Group #37561555 — subgroups

Subgroups — C₅×D₃×C₁₉×D₂₁ #37561555

Order 23940.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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	1	yes	maximal, characteristic, complemented
2	C₃×C₅×C₁₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₁₉×D₂₁	—	3	1	no	maximal
5	C₅×D₃×D₇×C₁₉	—	3	1	no	maximal
6	C₃²×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×C₁₉×D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₉×D₂₁	—	3	1	no	—
9	C₅×C₁₉×D₂₁	—	3	1	no	—
10	C₅×C₁₉×D₂₁	—	6	1	no	—
11	C₅×C₁₉×D₂₁	D₃	1	1	yes	characteristic, direct product factor
12	C₅×D₃×C₇×C₁₉	D₃	1	1	yes	characteristic, complemented
13	C₃×C₅×D₇×C₁₉	—	3	1	no	—
14	C₂×C₃×C₅×C₇×C₁₉	—	3	1	no	—
15	C₅×D₃²×C₁₉	—	7	1	no	maximal, Hall
16	C₂×C₅×D₇×C₁₉	—	9	1	no	Hall
17	C₁₉×C₃⋊D₂₁	C₂×C₅	1	1	yes	characteristic, complemented
18	C₃×C₁₉×D₂₁	C₂×C₅	1	1	yes	characteristic, complemented
19	C₃×D₃×C₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
20	C₃×C₅×C₇×C₁₉	—	2	1	no	—
21	C₃×C₅×C₇×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
22	C₃×C₅×C₇×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
23	C₅×C₃⋊D₃×C₁₉	—	7	1	no	—
24	C₃×C₅×D₃×C₁₉	—	7	1	no	—
25	C₃×C₅×D₃×C₁₉	D₇	1	1	yes	characteristic, complemented
26	C₂×C₁₉×D₂₁	—	3	1	no	—
27	D₃×D₇×C₁₉	—	3	1	no	—
28	C₂×C₅×C₇×C₁₉	—	3	1	no	—
29	C₅×D₇×C₁₉	—	3	1	no	—
30	C₅×D₇×C₁₉	—	9	1	no	—
31	C₅×D₃×D₂₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₃²×C₇×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×D₃×C₁₉	—	21	1	no	—
34	C₂×C₅×D₃×C₁₉	—	21	1	no	—
35	C₃²×C₅×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₇×C₁₉	—	3	1	no	—
37	C₁₉×D₂₁	—	3	1	no	—
38	C₁₉×D₂₁	—	3	1	no	—
39	C₁₉×D₂₁	—	6	1	no	—
40	C₁₉×D₂₁	C₅×D₃	1	1	yes	characteristic, direct product factor
41	D₃×C₇×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
42	C₃×D₇×C₁₉	—	3	1	no	—
43	D₃²×C₁₉	—	7	1	no	Hall
44	C₅×C₇×C₁₉	D₃²	1	1	yes	characteristic, complemented, Hall
45	C₅×C₃⋊D₂₁	C₂×C₁₉	1	1	yes	characteristic, complemented
46	C₃×C₅×D₂₁	C₂×C₁₉	1	1	yes	characteristic, complemented
47	C₃×C₅×D₃×C₇	C₂×C₁₉	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅×C₁₉	—	3	1	no	—
49	C₂×C₃×C₅×C₁₉	—	21	1	no	—
50	C₅×D₃×C₁₉	—	7	1	no	—
51	C₅×D₃×C₁₉	—	21	1	no	—
52	C₅×D₃×C₁₉	—	21	1	no	—
