Group #37561562 — subgroups

Subgroups — D₃×C₇×C₁₉×D₁₅ #37561562

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×C₇×C₁₉×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₉×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×C₁₉×D₁₅	—	3	1	no	maximal
5	D₃×C₇×D₅×C₁₉	—	3	1	no	maximal
6	C₃²×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃²×C₇×C₁₉	—	5	1	no	maximal, Hall
8	C₇×C₁₉×D₁₅	—	3	1	no	—
9	C₇×C₁₉×D₁₅	—	3	1	no	—
10	C₇×C₁₉×D₁₅	—	6	1	no	—
11	C₇×C₁₉×D₁₅	D₃	1	1	yes	characteristic, direct product factor
12	C₅×D₃×C₇×C₁₉	D₃	1	1	yes	characteristic, complemented
13	C₃×C₇×D₅×C₁₉	—	3	1	no	—
14	C₂×C₃×C₅×C₇×C₁₉	—	3	1	no	—
15	D₃×C₁₉×D₁₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₇×D₅×C₁₉	—	9	1	no	Hall
17	C₇×C₃⋊D₃×C₁₉	—	5	1	no	—
18	C₃×D₃×C₇×C₁₉	—	5	1	no	—
19	C₃×D₃×C₇×C₁₉	D₅	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	C₁₉×C₃⋊D₁₅	C₂×C₇	1	1	yes	characteristic, complemented
24	C₃×C₁₉×D₁₅	C₂×C₇	1	1	yes	characteristic, complemented
25	C₃×C₅×D₃×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
26	C₂×D₃×C₇×C₁₉	—	15	1	no	—
27	C₂×D₃×C₇×C₁₉	—	15	1	no	—
28	C₂×C₅×C₇×C₁₉	—	3	1	no	—
29	C₇×D₅×C₁₉	—	3	1	no	—
30	C₇×D₅×C₁₉	—	9	1	no	—
31	D₃×C₇×D₁₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₃²×C₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₉×D₁₅	—	3	1	no	—
34	D₃×D₅×C₁₉	—	3	1	no	—
35	C₃²×C₅×C₁₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₇×C₁₉	—	3	1	no	—
37	C₂×C₃×C₇×C₁₉	—	15	1	no	—
38	D₃×C₇×C₁₉	—	5	1	no	—
39	D₃×C₇×C₁₉	—	15	1	no	—
40	D₃×C₇×C₁₉	—	15	1	no	—
41	D₃×C₇×C₁₉	—	30	1	no	—
42	D₃×C₇×C₁₉	D₁₅	1	1	yes	characteristic, direct product factor
43	D₃²×C₁₉	—	5	1	no	Hall
44	C₅×C₇×C₁₉	D₃²	1	1	yes	characteristic, complemented, Hall
45	C₇×C₃⋊D₁₅	C₂×C₁₉	1	1	yes	characteristic, complemented
46	C₃×C₇×D₁₅	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	C₁₉×D₁₅	—	3	1	no	—
50	C₁₉×D₁₅	—	3	1	no	—
51	C₁₉×D₁₅	—	6	1	no	—
52	C₁₉×D₁₅	D₃×C₇	1	1	yes	characteristic, direct product factor
53	C₅×D₃×C₁₉	D₃×C₇	1	1	yes	characteristic, complemented
54	C₃×D₅×C₁₉	—	3	1	no	—
55	C₂²×C₇×C₁₉	—	45	1	no	Hall
56	C₂×C₇×D₁₅	—	3	1	no	—
57	D₃×C₇×D₅	—	3	1	no	—
58	C₃×C₇×C₁₉	—	2	1	no	—
59	C₃×C₇×C₁₉	D₃×D₅	1	1	yes	characteristic, complemented
60	C₃×C₇×C₁₉	C₂×D₁₅	1	1	yes	characteristic, complemented
61	C₂×D₅×C₁₉	—	9	1	no	Hall
62	C₃⋊D₃×C₁₉	—	5	1	no	—
63	C₃×D₃×C₁₉	—	5	1	no	—
64	C₃×D₃×C₁₉	C₇×D₅	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	C₂×D₃×C₇	1	1	yes	characteristic, complemented
68	C₃×C₅×C₁₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented
69	C₂×C₇×C₁₉	—	3	1	no	—
70	C₂×C₇×C₁₉	—	15	1	no	—
71	C₂×C₇×C₁₉	—	45	1	no	—
72	D₃²×C₇	—	5	1	no	Hall
73	C₂×D₃×C₁₉	—	15	1	no	—
74	C₂×D₃×C₁₉	—	15	1	no	—
75	C₂×C₃×C₅×C₇	—	3	1	no	—
76	C₇×D₁₅	—	3	1	no	—
77	C₇×D₁₅	—	3	1	no	—
78	C₇×D₁₅	—	6	1	no	—
79	C₇×D₁₅	D₃×C₁₉	1	1	yes	characteristic, direct product factor
80	C₅×D₃×C₇	D₃×C₁₉	1	1	yes	characteristic, complemented
81	C₃×C₇×D₅	—	3	1	no	—
82	C₂×C₅×C₁₉	—	3	1	no	—
83	D₅×C₁₉	—	3	1	no	—
84	D₅×C₁₉	—	9	1	no	—
85	D₃×D₁₅	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
86	C₃²×C₁₉	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
