Group #37561480 — subgroups

Subgroups — C₂×C₅×D₂₁×C₁₉⋊C₃ #37561480

Order 23940.

176 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 66 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	C₂×C₃×C₅×C₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₁×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₁₉×D₂₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₇×C₁₉⋊C₃	—	3	1	no	maximal
5	C₃×C₅×C₇×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₂₁×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₇×C₁₉⋊C₃	—	3	2	no	—
8	C₅×C₁₉×D₂₁	C₂×C₃	1	2	yes	complemented
9	C₂×C₅×C₇×C₁₉⋊C₃	—	2	1	no	—
10	C₂×C₅×C₇×C₁₉⋊C₃	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₅×D₃×C₁₉⋊C₃	—	7	1	no	maximal, Hall
13	C₂×C₅×D₇×C₁₉	—	3	1	no	Hall
14	C₂×C₃×C₇×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
15	D₂₁×C₁₉⋊C₃	C₂×C₅	1	2	yes	direct product factor
16	C₃×C₅×C₇×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
17	C₅×C₇×C₁₉⋊C₃	—	2	1	no	—
18	C₅×C₇×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
19	C₂×C₃×C₅×C₁₉⋊C₃	D₇	1	1	yes	characteristic, complemented
20	C₅×D₃×C₁₉⋊C₃	—	7	2	no	—
21	C₂×C₁₉×D₂₁	C₃×C₅	1	1	yes	characteristic, complemented
22	C₂×D₇×C₁₉⋊C₃	—	3	1	no	—
23	C₂×C₅×C₇×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
24	C₅×D₇×C₁₉	—	3	2	no	—
25	C₂×C₃×C₅×D₂₁	—	19	1	no	maximal, Hall
26	C₃×C₇×C₁₉⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×D₃×C₁₉	—	7	1	no	—
28	C₂²×C₅×C₁₉⋊C₃	—	21	1	no	—
29	C₃×C₅×C₁₉⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₇×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
31	C₁₉×D₂₁	C₂×C₃×C₅	1	2	yes	complemented
32	C₂×C₇×C₁₉⋊C₃	—	2	1	no	—
33	C₂×C₇×C₁₉⋊C₃	C₅×D₃	1	1	yes	characteristic, complemented
34	D₇×C₁₉⋊C₃	—	3	2	no	—
35	C₂×D₃×C₁₉⋊C₃	—	7	1	no	Hall
36	C₅×C₇×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃²×C₅×C₇	—	19	1	no	—
38	C₃×C₅×D₂₁	—	19	2	no	—
39	C₂×C₃×C₅×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
40	C₅×D₃×C₁₉	—	7	2	no	—
41	C₂×C₅×C₁₉⋊C₃	—	2	1	no	—
42	C₂×C₅×C₁₉⋊C₃	—	21	2	no	—
43	C₂×C₅×C₁₉⋊C₃	D₂₁	1	1	yes	characteristic, direct product factor
44	C₂×D₇×C₁₉	—	3	1	no	Hall
45	C₂×C₅×D₂₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂×C₃×C₅×D₇	—	57	1	no	—
47	C₃×C₇×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
48	C₇×C₁₉⋊C₃	—	2	1	no	—
49	C₇×C₁₉⋊C₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
50	C₂²×C₅×C₁₉	—	21	1	no	Hall
51	C₂×C₃×C₁₉⋊C₃	C₅×D₇	1	1	yes	characteristic, complemented
52	D₃×C₁₉⋊C₃	—	7	2	no	—
53	C₃²×C₅×C₇	—	19	1	no	Hall
54	C₃×C₅×C₁₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented
55	C₅×C₁₉⋊C₃	—	2	1	no	—
56	C₅×C₁₉⋊C₃	C₂×D₂₁	1	1	yes	characteristic, direct product factor
57	C₂×C₇×C₁₉	C₃×C₅×D₃	1	1	yes	characteristic, complemented
58	D₇×C₁₉	—	3	2	no	—
59	C₂×C₃×D₂₁	—	19	1	no	Hall
60	C₂×D₃×C₁₉	—	7	1	no	—
61	C₂²×C₁₉⋊C₃	—	21	1	no	—
62	C₂×C₃×C₅×C₇	—	19	1	no	—
63	C₂×C₃×C₅×C₇	—	38	1	no	—
64	C₂×C₃×C₅×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