53	C₅×D₃×C₁₉	—	42	1	no	—
54	C₅×D₃×C₁₉	D₂₁	1	1	yes	characteristic, direct product factor
55	C₂×D₇×C₁₉	—	9	1	no	Hall
56	C₂×C₅×D₂₁	—	3	1	no	—
57	C₅×D₃×D₇	—	3	1	no	—
58	C₃×C₇×C₁₉	—	2	1	no	—
59	C₃×C₇×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented
60	C₃×C₇×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented
61	C₂²×C₅×C₁₉	—	63	1	no	Hall
62	C₃⋊D₃×C₁₉	—	7	1	no	—
63	C₃×D₃×C₁₉	—	7	1	no	—
64	C₃×D₃×C₁₉	C₅×D₇	1	1	yes	characteristic, complemented
65	C₃²×C₅×C₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
66	C₃×C₅×C₁₉	—	2	1	no	—
67	C₃×C₅×C₁₉	D₃×D₇	1	1	yes	characteristic, complemented
68	C₃×C₅×C₁₉	C₂×D₂₁	1	1	yes	characteristic, complemented
69	C₂×C₇×C₁₉	—	3	1	no	—
70	D₇×C₁₉	—	3	1	no	—
71	D₇×C₁₉	—	9	1	no	—
72	D₃×D₂₁	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
73	C₂×D₃×C₁₉	—	21	1	no	—
74	C₂×D₃×C₁₉	—	21	1	no	—
75	C₂×C₃×C₅×C₇	—	3	1	no	—
76	C₅×D₂₁	—	3	1	no	—
77	C₅×D₂₁	—	3	1	no	—
78	C₅×D₂₁	—	6	1	no	—
79	C₅×D₂₁	D₃×C₁₉	1	1	yes	characteristic, direct product factor
80	C₅×D₃×C₇	D₃×C₁₉	1	1	yes	characteristic, complemented
81	C₃×C₅×D₇	—	3	1	no	—
82	C₂×C₅×C₁₉	—	3	1	no	—
83	C₂×C₅×C₁₉	—	21	1	no	—
84	C₂×C₅×C₁₉	—	63	1	no	—
85	C₅×D₃²	—	7	1	no	Hall
86	C₃²×C₁₉	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
87	C₂×C₅×D₇	—	9	1	no	Hall
88	C₇×C₁₉	C₅×D₃²	1	1	yes	characteristic, complemented, Hall
89	C₃⋊D₂₁	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
90	C₃×D₂₁	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
91	C₃×D₃×C₇	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
92	C₂×C₃×C₁₉	—	3	1	no	—
93	C₂×C₃×C₁₉	—	21	1	no	—
94	D₃×C₁₉	—	7	1	no	—
95	D₃×C₁₉	—	21	1	no	—
96	D₃×C₁₉	—	21	1	no	—
97	D₃×C₁₉	—	42	1	no	—
98	D₃×C₁₉	C₅×D₂₁	1	1	yes	characteristic, direct product factor
99	C₃×C₅×C₇	—	2	1	no	—
100	C₃×C₅×C₇	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented
101	C₃×C₅×C₇	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented
102	C₅×C₁₉	D₃×D₂₁	1	1	yes	characteristic, direct product factor, Hall
103	C₅×C₃⋊D₃	—	7	1	no	—
104	C₃×C₅×D₃	—	7	1	no	—
105	C₃×C₅×D₃	D₇×C₁₉	1	1	yes	characteristic, complemented
106	C₂×D₂₁	—	3	1	no	—
107	D₃×D₇	—	3	1	no	—
108	C₂²×C₁₉	—	63	1	no	Hall
109	C₂×C₅×C₇	—	3	1	no	—
110	C₅×D₇	—	3	1	no	—
111	C₅×D₇	—	9	1	no	—