87	C₂×C₇×D₅	—	9	1	no	Hall
88	C₇×C₁₉	D₃×D₁₅	1	1	yes	characteristic, direct product factor, Hall
89	C₇×C₃⋊D₃	—	5	1	no	—
90	C₃×D₃×C₇	—	5	1	no	—
91	C₃×D₃×C₇	D₅×C₁₉	1	1	yes	characteristic, complemented
92	C₂×C₃×C₁₉	—	3	1	no	—
93	C₂×C₃×C₁₉	—	15	1	no	—
94	D₃×C₁₉	—	5	1	no	—
95	D₃×C₁₉	—	15	1	no	—
96	D₃×C₁₉	—	15	1	no	—
97	D₃×C₁₉	—	30	1	no	—
98	D₃×C₁₉	C₇×D₁₅	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	D₃²×C₇	1	1	yes	characteristic, complemented, Hall
103	C₃⋊D₁₅	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented
104	C₃×D₁₅	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented
105	C₃×C₅×D₃	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented
106	C₂×D₃×C₇	—	15	1	no	—
107	C₂×D₃×C₇	—	15	1	no	—
108	C₂²×C₁₉	—	45	1	no	Hall
109	C₂×C₅×C₇	—	3	1	no	—
110	C₇×D₅	—	3	1	no	—
111	C₇×D₅	—	9	1	no	—
112	C₃²×C₇	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
113	C₂×D₁₅	—	3	1	no	—
114	D₃×D₅	—	3	1	no	—
115	C₃×C₁₉	—	2	1	no	—
116	C₃×C₁₉	D₃×C₇×D₅	1	1	yes	characteristic, complemented
117	C₃×C₁₉	C₂×C₇×D₁₅	1	1	yes	characteristic, complemented
118	C₃²×C₅	C₂²×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
119	C₂×C₃×C₇	—	3	1	no	—
120	C₂×C₃×C₇	—	15	1	no	—
121	D₃×C₇	—	5	1	no	—
122	D₃×C₇	—	15	1	no	—
123	D₃×C₇	—	15	1	no	—
124	D₃×C₇	—	30	1	no	—
125	D₃×C₇	C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
126	C₂×C₁₉	—	3	1	no	—
127	C₂×C₁₉	—	15	1	no	—
128	C₂×C₁₉	—	45	1	no	—
129	D₃²	—	5	1	no	Hall
130	C₅×C₇	D₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
131	C₂×C₃×C₅	—	3	1	no	—
132	D₁₅	—	3	1	no	—
133	D₁₅	—	3	1	no	—
134	D₁₅	—	6	1	no	—
135	D₁₅	D₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor
136	C₃×D₅	—	3	1	no	—
137	C₅×D₃	D₃×C₇×C₁₉	1	1	yes	characteristic, complemented
138	C₂²×C₇	—	45	1	no	Hall
139	C₃×C₇	—	2	1	no	—
140	C₃×C₇	D₃×D₅×C₁₉	1	1	yes	characteristic, complemented
141	C₃×C₇	C₂×C₁₉×D₁₅	1	1	yes	characteristic, complemented
142	C₂×D₅	—	9	1	no	Hall
143	C₁₉	D₃×C₇×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
144	C₃⋊D₃	—	5	1	no	—
145	C₃×D₃	—	5	1	no	—
146	C₃×D₃	C₇×D₅×C₁₉	1	1	yes	characteristic, complemented
147	C₃×C₅	—	2	1	no	—
148	C₃×C₅	C₂×D₃×C₇×C₁₉	1	1	yes	characteristic, complemented
149	C₃×C₅	C₂×D₃×C₇×C₁₉	1	1	yes	characteristic, complemented
150	C₂×C₇	—	3	1	no	—
151	C₂×C₇	—	15	1	no	—
152	C₂×C₇	—	45	1	no	—
153	C₂×D₃	—	15	1	no	—
154	C₂×D₃	—	15	1	no	—
155	C₂×C₅	—	3	1	no	—
156	D₅	—	3	1	no	—
157	D₅	—	9	1	no	—
158	C₃²	C₂×C₇×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
159	C₇	D₃×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
160	C₂×C₃	—	3	1	no	—
161	C₂×C₃	—	15	1	no	—
162	D₃	—	5	1	no	—
163	D₃	—	15	1	no	—
164	D₃	—	15	1	no	—
165	D₃	—	30	1	no	—
166	D₃	C₇×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
167	C₅	D₃²×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
168	C₂²	—	45	1	no	Sylow
169	C₃	—	2	1	no	—
170	C₃	D₃×C₇×D₅×C₁₉	1	1	yes	characteristic, complemented
171	C₃	C₂×C₇×C₁₉×D₁₅	1	1	yes	characteristic, complemented
172	C₂	—	3	1	no	—
173	C₂	—	15	1	no	—
174	C₂	—	45	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×D₃×C₇×C₁₉