65	C₅×D₂₁	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
66	C₃×C₅×D₇	—	57	2	no	—
67	C₂×C₅×C₁₉	—	21	2	no	—
68	C₂×C₅×C₁₉	C₃×D₂₁	1	1	yes	characteristic, complemented
69	C₂×C₃×C₅×D₃	—	133	1	no	Hall
70	C₃×C₁₉⋊C₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
71	C₂×C₅×D₇	—	3	1	no	Hall
72	C₇×C₁₉	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
73	C₂×C₃²×C₇	—	19	1	no	—
74	C₃×D₂₁	—	19	2	no	—
75	C₂×C₃×C₁₉	C₃×C₅×D₇	1	1	yes	characteristic, complemented
76	D₃×C₁₉	—	7	2	no	—
77	C₂×C₁₉⋊C₃	—	2	1	no	—
78	C₂×C₁₉⋊C₃	—	21	2	no	—
79	C₂×C₁₉⋊C₃	C₅×D₂₁	1	1	yes	characteristic, direct product factor
80	C₃×C₅×C₇	—	19	1	no	—
81	C₃×C₅×C₇	—	38	1	no	—
82	C₃×C₅×C₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
83	C₅×C₁₉	C₂×C₃×D₂₁	1	1	yes	characteristic, complemented, Hall
84	C₂×C₃²×C₅	—	19	1	no	—
85	C₃×C₅×D₃	—	133	2	no	—
86	C₂×D₂₁	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
87	C₂×C₃×D₇	—	57	1	no	—
88	C₂²×C₁₉	—	21	1	no	Hall
89	C₂×C₅×C₇	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
90	C₅×D₇	—	3	2	no	—
91	C₃²×C₇	—	19	1	no	Hall
92	C₂²×C₃×C₅	—	399	1	no	—
93	C₂×C₅×D₃	—	7	1	no	—
94	C₃×C₁₉	C₂×C₃×C₅×D₇	1	1	yes	characteristic, complemented
95	C₁₉⋊C₃	—	2	1	no	—
96	C₁₉⋊C₃	C₂×C₅×D₂₁	1	1	yes	characteristic, direct product factor
97	C₃²×C₅	—	19	1	no	Hall
98	C₂×C₃×C₇	—	19	1	no	—
99	C₂×C₃×C₇	—	38	1	no	—
100	C₂×C₃×C₇	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
101	D₂₁	C₂×C₅×C₁₉⋊C₃	1	2	yes	direct product factor
102	C₃×D₇	—	57	2	no	—
103	C₂×C₁₉	—	21	2	no	—
104	C₂×C₁₉	C₃×C₅×D₂₁	1	1	yes	characteristic, complemented
105	C₂×C₃×D₃	—	133	1	no	Hall
106	C₅×C₇	C₂×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
107	C₂×C₃×C₅	—	19	1	no	—
108	C₂×C₃×C₅	—	38	1	no	—
109	C₂×C₃×C₅	—	399	2	no	—
110	C₂×C₃×C₅	D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
111	C₅×D₃	—	7	2	no	—
112	C₂×D₇	—	3	1	no	Hall
113	C₃×C₇	—	19	1	no	—
114	C₃×C₇	—	38	1	no	—
115	C₃×C₇	C₂²×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
116	C₂²×C₅	—	21	1	no	Hall
117	C₁₉	C₂×C₃×C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
118	C₂×C₃²	—	19	1	no	—
119	C₃×D₃	—	133	2	no	—
120	C₃×C₅	—	19	1	no	—
121	C₃×C₅	—	38	1	no	—
122	C₃×C₅	C₂×D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
123	C₂×C₇	C₅×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
124	D₇	—	3	2	no	—
125	C₂²×C₃	—	399	1	no	—
126	C₂×D₃	—	7	1	no	—
127	C₂×C₅	—	21	2	no	—
128	C₂×C₅	D₂₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
129	C₃²	—	19	1	no	Sylow
130	C₇	C₂×C₅×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
131	C₂×C₃	—	19	1	no	—
132	C₂×C₃	—	38	1	no	—
133	C₂×C₃	—	399	2	no	—
134	C₂×C₃	C₅×D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
135	D₃	—	7	2	no	—
136	C₅	C₂×D₂₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
137	C₂²	—	21	1	no	Sylow
138	C₃	—	19	1	no	—
139	C₃	—	38	1	no	—
140	C₃	C₂×C₅×D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
141	C₂	—	21	2	no	—
142	C₂	C₅×D₂₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×C₅×C₇×C₁₉⋊C₃