112	C₃²×C₇	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
113	C₂×C₅×D₃	—	21	1	no	—
114	C₂×C₅×D₃	—	21	1	no	—
115	C₃×C₁₉	—	2	1	no	—
116	C₃×C₁₉	C₅×D₃×D₇	1	1	yes	characteristic, complemented
117	C₃×C₁₉	C₂×C₅×D₂₁	1	1	yes	characteristic, complemented
118	C₃²×C₅	C₂×D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
119	C₂×C₃×C₇	—	3	1	no	—
120	D₂₁	—	3	1	no	—
121	D₂₁	—	3	1	no	—
122	D₂₁	—	6	1	no	—
123	D₂₁	C₅×D₃×C₁₉	1	1	yes	characteristic, direct product factor
124	C₃×D₇	—	3	1	no	—
125	D₃×C₇	C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
126	C₂×C₁₉	—	3	1	no	—
127	C₂×C₁₉	—	21	1	no	—
128	C₂×C₁₉	—	63	1	no	—
129	D₃²	—	7	1	no	Hall
130	C₅×C₇	D₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
131	C₂×C₃×C₅	—	3	1	no	—
132	C₂×C₃×C₅	—	21	1	no	—
133	C₅×D₃	—	7	1	no	—
134	C₅×D₃	—	21	1	no	—
135	C₅×D₃	—	21	1	no	—
136	C₅×D₃	—	42	1	no	—
137	C₅×D₃	C₁₉×D₂₁	1	1	yes	characteristic, direct product factor
138	C₂×D₇	—	9	1	no	Hall
139	C₃×C₇	—	2	1	no	—
140	C₃×C₇	C₂×C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
141	C₃×C₇	C₂×C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
142	C₂²×C₅	—	63	1	no	Hall
143	C₁₉	C₅×D₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
144	C₃⋊D₃	—	7	1	no	—
145	C₃×D₃	—	7	1	no	—
146	C₃×D₃	C₅×D₇×C₁₉	1	1	yes	characteristic, complemented
147	C₃×C₅	—	2	1	no	—
148	C₃×C₅	D₃×D₇×C₁₉	1	1	yes	characteristic, complemented
149	C₃×C₅	C₂×C₁₉×D₂₁	1	1	yes	characteristic, complemented
150	C₂×C₇	—	3	1	no	—
151	D₇	—	3	1	no	—
152	D₇	—	9	1	no	—
153	C₂×D₃	—	21	1	no	—
154	C₂×D₃	—	21	1	no	—
155	C₂×C₅	—	3	1	no	—
156	C₂×C₅	—	21	1	no	—
157	C₂×C₅	—	63	1	no	—
158	C₃²	C₂×C₅×D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
159	C₇	C₅×D₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
160	C₂×C₃	—	3	1	no	—
161	C₂×C₃	—	21	1	no	—
162	D₃	—	7	1	no	—
163	D₃	—	21	1	no	—
164	D₃	—	21	1	no	—
165	D₃	—	42	1	no	—
166	D₃	C₅×C₁₉×D₂₁	1	1	yes	characteristic, direct product factor
167	C₅	D₃×C₁₉×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
168	C₂²	—	63	1	no	Sylow
169	C₃	—	2	1	no	—
170	C₃	C₅×D₃×D₇×C₁₉	1	1	yes	characteristic, complemented
171	C₃	C₂×C₅×C₁₉×D₂₁	1	1	yes	characteristic, complemented
172	C₂	—	3	1	no	—
173	C₂	—	21	1	no	—
174	C₂	—	63	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×D₃×C₇×C₁₉