C₂

yes

maximal, characteristic, complemented

C₃×C₇×C₁₉×D₁₅

C₂

yes

maximal, characteristic, complemented

C₇×C₁₉×C₃⋊D₁₅

C₂

yes

maximal, characteristic, complemented

C₂×C₇×C₁₉×D₁₅

—

maximal

D₃×C₇×D₅×C₁₉

—

maximal

C₃²×C₅×C₇×C₁₉

C₂²

yes

characteristic, complemented, Hall

D₃²×C₇×C₁₉

—

maximal, Hall

C₇×C₁₉×D₁₅

—

C₇×C₁₉×D₁₅

—

C₇×C₁₉×D₁₅

—

C₇×C₁₉×D₁₅

D₃

yes

characteristic, direct product factor

C₅×D₃×C₇×C₁₉

D₃

yes

characteristic, complemented

C₃×C₇×D₅×C₁₉

—

C₂×C₃×C₅×C₇×C₁₉

—

D₃×C₁₉×D₁₅

C₇

yes

maximal, characteristic, direct product factor, Hall

C₂×C₇×D₅×C₁₉

—

Hall

C₇×C₃⋊D₃×C₁₉

—

C₃×D₃×C₇×C₁₉

—

C₃×D₃×C₇×C₁₉

D₅

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

C₁₉×C₃⋊D₁₅

C₂×C₇

yes

characteristic, complemented

C₃×C₁₉×D₁₅

C₂×C₇

yes

characteristic, complemented

C₃×C₅×D₃×C₁₉

C₂×C₇

yes

characteristic, complemented

C₂×D₃×C₇×C₁₉

—

C₂×D₃×C₇×C₁₉

—

C₂×C₅×C₇×C₁₉

—

C₇×D₅×C₁₉

—

C₇×D₅×C₁₉

—

D₃×C₇×D₁₅

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₇×C₁₉

C₂×D₅

yes

characteristic, complemented, Hall

C₂×C₁₉×D₁₅

—

D₃×D₅×C₁₉

—

C₃²×C₅×C₁₉

C₂²×C₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

—

D₃×C₇×C₁₉

—

D₃×C₇×C₁₉

—

D₃×C₇×C₁₉

—

D₃×C₇×C₁₉

—

D₃×C₇×C₁₉

D₁₅

yes

characteristic, direct product factor

D₃²×C₁₉

—

Hall

C₅×C₇×C₁₉

D₃²

yes

characteristic, complemented, Hall

C₇×C₃⋊D₁₅

C₂×C₁₉

yes

characteristic, complemented

C₃×C₇×D₁₅

C₂×C₁₉

yes

characteristic, complemented

C₃×C₅×D₃×C₇

C₂×C₁₉

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉

—

C₁₉×D₁₅

—

C₁₉×D₁₅

—

C₁₉×D₁₅

—

C₁₉×D₁₅

D₃×C₇

yes

characteristic, direct product factor

C₅×D₃×C₁₉

D₃×C₇

yes

characteristic, complemented

C₃×D₅×C₁₉

—

C₂²×C₇×C₁₉

—

Hall

C₂×C₇×D₁₅

—

D₃×C₇×D₅

—

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

D₃×D₅

yes

characteristic, complemented

C₃×C₇×C₁₉

C₂×D₁₅

yes

characteristic, complemented

C₂×D₅×C₁₉

—

Hall

C₃⋊D₃×C₁₉

—

C₃×D₃×C₁₉

—

C₃×D₃×C₁₉

C₇×D₅

yes

characteristic, complemented

C₃²×C₅×C₇

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×D₃×C₇

yes

characteristic, complemented

C₃×C₅×C₁₉

C₂×D₃×C₇

yes

characteristic, complemented

C₂×C₇×C₁₉

—

C₂×C₇×C₁₉

—

C₂×C₇×C₁₉

—

D₃²×C₇

—

Hall

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

—

C₂×C₃×C₅×C₇

—

C₇×D₁₅

—

C₇×D₁₅

—

C₇×D₁₅

—

C₇×D₁₅

D₃×C₁₉

yes

characteristic, direct product factor

C₅×D₃×C₇

D₃×C₁₉

yes

characteristic, complemented

C₃×C₇×D₅

—

C₂×C₅×C₁₉

—

D₅×C₁₉

—

D₅×C₁₉

—

D₃×D₁₅

C₇×C₁₉

yes

characteristic, direct product factor, Hall

