×D₃

D₃×C₇×C₁₉

yes

direct product factor

C₂²×C₇

—

Hall

C₃×C₇

—

C₃×C₇

C₂×C₅×D₃×C₁₉

yes

complemented

C₂²×C₅

—

Hall

C₁₉

C₅×D₃²×C₇

yes

characteristic, direct product factor, Sylow

C₃⋊D₃

C₂×C₅×C₇×C₁₉

yes

characteristic, complemented

C₃×D₃

C₂×C₅×C₇×C₁₉

yes

complemented

100

C₃×C₅

—

101

C₃×C₅

C₂×D₃×C₇×C₁₉

yes

complemented

102

C₂×C₇

—

103

C₂×C₇

—

104

C₂×D₃

—

105

C₂×C₅

—

106

C₂×C₅

—

107

C₃²

C₂²×C₅×C₇×C₁₉

yes

characteristic, complemented, Sylow

108

C₇

C₅×D₃²×C₁₉

yes

characteristic, direct product factor, Sylow

109

C₂×C₃

—

110

D₃

—

111

D₃

—

112

D₃

C₅×D₃×C₇×C₁₉

yes

direct product factor

113

C₅

D₃²×C₇×C₁₉

yes

characteristic, direct product factor, Sylow

114

C₂²

—

Sylow

115

C₃

—

116

C₃

C₂×C₅×D₃×C₇×C₁₉

yes

complemented

117

C₂

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₅×C₇×C₁₉	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₇×C₁₉

subgroup

G/H

center, hypercenter

C₅×C₇×C₁₉

D₃²

commutator, cosocle, hypocenter

C₃²

C₂²×C₅×C₇×C₁₉

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₁₉

C₂²

LCS

G ▷ C₃²

UCS

C₁ ◁ C₅×C₇×C₁₉

N	H ≅ G/N	type
1. C₃×C₅×D₃×C₇×C₁₉	C₂	semidirect
2. C₅×C₇×C₃⋊D₃×C₁₉	C₂	semidirect
4. C₃²×C₅×C₇×C₁₉	C₂²	semidirect
5. D₃²×C₇×C₁₉	C₅	direct (N × H)
8. C₅×D₃×C₇×C₁₉	D₃	direct (N × H)
10. C₅×D₃²×C₁₉	C₇	direct (N × H)
12. C₇×C₃⋊D₃×C₁₉	C₂×C₅	semidirect
13. C₃×D₃×C₇×C₁₉	C₂×C₅	semidirect
15. C₃×C₅×C₇×C₁₉	C₂×D₃	semidirect
16. C₅×C₃⋊D₃×C₁₉	C₂×C₇	semidirect
17. C₃×C₅×D₃×C₁₉	C₂×C₇	semidirect
21. C₅×D₃²×C₇	C₁₉	direct (N × H)
22. C₃²×C₇×C₁₉	C₂²×C₅	semidirect
24. C₃²×C₅×C₁₉	C₂²×C₇	semidirect
28. D₃×C₇×C₁₉	C₅×D₃	direct (N × H)
29. D₃²×C₁₉	C₅×C₇	direct (N × H)
30. C₅×C₇×C₁₉	D₃²	direct (N × H)
31. C₅×C₇×C₃⋊D₃	C₂×C₁₉	semidirect
32. C₃×C₅×D₃×C₇	C₂×C₁₉	semidirect
36. C₅×D₃×C₁₉	D₃×C₇	direct (N × H)
40. C₃×C₇×C₁₉	C₂×C₅×D₃	semidirect
42. C₃⋊D₃×C₁₉	C₂×C₅×C₇	semidirect
43. C₃×D₃×C₁₉	C₂×C₅×C₇	semidirect
44. C₃²×C₅×C₇	C₂²×C₁₉	semidirect
46. C₃×C₅×C₁₉	C₂×D₃×C₇	semidirect
49. D₃²×C₇	C₅×C₁₉	direct (N × H)
54. C₅×D₃×C₇	D₃×C₁₉	direct (N × H)
57. C₅×D₃²	C₇×C₁₉	direct (N × H)
58. C₃²×C₁₉	C₂²×C₅×C₇	semidirect
60. C₇×C₁₉	C₅×D₃²	direct (N × H)
61. C₇×C₃⋊D₃	C₂×C₅×C₁₉	semidirect
62. C₃×D₃×C₇	C₂×C₅×C₁₉	semidirect
66. D₃×C₁₉	C₅×D₃×C₇	direct (N × H)
68. C₃×C₅×C₇	C₂×D₃×C₁₉	semidirect
69. C₅×C₁₉	D₃²×C₇	direct (N × H)
70. C₅×C₃⋊D₃	C₂×C₇×C₁₉	semidirect
71. C₃×C₅×D₃	C₂×C₇×C₁₉	semidirect
76. C₃²×C₇	C₂²×C₅×C₁₉	semidirect
79. C₃×C₁₉	C₂×C₅×D₃×C₇	semidirect
80. C₃²×C₅	C₂²×C₇×C₁₉	semidirect
84. D₃×C₇	C₅×D₃×C₁₉	direct (N × H)
87. D₃²	C₅×C₇×C₁₉	direct (N × H)
88. C₅×C₇	D₃²×C₁₉	direct (N × H)
92. C₅×D₃	D₃×C₇×C₁₉	direct (N × H)
95. C₃×C₇	C₂×C₅×D₃×C₁₉	semidirect
97. C₁₉	C₅×D₃²×C₇	direct (N × H)
98. C₃⋊D₃	C₂×C₅×C₇×C₁₉	semidirect
99. C₃×D₃	C₂×C₅×C₇×C₁₉	semidirect
101. C₃×C₅	C₂×D₃×C₇×C₁₉	semidirect
107. C₃²	C₂²×C₅×C₇×C₁₉	semidirect
108. C₇	C₅×D₃²×C₁₉	direct (N × H)
112. D₃	C₅×D₃×C₇×C₁₉	direct (N × H)
113. C₅	D₃²×C₇×C₁₉	direct (N × H)
116. C₃	C₂×C₅×D₃×C₇×C₁₉	semidirect