C₂

yes

maximal, characteristic, complemented

C₃×C₅×C₁₉×D₂₁

C₂

yes

maximal, characteristic, complemented

C₅×C₁₉×C₃⋊D₂₁

C₂

yes

maximal, characteristic, complemented

C₂×C₅×C₁₉×D₂₁

—

maximal

C₅×D₃×D₇×C₁₉

—

maximal

C₃²×C₅×C₇×C₁₉

C₂²

yes

characteristic, complemented, Hall

D₃×C₁₉×D₂₁

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₁₉×D₂₁

—

C₅×C₁₉×D₂₁

—

C₅×C₁₉×D₂₁

—

C₅×C₁₉×D₂₁

D₃

yes

characteristic, direct product factor

C₅×D₃×C₇×C₁₉

D₃

yes

characteristic, complemented

C₃×C₅×D₇×C₁₉

—

C₂×C₃×C₅×C₇×C₁₉

—

C₅×D₃²×C₁₉

—

maximal, Hall

C₂×C₅×D₇×C₁₉

—

Hall

C₁₉×C₃⋊D₂₁

C₂×C₅

yes

characteristic, complemented

C₃×C₁₉×D₂₁

C₂×C₅

yes

characteristic, complemented

C₃×D₃×C₇×C₁₉

C₂×C₅

yes

characteristic, complemented

C₃×C₅×C₇×C₁₉

—

C₃×C₅×C₇×C₁₉

C₂×D₃

yes

characteristic, complemented

C₃×C₅×C₇×C₁₉

C₂×D₃

yes

characteristic, complemented

C₅×C₃⋊D₃×C₁₉

—

C₃×C₅×D₃×C₁₉

—

C₃×C₅×D₃×C₁₉

D₇

yes

characteristic, complemented

C₂×C₁₉×D₂₁

—

D₃×D₇×C₁₉

—

C₂×C₅×C₇×C₁₉

—

C₅×D₇×C₁₉

—

C₅×D₇×C₁₉

—

C₅×D₃×D₂₁

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₇×C₁₉

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₁₉

—

C₂×C₅×D₃×C₁₉

—

C₃²×C₅×C₁₉

C₂×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₉

—

C₁₉×D₂₁

—

C₁₉×D₂₁

—

C₁₉×D₂₁

—

C₁₉×D₂₁

C₅×D₃

yes

characteristic, direct product factor

D₃×C₇×C₁₉

C₅×D₃

yes

characteristic, complemented

C₃×D₇×C₁₉

—

D₃²×C₁₉

—

Hall

C₅×C₇×C₁₉

D₃²

yes

characteristic, complemented, Hall

C₅×C₃⋊D₂₁

C₂×C₁₉

yes

characteristic, complemented

C₃×C₅×D₂₁

C₂×C₁₉

yes

characteristic, complemented

C₃×C₅×D₃×C₇

C₂×C₁₉

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₅×D₃×C₁₉

—

C₅×D₃×C₁₉

—

C₅×D₃×C₁₉

—

C₅×D₃×C₁₉

—

C₅×D₃×C₁₉

D₂₁

yes

characteristic, direct product factor

C₂×D₇×C₁₉

—

Hall

C₂×C₅×D₂₁

—

C₅×D₃×D₇

—

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

C₂×C₅×D₃

yes

characteristic, complemented

C₃×C₇×C₁₉

C₂×C₅×D₃

yes

characteristic, complemented

C₂²×C₅×C₁₉

—

Hall

C₃⋊D₃×C₁₉

—

C₃×D₃×C₁₉

—

C₃×D₃×C₁₉

C₅×D₇

yes

characteristic, complemented

C₃²×C₅×C₇

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

D₃×D₇

yes

characteristic, complemented

C₃×C₅×C₁₉

C₂×D₂₁

yes

characteristic, complemented

C₂×C₇×C₁₉

—

D₇×C₁₉

—

D₇×C₁₉

—

D₃×D₂₁

C₅×C₁₉

yes

characteristic, direct product factor, Hall

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

—

C₂×C₃×C₅×C₇

—

C₅×D₂₁

—

C₅×D₂₁

—

C₅×D₂₁

—

C₅×D₂₁

D₃×C₁₉

yes

characteristic, direct product factor

C₅×D₃×C₇

D₃×C₁₉

yes

characteristic, complemented

C₃×C₅×D₇

—

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

—

C₅×D₃²

—

Hall

C₃²×C₁₉

C₂×C₅×D₇

yes

characteristic, complemented, Hall

C₂×C₅×D₇