C₂

yes

maximal, characteristic, complemented

C₅×D₂₁×C₁₉⋊C₃

C₂

yes

maximal, direct product factor

C₂×C₅×C₁₉×D₂₁

C₃

yes

maximal, characteristic, complemented

C₂×C₅×D₇×C₁₉⋊C₃

—

maximal

C₃×C₅×C₇×C₁₉⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₂×D₂₁×C₁₉⋊C₃

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×D₇×C₁₉⋊C₃

—

C₅×C₁₉×D₂₁

C₂×C₃

yes

complemented

C₂×C₅×C₇×C₁₉⋊C₃

—

C₂×C₅×C₇×C₁₉⋊C₃

D₃

yes

characteristic, complemented

C₂×C₃×C₅×C₇×C₁₉

C₂×C₃

yes

characteristic, complemented

C₂×C₅×D₃×C₁₉⋊C₃

—

maximal, Hall

C₂×C₅×D₇×C₁₉

—

Hall

C₂×C₃×C₇×C₁₉⋊C₃

C₂×C₅

yes

characteristic, complemented

D₂₁×C₁₉⋊C₃

C₂×C₅

yes

direct product factor

C₃×C₅×C₇×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₅×C₇×C₁₉⋊C₃

—

C₅×C₇×C₁₉⋊C₃

C₂×D₃

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉⋊C₃

D₇

yes

characteristic, complemented

C₅×D₃×C₁₉⋊C₃

—

C₂×C₁₉×D₂₁

C₃×C₅

yes

characteristic, complemented

C₂×D₇×C₁₉⋊C₃

—

C₂×C₅×C₇×C₁₉

C₃×D₃

yes

characteristic, complemented

C₅×D₇×C₁₉

—

C₂×C₃×C₅×D₂₁

—

maximal, Hall

C₃×C₇×C₁₉⋊C₃

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₁₉

—

C₂²×C₅×C₁₉⋊C₃

—

C₃×C₅×C₁₉⋊C₃

C₂×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₉

C₂×C₃×C₅

yes

characteristic, complemented

C₁₉×D₂₁

C₂×C₃×C₅

yes

complemented

C₂×C₇×C₁₉⋊C₃

—

C₂×C₇×C₁₉⋊C₃

C₅×D₃

yes

characteristic, complemented

D₇×C₁₉⋊C₃

—

C₂×D₃×C₁₉⋊C₃

—

Hall

C₅×C₇×C₁₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₅×C₇

—

C₃×C₅×D₂₁

—

C₂×C₃×C₅×C₁₉

C₃×D₇

yes

characteristic, complemented

C₅×D₃×C₁₉

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

D₂₁

yes

characteristic, direct product factor

C₂×D₇×C₁₉

—

Hall

C₂×C₅×D₂₁

C₁₉⋊C₃

yes

characteristic, direct product factor

C₂×C₃×C₅×D₇

—

C₃×C₇×C₁₉

C₂²×C₃×C₅

yes

characteristic, complemented

C₇×C₁₉⋊C₃

—

C₇×C₁₉⋊C₃

C₂×C₅×D₃

yes

characteristic, complemented

C₂²×C₅×C₁₉

—

Hall

C₂×C₃×C₁₉⋊C₃

C₅×D₇

yes

characteristic, complemented

D₃×C₁₉⋊C₃

—

C₃²×C₅×C₇

—

Hall

C₃×C₅×C₁₉

C₂×C₃×D₇

yes

characteristic, complemented

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

C₂×D₂₁

yes

characteristic, direct product factor

C₂×C₇×C₁₉

C₃×C₅×D₃

yes

characteristic, complemented

D₇×C₁₉

—

C₂×C₃×D₂₁

—

Hall

C₂×D₃×C₁₉

—

C₂²×C₁₉⋊C₃

—

C₂×C₃×C₅×C₇

—

C₂×C₃×C₅×C₇

—

C₂×C₃×C₅×C₇

C₂×C₁₉⋊C₃

yes

characteristic, complemented

C₅×D₂₁

C₂×C₁₉⋊C₃

yes

direct product factor

C₃×C₅×D₇

—