H ≅ G/N

type

1. C₃×C₅×D₃×C₇×C₁₉

C₂

semidirect

2. C₅×C₇×C₃⋊D₃×C₁₉

C₂

semidirect

4. C₃²×C₅×C₇×C₁₉

C₂²

semidirect

5. D₃²×C₇×C₁₉

C₅

direct (N × H)

8. C₅×D₃×C₇×C₁₉

D₃

direct (N × H)

10. C₅×D₃²×C₁₉

C₇

direct (N × H)

12. C₇×C₃⋊D₃×C₁₉

C₂×C₅

semidirect

13. C₃×D₃×C₇×C₁₉

C₂×C₅

semidirect

15. C₃×C₅×C₇×C₁₉

C₂×D₃

semidirect

16. C₅×C₃⋊D₃×C₁₉

C₂×C₇

semidirect

17. C₃×C₅×D₃×C₁₉

C₂×C₇

semidirect

21. C₅×D₃²×C₇

C₁₉

direct (N × H)

22. C₃²×C₇×C₁₉

C₂²×C₅

semidirect

24. C₃²×C₅×C₁₉

C₂²×C₇

semidirect

28. D₃×C₇×C₁₉

C₅×D₃

direct (N × H)

29. D₃²×C₁₉

C₅×C₇

direct (N × H)

30. C₅×C₇×C₁₉

D₃²

direct (N × H)

31. C₅×C₇×C₃⋊D₃

C₂×C₁₉

semidirect

32. C₃×C₅×D₃×C₇

C₂×C₁₉

semidirect

36. C₅×D₃×C₁₉

D₃×C₇

direct (N × H)

40. C₃×C₇×C₁₉

C₂×C₅×D₃

semidirect

42. C₃⋊D₃×C₁₉

C₂×C₅×C₇

semidirect

43. C₃×D₃×C₁₉

C₂×C₅×C₇

semidirect

44. C₃²×C₅×C₇

C₂²×C₁₉

semidirect

46. C₃×C₅×C₁₉

C₂×D₃×C₇

semidirect

49. D₃²×C₇

C₅×C₁₉

direct (N × H)

54. C₅×D₃×C₇

D₃×C₁₉

direct (N × H)

57. C₅×D₃²

C₇×C₁₉

direct (N × H)

58. C₃²×C₁₉

C₂²×C₅×C₇

semidirect

60. C₇×C₁₉

C₅×D₃²

direct (N × H)

61. C₇×C₃⋊D₃

C₂×C₅×C₁₉

semidirect

62. C₃×D₃×C₇

C₂×C₅×C₁₉

semidirect

66. D₃×C₁₉

C₅×D₃×C₇

direct (N × H)

68. C₃×C₅×C₇

C₂×D₃×C₁₉

semidirect

69. C₅×C₁₉

D₃²×C₇

direct (N × H)

70. C₅×C₃⋊D₃

C₂×C₇×C₁₉

semidirect

71. C₃×C₅×D₃

C₂×C₇×C₁₉

semidirect

76. C₃²×C₇

C₂²×C₅×C₁₉

semidirect

79. C₃×C₁₉

C₂×C₅×D₃×C₇

semidirect

80. C₃²×C₅

C₂²×C₇×C₁₉

semidirect

84. D₃×C₇

C₅×D₃×C₁₉

direct (N × H)

87. D₃²

C₅×C₇×C₁₉

direct (N × H)

88. C₅×C₇

D₃²×C₁₉

direct (N × H)

92. C₅×D₃

D₃×C₇×C₁₉

direct (N × H)

95. C₃×C₇

C₂×C₅×D₃×C₁₉

semidirect

97. C₁₉

C₅×D₃²×C₇

direct (N × H)

98. C₃⋊D₃

C₂×C₅×C₇×C₁₉

semidirect

99. C₃×D₃

C₂×C₅×C₇×C₁₉

semidirect

101. C₃×C₅

C₂×D₃×C₇×C₁₉

semidirect

107. C₃²

C₂²×C₅×C₇×C₁₉

semidirect

108. C₇

C₅×D₃²×C₁₉

direct (N × H)

112. D₃

C₅×D₃×C₇×C₁₉

direct (N × H)

113. C₅

D₃²×C₇×C₁₉

direct (N × H)

116. C₃

C₂×C₅×D₃×C₇×C₁₉

semidirect

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

subgroup	index
C₃×C₅×D₃×C₇×C₁₉	2
C₅×C₇×C₃⋊D₃×C₁₉	2
C₂×C₅×D₃×C₇×C₁₉	3
D₃²×C₇×C₁₉	5
C₅×D₃²×C₁₉	7
C₅×D₃²×C₇	19

subgroup

index

C₃×C₅×D₃×C₇×C₁₉

C₅×C₇×C₃⋊D₃×C₁₉

C₂×C₅×D₃×C₇×C₁₉

D₃²×C₇×C₁₉

C₅×D₃²×C₁₉

C₅×D₃²×C₇

Subgroups — C₅×D₃²×C₇×C₁₉ #37561552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D32×C7×C19 #37561552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃²×C₇×C₁₉ #37561552