—

Hall

C₇×C₁₉

C₅×D₃²

yes

characteristic, complemented, Hall

C₃⋊D₂₁

C₂×C₅×C₁₉

yes

characteristic, complemented

C₃×D₂₁

C₂×C₅×C₁₉

yes

characteristic, complemented

C₃×D₃×C₇

C₂×C₅×C₁₉

yes

characteristic, complemented

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

C₅×D₂₁

yes

characteristic, direct product factor

C₃×C₅×C₇

—

100

C₃×C₅×C₇

C₂×D₃×C₁₉

yes

characteristic, complemented

101

C₃×C₅×C₇

C₂×D₃×C₁₉

yes

characteristic, complemented

102

C₅×C₁₉

D₃×D₂₁

yes

characteristic, direct product factor, Hall

103

C₅×C₃⋊D₃

—

104

C₃×C₅×D₃

—

105

C₃×C₅×D₃

D₇×C₁₉

yes

characteristic, complemented

106

C₂×D₂₁

—

107

D₃×D₇

—

108

C₂²×C₁₉

—

Hall

109

C₂×C₅×C₇

—

110

C₅×D₇

—

111

C₅×D₇

—

112

C₃²×C₇

C₂²×C₅×C₁₉

yes

characteristic, complemented, Hall

113

C₂×C₅×D₃

—

114

C₂×C₅×D₃

—

115

C₃×C₁₉

—

116

C₃×C₁₉

C₅×D₃×D₇

yes

characteristic, complemented

117

C₃×C₁₉

C₂×C₅×D₂₁

yes

characteristic, complemented

118

C₃²×C₅

C₂×D₇×C₁₉

yes

characteristic, complemented, Hall

119

C₂×C₃×C₇

—

120

D₂₁

—

121

D₂₁

—

122

D₂₁

—

123

D₂₁

C₅×D₃×C₁₉

yes

characteristic, direct product factor

124

C₃×D₇

—

125

D₃×C₇

C₅×D₃×C₁₉

yes

characteristic, complemented

126

C₂×C₁₉

—

127

C₂×C₁₉

—

128

C₂×C₁₉

—

129

D₃²

—

Hall

130

C₅×C₇

D₃²×C₁₉

yes

characteristic, complemented, Hall

131

C₂×C₃×C₅

—

132

C₂×C₃×C₅

—

133

C₅×D₃

—

134

C₅×D₃

—

135

C₅×D₃

—

136

C₅×D₃

—

137

C₅×D₃

C₁₉×D₂₁

yes

characteristic, direct product factor

138

C₂×D₇

—

Hall

139

C₃×C₇

—

140

C₃×C₇

C₂×C₅×D₃×C₁₉

yes

characteristic, complemented

141

C₃×C₇

C₂×C₅×D₃×C₁₉

yes

characteristic, complemented

142

C₂²×C₅

—

Hall

143

C₁₉

C₅×D₃×D₂₁

yes

characteristic, direct product factor, Sylow

144

C₃⋊D₃

—

145

C₃×D₃

—

146

C₃×D₃

C₅×D₇×C₁₉

yes

characteristic, complemented

147

C₃×C₅

—

148

C₃×C₅

D₃×D₇×C₁₉

yes

characteristic, complemented

149

C₃×C₅

C₂×C₁₉×D₂₁

yes

characteristic, complemented

150

C₂×C₇

—

151

D₇

—

152

D₇

—

153

C₂×D₃

—

154

C₂×D₃

—

155

C₂×C₅

—

156

C₂×C₅

—

157

C₂×C₅

—

158

C₃²

C₂×C₅×D₇×C₁₉

yes

characteristic, complemented, Sylow

159

C₇

C₅×D₃²×C₁₉

yes

characteristic, complemented, Sylow

160

C₂×C₃

—

161

C₂×C₃

—

162

D₃

—

163

D₃

—

164

D₃

—

165

D₃

—

166

D₃

C₅×C₁₉×D₂₁

yes

characteristic, direct product factor

167

C₅

D₃×C₁₉×D₂₁

yes

characteristic, direct product factor, Sylow

168

C₂²

—

Sylow

169

C₃

—

170

C₃

C₅×D₃×D₇×C₁₉

yes

characteristic, complemented

171

C₃

C₂×C₅×C₁₉×D₂₁

yes

characteristic, complemented

172

C₂

—

173

C₂

—

174

C₂

—

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₃×D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₅×C₁₉