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃×D₂₁

yes

characteristic, complemented

C₂×C₃×C₅×D₃

—

133

Hall

C₃×C₁₉⋊C₃

C₂×C₅×D₇

yes

characteristic, complemented, Hall

C₂×C₅×D₇

—

Hall

C₇×C₁₉

C₂×C₃×C₅×D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₇

—

C₃×D₂₁

—

C₂×C₃×C₁₉

C₃×C₅×D₇

yes

characteristic, complemented

D₃×C₁₉

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

C₅×D₂₁

yes

characteristic, direct product factor

C₃×C₅×C₇

—

C₃×C₅×C₇

—

C₃×C₅×C₇

C₂²×C₁₉⋊C₃

yes

characteristic, complemented

C₅×C₁₉

C₂×C₃×D₂₁

yes

characteristic, complemented, Hall

C₂×C₃²×C₅

—

C₃×C₅×D₃

—

133

—

C₂×D₂₁

C₅×C₁₉⋊C₃

yes

characteristic, direct product factor

C₂×C₃×D₇

—

C₂²×C₁₉

—

Hall

C₂×C₅×C₇

D₃×C₁₉⋊C₃

yes

characteristic, complemented

C₅×D₇

—

C₃²×C₇

—

Hall

C₂²×C₃×C₅

—

399

—

C₂×C₅×D₃

—

C₃×C₁₉

C₂×C₃×C₅×D₇

yes

characteristic, complemented

C₁₉⋊C₃

—

C₁₉⋊C₃

C₂×C₅×D₂₁

yes

characteristic, direct product factor

C₃²×C₅

—

Hall

C₂×C₃×C₇

—

C₂×C₃×C₇

—

100

C₂×C₃×C₇

C₂×C₅×C₁₉⋊C₃

yes

characteristic, complemented

101

D₂₁

C₂×C₅×C₁₉⋊C₃

yes

direct product factor

102

C₃×D₇

—

103

C₂×C₁₉

—

104

C₂×C₁₉

C₃×C₅×D₂₁

yes

characteristic, complemented

105

C₂×C₃×D₃

—

133

Hall

106

C₅×C₇

C₂×D₃×C₁₉⋊C₃

yes

characteristic, complemented, Hall

107

C₂×C₃×C₅

—

108

C₂×C₃×C₅

—

109

C₂×C₃×C₅

—

399

—

110

C₂×C₃×C₅

D₇×C₁₉⋊C₃

yes

characteristic, complemented

111

C₅×D₃

—

112

C₂×D₇

—

Hall

113

C₃×C₇

—

114

C₃×C₇

—

115

C₃×C₇

C₂²×C₅×C₁₉⋊C₃

yes

characteristic, complemented

116

C₂²×C₅

—

Hall

117

C₁₉

C₂×C₃×C₅×D₂₁

yes

characteristic, complemented, Sylow

118

C₂×C₃²

—

119

C₃×D₃

—

133

—

120

C₃×C₅

—

121

C₃×C₅

—

122

C₃×C₅

C₂×D₇×C₁₉⋊C₃

yes

characteristic, complemented

123

C₂×C₇

C₅×D₃×C₁₉⋊C₃

yes

characteristic, complemented

124

D₇

—

125

C₂²×C₃

—

399

—

126

C₂×D₃

—

127

C₂×C₅

—

128

C₂×C₅

D₂₁×C₁₉⋊C₃

yes

characteristic, direct product factor

129

C₃²

—

Sylow

130

C₇

C₂×C₅×D₃×C₁₉⋊C₃

yes

characteristic, complemented, Sylow

131

C₂×C₃

—

132

C₂×C₃

—

133

C₂×C₃

—

399

—

134

C₂×C₃

C₅×D₇×C₁₉⋊C₃

yes

characteristic, complemented

135

D₃

—

136

C₅

C₂×D₂₁×C₁₉⋊C₃

yes

characteristic, direct product factor, Sylow

137

C₂²

—

Sylow

138

C₃

—

139

C₃

—

140

C₃

C₂×C₅×D₇×C₁₉⋊C₃

yes

characteristic, complemented

141

C₂

—

142

C₂

C₅×D₂₁×C₁₉⋊C₃