C₃²×C₁₉

C₂×C₇×D₅

yes

characteristic, complemented, Hall

C₂×C₇×D₅

—

Hall

C₇×C₁₉

D₃×D₁₅

yes

characteristic, direct product factor, Hall

C₇×C₃⋊D₃

—

C₃×D₃×C₇

—

C₃×D₃×C₇

D₅×C₁₉

yes

characteristic, complemented

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

C₇×D₁₅

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

D₃²×C₇

yes

characteristic, complemented, Hall

103

C₃⋊D₁₅

C₂×C₇×C₁₉

yes

characteristic, complemented

104

C₃×D₁₅

C₂×C₇×C₁₉

yes

characteristic, complemented

105

C₃×C₅×D₃

C₂×C₇×C₁₉

yes

characteristic, complemented

106

C₂×D₃×C₇

—

107

C₂×D₃×C₇

—

108

C₂²×C₁₉

—

Hall

109

C₂×C₅×C₇

—

110

C₇×D₅

—

111

C₇×D₅

—

112

C₃²×C₇

C₂×D₅×C₁₉

yes

characteristic, complemented, Hall

113

C₂×D₁₅

—

114

D₃×D₅

—

115

C₃×C₁₉

—

116

C₃×C₁₉

D₃×C₇×D₅

yes

characteristic, complemented

117

C₃×C₁₉

C₂×C₇×D₁₅

yes

characteristic, complemented

118

C₃²×C₅

C₂²×C₇×C₁₉

yes

characteristic, complemented, Hall

119

C₂×C₃×C₇

—

120

C₂×C₃×C₇

—

121

D₃×C₇

—

122

D₃×C₇

—

123

D₃×C₇

—

124

D₃×C₇

—

125

D₃×C₇

C₁₉×D₁₅

yes

characteristic, direct product factor

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

D₁₅

—

133

D₁₅

—

134

D₁₅

—

135

D₁₅

D₃×C₇×C₁₉

yes

characteristic, direct product factor

136

C₃×D₅

—

137

C₅×D₃

D₃×C₇×C₁₉

yes

characteristic, complemented

138

C₂²×C₇

—

Hall

139

C₃×C₇

—

140

C₃×C₇

D₃×D₅×C₁₉

yes

characteristic, complemented

141

C₃×C₇

C₂×C₁₉×D₁₅

yes

characteristic, complemented

142

C₂×D₅

—

Hall

143

C₁₉

D₃×C₇×D₁₅

yes

characteristic, direct product factor, Sylow

144

C₃⋊D₃

—

145

C₃×D₃

—

146

C₃×D₃

C₇×D₅×C₁₉

yes

characteristic, complemented

147

C₃×C₅

—

148

C₃×C₅

C₂×D₃×C₇×C₁₉

yes

characteristic, complemented

149

C₃×C₅

C₂×D₃×C₇×C₁₉

yes

characteristic, complemented

150

C₂×C₇

—

151

C₂×C₇

—

152

C₂×C₇

—

153

C₂×D₃

—

154

C₂×D₃

—

155

C₂×C₅

—

156

D₅

—

157

D₅

—

158

C₃²

C₂×C₇×D₅×C₁₉

yes

characteristic, complemented, Sylow

159

C₇

D₃×C₁₉×D₁₅

yes

characteristic, direct product factor, Sylow

160

C₂×C₃

—

161

C₂×C₃

—

162

D₃

—

163

D₃

—

164

D₃

—

165

D₃

—

166

D₃

C₇×C₁₉×D₁₅

yes

characteristic, direct product factor

167

C₅

D₃²×C₇×C₁₉

yes

characteristic, complemented, Sylow

168

C₂²

—

Sylow

169

C₃

—

170

C₃

D₃×C₇×D₅×C₁₉

yes

characteristic, complemented

171

C₃

C₂×C₇×C₁₉×D₁₅

yes

characteristic, complemented

172

C₂

—

173

C₂

—

174

C₂

—

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₃×D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇×C₁₉