subgroup

G/H

center, hypercenter

C₅×C₁₉

D₃×D₂₁

commutator, cosocle, hypocenter

C₃²×C₇

C₂²×C₅×C₁₉

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₁₉

C₂²

LCS

G ▷ C₃²×C₇

UCS

C₁ ◁ C₅×C₁₉

N	H ≅ G/N	type
1. C₃×C₅×D₃×C₇×C₁₉	C₂	semidirect
2. C₃×C₅×C₁₉×D₂₁	C₂	semidirect
3. C₅×C₁₉×C₃⋊D₂₁	C₂	semidirect
6. C₃²×C₅×C₇×C₁₉	C₂²	semidirect
7. D₃×C₁₉×D₂₁	C₅	direct (N × H)
11. C₅×C₁₉×D₂₁	D₃	direct (N × H)
12. C₅×D₃×C₇×C₁₉	D₃	semidirect
17. C₁₉×C₃⋊D₂₁	C₂×C₅	semidirect
18. C₃×C₁₉×D₂₁	C₂×C₅	semidirect
19. C₃×D₃×C₇×C₁₉	C₂×C₅	semidirect
21. C₃×C₅×C₇×C₁₉	C₂×D₃	semidirect
22. C₃×C₅×C₇×C₁₉	C₂×D₃	semidirect
25. C₃×C₅×D₃×C₁₉	D₇	semidirect
31. C₅×D₃×D₂₁	C₁₉	direct (N × H)
32. C₃²×C₇×C₁₉	C₂²×C₅	semidirect
35. C₃²×C₅×C₁₉	C₂×D₇	semidirect
40. C₁₉×D₂₁	C₅×D₃	direct (N × H)
41. D₃×C₇×C₁₉	C₅×D₃	semidirect
44. C₅×C₇×C₁₉	D₃²	semidirect
45. C₅×C₃⋊D₂₁	C₂×C₁₉	semidirect
46. C₃×C₅×D₂₁	C₂×C₁₉	semidirect
47. C₃×C₅×D₃×C₇	C₂×C₁₉	semidirect
54. C₅×D₃×C₁₉	D₂₁	direct (N × H)
59. C₃×C₇×C₁₉	C₂×C₅×D₃	semidirect
60. C₃×C₇×C₁₉	C₂×C₅×D₃	semidirect
64. C₃×D₃×C₁₉	C₅×D₇	semidirect
65. C₃²×C₅×C₇	C₂²×C₁₉	semidirect
67. C₃×C₅×C₁₉	D₃×D₇	semidirect
68. C₃×C₅×C₁₉	C₂×D₂₁	semidirect
72. D₃×D₂₁	C₅×C₁₉	direct (N × H)
79. C₅×D₂₁	D₃×C₁₉	direct (N × H)
80. C₅×D₃×C₇	D₃×C₁₉	semidirect
86. C₃²×C₁₉	C₂×C₅×D₇	semidirect
88. C₇×C₁₉	C₅×D₃²	semidirect
89. C₃⋊D₂₁	C₂×C₅×C₁₉	semidirect
90. C₃×D₂₁	C₂×C₅×C₁₉	semidirect
91. C₃×D₃×C₇	C₂×C₅×C₁₉	semidirect
98. D₃×C₁₉	C₅×D₂₁	direct (N × H)
100. C₃×C₅×C₇	C₂×D₃×C₁₉	semidirect
101. C₃×C₅×C₇	C₂×D₃×C₁₉	semidirect
102. C₅×C₁₉	D₃×D₂₁	direct (N × H)
105. C₃×C₅×D₃	D₇×C₁₉	semidirect
112. C₃²×C₇	C₂²×C₅×C₁₉	semidirect
116. C₃×C₁₉	C₅×D₃×D₇	semidirect
117. C₃×C₁₉	C₂×C₅×D₂₁	semidirect
118. C₃²×C₅	C₂×D₇×C₁₉	semidirect
123. D₂₁	C₅×D₃×C₁₉	direct (N × H)
125. D₃×C₇	C₅×D₃×C₁₉	semidirect
130. C₅×C₇	D₃²×C₁₉	semidirect
137. C₅×D₃	C₁₉×D₂₁	direct (N × H)
140. C₃×C₇	C₂×C₅×D₃×C₁₉	semidirect
141. C₃×C₇	C₂×C₅×D₃×C₁₉	semidirect
143. C₁₉	C₅×D₃×D₂₁	direct (N × H)
146. C₃×D₃	C₅×D₇×C₁₉	semidirect
148. C₃×C₅	D₃×D₇×C₁₉	semidirect
149. C₃×C₅	C₂×C₁₉×D₂₁	semidirect
158. C₃²	C₂×C₅×D₇×C₁₉	semidirect
159. C₇	C₅×D₃²×C₁₉	semidirect
166. D₃	C₅×C₁₉×D₂₁	direct (N × H)
167. C₅	D₃×C₁₉×D₂₁	direct (N × H)
170. C₃	C₅×D₃×D₇×C₁₉	semidirect
171. C₃	C₂×C₅×C₁₉×D₂₁	semidirect

H ≅ G/N

type

1. C₃×C₅×D₃×C₇×C₁₉

C₂

semidirect

2. C₃×C₅×C₁₉×D₂₁

C₂

semidirect

3. C₅×C₁₉×C₃⋊D₂₁

C₂

semidirect

6. C₃²×C₅×C₇×C₁₉

C₂²

semidirect

7. D₃×C₁₉×D₂₁

C₅

direct (N × H)

11. C₅×C₁₉×D₂₁

D₃

direct (N × H)

12. C₅×D₃×C₇×C₁₉

D₃

semidirect

17. C₁₉×C₃⋊D₂₁

C₂×C₅

semidirect

18. C₃×C₁₉×D₂₁

C₂×C₅

semidirect

19. C₃×D₃×C₇×C₁₉

C₂×C₅

semidirect

21. C₃×C₅×C₇×C₁₉

C₂×D₃

semidirect

22. C₃×C₅×C₇×C₁₉

C₂×D₃

semidirect

25. C₃×C₅×D₃×C₁₉

D₇

semidirect

31. C₅×D₃×D₂₁

C₁₉

direct (N × H)

32. C₃²×C₇×C₁₉

C₂²×C₅

semidirect

35. C₃²×C₅×C₁₉

C₂×D₇

semidirect

40. C₁₉×D₂₁

C₅×D₃

direct (N × H)