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₂₁×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₇×C₁₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₉
UCS	C₁ ◁ C₂×C₅

subgroup

G/H

center, hypercenter

C₂×C₅

D₂₁×C₁₉⋊C₃

commutator, cosocle, hypocenter

C₃×C₇×C₁₉

C₂²×C₃×C₅

Frattini

C₁

Fitting, socle

C₂×C₃×C₅×C₇×C₁₉

C₂×C₃

LCS

G ▷ C₃×C₇×C₁₉

UCS

C₁ ◁ C₂×C₅

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₇×C₁₉⋊C₃	C₂	semidirect
2. C₅×D₂₁×C₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₅×C₁₉×D₂₁	C₃	semidirect
5. C₃×C₅×C₇×C₁₉⋊C₃	C₂²	semidirect
6. C₂×D₂₁×C₁₉⋊C₃	C₅	direct (N × H)
8. C₅×C₁₉×D₂₁	C₂×C₃	semidirect
10. C₂×C₅×C₇×C₁₉⋊C₃	D₃	semidirect
11. C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	semidirect
14. C₂×C₃×C₇×C₁₉⋊C₃	C₂×C₅	semidirect
15. D₂₁×C₁₉⋊C₃	C₂×C₅	direct (N × H)
16. C₃×C₅×C₇×C₁₉	C₂²×C₃	semidirect
18. C₅×C₇×C₁₉⋊C₃	C₂×D₃	semidirect
19. C₂×C₃×C₅×C₁₉⋊C₃	D₇	semidirect
21. C₂×C₁₉×D₂₁	C₃×C₅	semidirect
23. C₂×C₅×C₇×C₁₉	C₃×D₃	semidirect
26. C₃×C₇×C₁₉⋊C₃	C₂²×C₅	semidirect
29. C₃×C₅×C₁₉⋊C₃	C₂×D₇	semidirect
30. C₂×C₃×C₇×C₁₉	C₂×C₃×C₅	semidirect
31. C₁₉×D₂₁	C₂×C₃×C₅	semidirect
33. C₂×C₇×C₁₉⋊C₃	C₅×D₃	semidirect
36. C₅×C₇×C₁₉	C₂×C₃×D₃	semidirect
39. C₂×C₃×C₅×C₁₉	C₃×D₇	semidirect
43. C₂×C₅×C₁₉⋊C₃	D₂₁	direct (N × H)
45. C₂×C₅×D₂₁	C₁₉⋊C₃	direct (N × H)
47. C₃×C₇×C₁₉	C₂²×C₃×C₅	semidirect
49. C₇×C₁₉⋊C₃	C₂×C₅×D₃	semidirect
51. C₂×C₃×C₁₉⋊C₃	C₅×D₇	semidirect
54. C₃×C₅×C₁₉	C₂×C₃×D₇	semidirect
56. C₅×C₁₉⋊C₃	C₂×D₂₁	direct (N × H)
57. C₂×C₇×C₁₉	C₃×C₅×D₃	semidirect
64. C₂×C₃×C₅×C₇	C₂×C₁₉⋊C₃	semidirect
65. C₅×D₂₁	C₂×C₁₉⋊C₃	direct (N × H)
68. C₂×C₅×C₁₉	C₃×D₂₁	semidirect
70. C₃×C₁₉⋊C₃	C₂×C₅×D₇	semidirect
72. C₇×C₁₉	C₂×C₃×C₅×D₃	semidirect
75. C₂×C₃×C₁₉	C₃×C₅×D₇	semidirect
79. C₂×C₁₉⋊C₃	C₅×D₂₁	direct (N × H)
82. C₃×C₅×C₇	C₂²×C₁₉⋊C₃	semidirect
83. C₅×C₁₉	C₂×C₃×D₂₁	semidirect
86. C₂×D₂₁	C₅×C₁₉⋊C₃	direct (N × H)
89. C₂×C₅×C₇	D₃×C₁₉⋊C₃	semidirect
94. C₃×C₁₉	C₂×C₃×C₅×D₇	semidirect
96. C₁₉⋊C₃	C₂×C₅×D₂₁	direct (N × H)
100. C₂×C₃×C₇	C₂×C₅×C₁₉⋊C₃	semidirect
101. D₂₁	C₂×C₅×C₁₉⋊C₃	direct (N × H)
104. C₂×C₁₉	C₃×C₅×D₂₁	semidirect
106. C₅×C₇	C₂×D₃×C₁₉⋊C₃	semidirect
110. C₂×C₃×C₅	D₇×C₁₉⋊C₃	semidirect
115. C₃×C₇	C₂²×C₅×C₁₉⋊C₃	semidirect
117. C₁₉	C₂×C₃×C₅×D₂₁	semidirect
122. C₃×C₅	C₂×D₇×C₁₉⋊C₃	semidirect
123. C₂×C₇	C₅×D₃×C₁₉⋊C₃	semidirect
128. C₂×C₅	D₂₁×C₁₉⋊C₃	direct (N × H)
130. C₇	C₂×C₅×D₃×C₁₉⋊C₃	semidirect
134. C₂×C₃	C₅×D₇×C₁₉⋊C₃	semidirect
136. C₅	C₂×D₂₁×C₁₉⋊C₃	direct (N × H)
140. C₃	C₂×C₅×D₇×C₁₉⋊C₃	semidirect
142. C₂	C₅×D₂₁×C₁₉⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₂×C₃×C₅×C₇×C₁₉⋊C₃