subgroup

G/H

center, hypercenter

C₇×C₁₉

D₃×D₁₅

commutator, cosocle, hypocenter

C₃²×C₅

C₂²×C₇×C₁₉

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₁₉

C₂²

LCS

G ▷ C₃²×C₅

UCS

C₁ ◁ C₇×C₁₉

N	H ≅ G/N	type
1. C₃×C₅×D₃×C₇×C₁₉	C₂	semidirect
2. C₃×C₇×C₁₉×D₁₅	C₂	semidirect
3. C₇×C₁₉×C₃⋊D₁₅	C₂	semidirect
6. C₃²×C₅×C₇×C₁₉	C₂²	semidirect
11. C₇×C₁₉×D₁₅	D₃	direct (N × H)
12. C₅×D₃×C₇×C₁₉	D₃	semidirect
15. D₃×C₁₉×D₁₅	C₇	direct (N × H)
19. C₃×D₃×C₇×C₁₉	D₅	semidirect
21. C₃×C₅×C₇×C₁₉	C₂×D₃	semidirect
22. C₃×C₅×C₇×C₁₉	C₂×D₃	semidirect
23. C₁₉×C₃⋊D₁₅	C₂×C₇	semidirect
24. C₃×C₁₉×D₁₅	C₂×C₇	semidirect
25. C₃×C₅×D₃×C₁₉	C₂×C₇	semidirect
31. D₃×C₇×D₁₅	C₁₉	direct (N × H)
32. C₃²×C₇×C₁₉	C₂×D₅	semidirect
35. C₃²×C₅×C₁₉	C₂²×C₇	semidirect
42. D₃×C₇×C₁₉	D₁₅	direct (N × H)
44. C₅×C₇×C₁₉	D₃²	semidirect
45. C₇×C₃⋊D₁₅	C₂×C₁₉	semidirect
46. C₃×C₇×D₁₅	C₂×C₁₉	semidirect
47. C₃×C₅×D₃×C₇	C₂×C₁₉	semidirect
52. C₁₉×D₁₅	D₃×C₇	direct (N × H)
53. C₅×D₃×C₁₉	D₃×C₇	semidirect
59. C₃×C₇×C₁₉	D₃×D₅	semidirect
60. C₃×C₇×C₁₉	C₂×D₁₅	semidirect
64. C₃×D₃×C₁₉	C₇×D₅	semidirect
65. C₃²×C₅×C₇	C₂²×C₁₉	semidirect
67. C₃×C₅×C₁₉	C₂×D₃×C₇	semidirect
68. C₃×C₅×C₁₉	C₂×D₃×C₇	semidirect
79. C₇×D₁₅	D₃×C₁₉	direct (N × H)
80. C₅×D₃×C₇	D₃×C₁₉	semidirect
85. D₃×D₁₅	C₇×C₁₉	direct (N × H)
86. C₃²×C₁₉	C₂×C₇×D₅	semidirect
88. C₇×C₁₉	D₃×D₁₅	direct (N × H)
91. C₃×D₃×C₇	D₅×C₁₉	semidirect
98. D₃×C₁₉	C₇×D₁₅	direct (N × H)
100. C₃×C₅×C₇	C₂×D₃×C₁₉	semidirect