41. D₃×C₇×C₁₉

C₅×D₃

semidirect

44. C₅×C₇×C₁₉

D₃²

semidirect

45. C₅×C₃⋊D₂₁

C₂×C₁₉

semidirect

46. C₃×C₅×D₂₁

C₂×C₁₉

semidirect

47. C₃×C₅×D₃×C₇

C₂×C₁₉

semidirect

54. C₅×D₃×C₁₉

D₂₁

direct (N × H)

59. C₃×C₇×C₁₉

C₂×C₅×D₃

semidirect

60. C₃×C₇×C₁₉

C₂×C₅×D₃

semidirect

64. C₃×D₃×C₁₉

C₅×D₇

semidirect

65. C₃²×C₅×C₇

C₂²×C₁₉

semidirect

67. C₃×C₅×C₁₉

D₃×D₇

semidirect

68. C₃×C₅×C₁₉

C₂×D₂₁

semidirect

72. D₃×D₂₁

C₅×C₁₉

direct (N × H)

79. C₅×D₂₁

D₃×C₁₉

direct (N × H)

80. C₅×D₃×C₇

D₃×C₁₉

semidirect

86. C₃²×C₁₉

C₂×C₅×D₇

semidirect

88. C₇×C₁₉

C₅×D₃²

semidirect

89. C₃⋊D₂₁

C₂×C₅×C₁₉

semidirect

90. C₃×D₂₁

C₂×C₅×C₁₉

semidirect

91. C₃×D₃×C₇

C₂×C₅×C₁₉

semidirect

98. D₃×C₁₉

C₅×D₂₁

direct (N × H)

100. C₃×C₅×C₇

C₂×D₃×C₁₉

semidirect

101. C₃×C₅×C₇

C₂×D₃×C₁₉

semidirect

102. C₅×C₁₉

D₃×D₂₁

direct (N × H)

105. C₃×C₅×D₃

D₇×C₁₉

semidirect

112. C₃²×C₇

C₂²×C₅×C₁₉

semidirect

116. C₃×C₁₉

C₅×D₃×D₇

semidirect

117. C₃×C₁₉

C₂×C₅×D₂₁

semidirect

118. C₃²×C₅

C₂×D₇×C₁₉

semidirect

123. D₂₁

C₅×D₃×C₁₉

direct (N × H)

125. D₃×C₇

C₅×D₃×C₁₉

semidirect

130. C₅×C₇

D₃²×C₁₉

semidirect

137. C₅×D₃

C₁₉×D₂₁

direct (N × H)

140. C₃×C₇

C₂×C₅×D₃×C₁₉

semidirect

141. C₃×C₇

C₂×C₅×D₃×C₁₉

semidirect

143. C₁₉

C₅×D₃×D₂₁

direct (N × H)

146. C₃×D₃

C₅×D₇×C₁₉

semidirect

148. C₃×C₅

D₃×D₇×C₁₉

semidirect

149. C₃×C₅

C₂×C₁₉×D₂₁

semidirect

158. C₃²

C₂×C₅×D₇×C₁₉

semidirect

159. C₇

C₅×D₃²×C₁₉

semidirect

166. D₃

C₅×C₁₉×D₂₁

direct (N × H)

167. C₅

D₃×C₁₉×D₂₁

direct (N × H)

170. C₃

C₅×D₃×D₇×C₁₉

semidirect

171. C₃

C₂×C₅×C₁₉×D₂₁

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
C₃×C₅×C₁₉×D₂₁	2
C₅×C₁₉×C₃⋊D₂₁	2
C₂×C₅×C₁₉×D₂₁	3
C₅×D₃×D₇×C₁₉	3
D₃×C₁₉×D₂₁	5
C₅×D₃²×C₁₉	7
C₅×D₃×D₂₁	19

subgroup

index

C₃×C₅×D₃×C₇×C₁₉

C₃×C₅×C₁₉×D₂₁

C₅×C₁₉×C₃⋊D₂₁

C₂×C₅×C₁₉×D₂₁

C₅×D₃×D₇×C₁₉

D₃×C₁₉×D₂₁

C₅×D₃²×C₁₉

C₅×D₃×D₂₁

Subgroups — C₅×D₃×C₁₉×D₂₁ #37561555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D3×C19×D21 #37561555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₁₉×D₂₁ #37561555