C₂

semidirect

2. C₅×D₂₁×C₁₉⋊C₃

C₂

direct (N × H)

3. C₂×C₅×C₁₉×D₂₁

C₃

semidirect

5. C₃×C₅×C₇×C₁₉⋊C₃

C₂²

semidirect

6. C₂×D₂₁×C₁₉⋊C₃

C₅

direct (N × H)

8. C₅×C₁₉×D₂₁

C₂×C₃

semidirect

10. C₂×C₅×C₇×C₁₉⋊C₃

D₃

semidirect

11. C₂×C₃×C₅×C₇×C₁₉

C₂×C₃

semidirect

14. C₂×C₃×C₇×C₁₉⋊C₃

C₂×C₅

semidirect

15. D₂₁×C₁₉⋊C₃

C₂×C₅

direct (N × H)

16. C₃×C₅×C₇×C₁₉

C₂²×C₃

semidirect

18. C₅×C₇×C₁₉⋊C₃

C₂×D₃

semidirect

19. C₂×C₃×C₅×C₁₉⋊C₃

D₇

semidirect

21. C₂×C₁₉×D₂₁

C₃×C₅

semidirect

23. C₂×C₅×C₇×C₁₉

C₃×D₃

semidirect

26. C₃×C₇×C₁₉⋊C₃

C₂²×C₅

semidirect

29. C₃×C₅×C₁₉⋊C₃

C₂×D₇

semidirect

30. C₂×C₃×C₇×C₁₉

C₂×C₃×C₅

semidirect

31. C₁₉×D₂₁

C₂×C₃×C₅

semidirect

33. C₂×C₇×C₁₉⋊C₃

C₅×D₃

semidirect

36. C₅×C₇×C₁₉

C₂×C₃×D₃

semidirect

39. C₂×C₃×C₅×C₁₉

C₃×D₇

semidirect

43. C₂×C₅×C₁₉⋊C₃

D₂₁

direct (N × H)