101. C₃×C₅×C₇	C₂×D₃×C₁₉	semidirect
102. C₅×C₁₉	D₃²×C₇	semidirect
103. C₃⋊D₁₅	C₂×C₇×C₁₉	semidirect
104. C₃×D₁₅	C₂×C₇×C₁₉	semidirect
105. C₃×C₅×D₃	C₂×C₇×C₁₉	semidirect
112. C₃²×C₇	C₂×D₅×C₁₉	semidirect
116. C₃×C₁₉	D₃×C₇×D₅	semidirect
117. C₃×C₁₉	C₂×C₇×D₁₅	semidirect
118. C₃²×C₅	C₂²×C₇×C₁₉	semidirect
125. D₃×C₇	C₁₉×D₁₅	direct (N × H)
130. C₅×C₇	D₃²×C₁₉	semidirect
135. D₁₅	D₃×C₇×C₁₉	direct (N × H)
137. C₅×D₃	D₃×C₇×C₁₉	semidirect
140. C₃×C₇	D₃×D₅×C₁₉	semidirect
141. C₃×C₇	C₂×C₁₉×D₁₅	semidirect
143. C₁₉	D₃×C₇×D₁₅	direct (N × H)
146. C₃×D₃	C₇×D₅×C₁₉	semidirect
148. C₃×C₅	C₂×D₃×C₇×C₁₉	semidirect
149. C₃×C₅	C₂×D₃×C₇×C₁₉	semidirect
158. C₃²	C₂×C₇×D₅×C₁₉	semidirect
159. C₇	D₃×C₁₉×D₁₅	direct (N × H)
166. D₃	C₇×C₁₉×D₁₅	direct (N × H)
167. C₅	D₃²×C₇×C₁₉	semidirect
170. C₃	D₃×C₇×D₅×C₁₉	semidirect
171. C₃	C₂×C₇×C₁₉×D₁₅	semidirect

H ≅ G/N

type

1. C₃×C₅×D₃×C₇×C₁₉

C₂

semidirect

2. C₃×C₇×C₁₉×D₁₅

C₂

semidirect

3. C₇×C₁₉×C₃⋊D₁₅

C₂

semidirect

6. C₃²×C₅×C₇×C₁₉

C₂²

semidirect

11. C₇×C₁₉×D₁₅

D₃

direct (N × H)

12. C₅×D₃×C₇×C₁₉

D₃

semidirect

15. D₃×C₁₉×D₁₅

C₇

direct (N × H)

19. C₃×D₃×C₇×C₁₉

D₅

semidirect

21. C₃×C₅×C₇×C₁₉

C₂×D₃

semidirect

22. C₃×C₅×C₇×C₁₉

C₂×D₃

semidirect

23. C₁₉×C₃⋊D₁₅

C₂×C₇

semidirect

24. C₃×C₁₉×D₁₅

C₂×C₇

semidirect

25. C₃×C₅×D₃×C₁₉

C₂×C₇

semidirect

31. D₃×C₇×D₁₅

C₁₉

direct (N × H)

32. C₃²×C₇×C₁₉

C₂×D₅

semidirect

35. C₃²×C₅×C₁₉

C₂²×C₇

semidirect

42. D₃×C₇×C₁₉

D₁₅

direct (N × H)