45. C₂×C₅×D₂₁

C₁₉⋊C₃

direct (N × H)

47. C₃×C₇×C₁₉

C₂²×C₃×C₅

semidirect

49. C₇×C₁₉⋊C₃

C₂×C₅×D₃

semidirect

51. C₂×C₃×C₁₉⋊C₃

C₅×D₇

semidirect

54. C₃×C₅×C₁₉

C₂×C₃×D₇

semidirect

56. C₅×C₁₉⋊C₃

C₂×D₂₁

direct (N × H)

57. C₂×C₇×C₁₉

C₃×C₅×D₃

semidirect

64. C₂×C₃×C₅×C₇

C₂×C₁₉⋊C₃

semidirect

65. C₅×D₂₁

C₂×C₁₉⋊C₃

direct (N × H)

68. C₂×C₅×C₁₉

C₃×D₂₁

semidirect

70. C₃×C₁₉⋊C₃

C₂×C₅×D₇

semidirect

72. C₇×C₁₉

C₂×C₃×C₅×D₃

semidirect

75. C₂×C₃×C₁₉

C₃×C₅×D₇

semidirect

79. C₂×C₁₉⋊C₃

C₅×D₂₁

direct (N × H)

82. C₃×C₅×C₇

C₂²×C₁₉⋊C₃

semidirect

83. C₅×C₁₉

C₂×C₃×D₂₁

semidirect

86. C₂×D₂₁

C₅×C₁₉⋊C₃

direct (N × H)

89. C₂×C₅×C₇

D₃×C₁₉⋊C₃

semidirect

94. C₃×C₁₉

C₂×C₃×C₅×D₇

semidirect

96. C₁₉⋊C₃

C₂×C₅×D₂₁

direct (N × H)

100. C₂×C₃×C₇

C₂×C₅×C₁₉⋊C₃

semidirect

101. D₂₁

C₂×C₅×C₁₉⋊C₃

direct (N × H)

104. C₂×C₁₉

C₃×C₅×D₂₁

semidirect

106. C₅×C₇

C₂×D₃×C₁₉⋊C₃

semidirect

110. C₂×C₃×C₅

D₇×C₁₉⋊C₃

semidirect

115. C₃×C₇

C₂²×C₅×C₁₉⋊C₃

semidirect

117. C₁₉

C₂×C₃×C₅×D₂₁

semidirect

122. C₃×C₅

C₂×D₇×C₁₉⋊C₃

semidirect

123. C₂×C₇

C₅×D₃×C₁₉⋊C₃

semidirect

128. C₂×C₅

D₂₁×C₁₉⋊C₃

direct (N × H)

130. C₇

C₂×C₅×D₃×C₁₉⋊C₃

semidirect

134. C₂×C₃

C₅×D₇×C₁₉⋊C₃

semidirect

136. C₅

C₂×D₂₁×C₁₉⋊C₃

direct (N × H)

140. C₃

C₂×C₅×D₇×C₁₉⋊C₃

semidirect

142. C₂

C₅×D₂₁×C₁₉⋊C₃

direct (N × H)

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

subgroup	index
C₂×C₃×C₅×C₇×C₁₉⋊C₃	2
C₅×D₂₁×C₁₉⋊C₃	2
C₂×C₅×C₁₉×D₂₁	3
C₂×C₅×D₇×C₁₉⋊C₃	3
C₂×D₂₁×C₁₉⋊C₃	5
C₂×C₅×D₃×C₁₉⋊C₃	7
C₂×C₃×C₅×D₂₁	19

subgroup

index

C₂×C₃×C₅×C₇×C₁₉⋊C₃

C₅×D₂₁×C₁₉⋊C₃

C₂×C₅×C₁₉×D₂₁

C₂×C₅×D₇×C₁₉⋊C₃

C₂×D₂₁×C₁₉⋊C₃

C₂×C₅×D₃×C₁₉⋊C₃

C₂×C₃×C₅×D₂₁

Subgroups — C₂×C₅×D₂₁×C₁₉⋊C₃ #37561480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C5×D21×C19⋊C3 #37561480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₂₁×C₁₉⋊C₃ #37561480