44. C₅×C₇×C₁₉

D₃²

semidirect

45. C₇×C₃⋊D₁₅

C₂×C₁₉

semidirect

46. C₃×C₇×D₁₅

C₂×C₁₉

semidirect

47. C₃×C₅×D₃×C₇

C₂×C₁₉

semidirect

52. C₁₉×D₁₅

D₃×C₇

direct (N × H)

53. C₅×D₃×C₁₉

D₃×C₇

semidirect

59. C₃×C₇×C₁₉

D₃×D₅

semidirect

60. C₃×C₇×C₁₉

C₂×D₁₅

semidirect

64. C₃×D₃×C₁₉

C₇×D₅

semidirect

65. C₃²×C₅×C₇

C₂²×C₁₉

semidirect

67. C₃×C₅×C₁₉

C₂×D₃×C₇

semidirect

68. C₃×C₅×C₁₉

C₂×D₃×C₇

semidirect

79. C₇×D₁₅

D₃×C₁₉

direct (N × H)

80. C₅×D₃×C₇

D₃×C₁₉

semidirect

85. D₃×D₁₅

C₇×C₁₉

direct (N × H)

86. C₃²×C₁₉

C₂×C₇×D₅

semidirect

88. C₇×C₁₉

D₃×D₁₅

direct (N × H)

91. C₃×D₃×C₇

D₅×C₁₉

semidirect

98. D₃×C₁₉

C₇×D₁₅

direct (N × H)

100. C₃×C₅×C₇

C₂×D₃×C₁₉

semidirect

101. C₃×C₅×C₇

C₂×D₃×C₁₉

semidirect

102. C₅×C₁₉

D₃²×C₇

semidirect

103. C₃⋊D₁₅

C₂×C₇×C₁₉

semidirect

104. C₃×D₁₅

C₂×C₇×C₁₉

semidirect

105. C₃×C₅×D₃

C₂×C₇×C₁₉

semidirect

112. C₃²×C₇

C₂×D₅×C₁₉

semidirect

116. C₃×C₁₉

D₃×C₇×D₅

semidirect

117. C₃×C₁₉

C₂×C₇×D₁₅

semidirect

118. C₃²×C₅

C₂²×C₇×C₁₉

semidirect

125. D₃×C₇

C₁₉×D₁₅

direct (N × H)

130. C₅×C₇

D₃²×C₁₉

semidirect

135. D₁₅

D₃×C₇×C₁₉

direct (N × H)

137. C₅×D₃

D₃×C₇×C₁₉

semidirect

140. C₃×C₇

D₃×D₅×C₁₉

semidirect

141. C₃×C₇

C₂×C₁₉×D₁₅

semidirect

143. C₁₉

D₃×C₇×D₁₅

direct (N × H)

146. C₃×D₃

C₇×D₅×C₁₉

semidirect

148. C₃×C₅

C₂×D₃×C₇×C₁₉

semidirect

149. C₃×C₅

C₂×D₃×C₇×C₁₉

semidirect

158. C₃²

C₂×C₇×D₅×C₁₉

semidirect

159. C₇

D₃×C₁₉×D₁₅

direct (N × H)

166. D₃

C₇×C₁₉×D₁₅

direct (N × H)

167. C₅

D₃²×C₇×C₁₉

semidirect

170. C₃

D₃×C₇×D₅×C₁₉

semidirect

171. C₃

C₂×C₇×C₁₉×D₁₅

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×C₇×C₁₉×D₁₅	2
C₇×C₁₉×C₃⋊D₁₅	2
C₂×C₇×C₁₉×D₁₅	3
D₃×C₇×D₅×C₁₉	3
D₃²×C₇×C₁₉	5
D₃×C₁₉×D₁₅	7
D₃×C₇×D₁₅	19

subgroup

index

C₃×C₅×D₃×C₇×C₁₉

C₃×C₇×C₁₉×D₁₅

C₇×C₁₉×C₃⋊D₁₅

C₂×C₇×C₁₉×D₁₅

D₃×C₇×D₅×C₁₉

D₃²×C₇×C₁₉

D₃×C₁₉×D₁₅

D₃×C₇×D₁₅

Subgroups — D₃×C₇×C₁₉×D₁₅ #37561562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×C7×C19×D15 #37561562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×C₁₉×D₁₅ #37561562