Group #49141590 — subgroups

Subgroups — C₃×C₂₉×D₁₅⋊D₇ #49141590

Order 36540.

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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	C₃²×C₂₉×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×C₂₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₂₉×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×D₁₅⋊D₇	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₅×D₇×C₂₉	—	3	1	no	maximal
6	C₃²×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃×D₇×C₂₉	—	5	1	no	maximal, Hall
8	C₇×C₂₉×D₁₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₂₉×D₂₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₂₉×D₃₅	—	2	1	no	—
11	C₃×C₂₉×D₃₅	D₃	1	1	yes	characteristic, complemented
12	C₃×C₂₉×D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₇×D₅×C₂₉	—	3	1	no	—
14	C₃×C₅×D₇×C₂₉	—	3	1	no	—
15	C₃×D₃×D₅×C₂₉	—	7	1	no	maximal, Hall
16	D₅×D₇×C₂₉	—	3	1	no	Hall
17	C₃×C₂₉×D₂₁	D₅	1	1	yes	characteristic, complemented
18	C₃×D₃×C₇×C₂₉	—	5	1	no	—
19	C₃²×D₇×C₂₉	—	5	1	no	—
20	C₃×C₅×C₇×C₂₉	—	2	1	no	—
21	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
22	C₃×C₅×C₇×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
23	C₃×C₂₉×D₁₅	D₇	1	1	yes	characteristic, complemented
24	C₃×C₅×D₃×C₂₉	—	7	1	no	—
25	C₃²×D₅×C₂₉	—	7	1	no	—
26	C₂×C₃×D₇×C₂₉	—	15	1	no	—
27	D₃×D₇×C₂₉	—	5	1	no	—
28	C₂₉×D₃₅	C₃×D₃	1	1	yes	characteristic, complemented
29	C₇×D₅×C₂₉	—	3	1	no	—
30	C₅×D₇×C₂₉	—	3	1	no	—
31	C₃²×C₇×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×D₅×C₂₉	—	21	1	no	—
33	D₃×D₅×C₂₉	—	7	1	no	—
34	C₃²×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
35	C₃×D₁₅⋊D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂×C₃×C₇×C₂₉	—	15	1	no	—
37	C₂₉×D₂₁	C₃×D₅	1	1	yes	characteristic, complemented
38	D₃×C₇×C₂₉	—	5	1	no	—
39	C₃×D₇×C₂₉	—	3	1	no	—
40	C₃×D₇×C₂₉	—	5	1	no	—
41	C₃×D₇×C₂₉	—	5	1	no	—
42	C₃×D₇×C₂₉	—	10	1	no	—
43	C₂×C₃×D₃×C₂₉	—	35	1	no	Hall
44	C₅×C₇×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×C₅×C₂₉	—	21	1	no	—
46	C₂₉×D₁₅	C₃×D₇	1	1	yes	characteristic, complemented
47	C₅×D₃×C₂₉	—	7	1	no	—
48	C₃×D₅×C₂₉	—	3	1	no	—
49	C₃×D₅×C₂₉	—	7	1	no	—
50	C₃×D₅×C₂₉	—	7	1	no	—
51	C₃×D₅×C₂₉	—	14	1	no	—
52	C₂×D₇×C₂₉	—	15	1	no	Hall
53	C₃×C₇×D₁₅	C₂×C₂₉	1	1	yes	characteristic, complemented
54	C₃×C₅×D₂₁	C₂×C₂₉	1	1	yes	characteristic, complemented
55	C₃²×D₃₅	C₂×C₂₉	1	1	yes	characteristic, complemented
56	C₃×C₇×C₂₉	—	2	1	no	—
57	C₃×C₇×C₂₉	D₃×D₅	1	1	yes	characteristic, complemented
58	C₃×C₇×C₂₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
59	C₂×D₅×C₂₉	—	21	1	no	Hall
60	C₂×C₃²×C₂₉	—	35	1	no	—
61	C₃×D₃×C₂₉	—	5	1	no	—
62	C₃×D₃×C₂₉	—	7	1	no	—
63	C₃×C₅×C₂₉	—	2	1	no	—
64	C₃×C₅×C₂₉	D₃×D₇	1	1	yes	characteristic, complemented
65	C₃×C₅×C₂₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented
66	D₁₅⋊D₇	C₃×C₂₉	1	1	yes	characteristic, direct product factor
67	C₃×D₅×D₇	—	3	1	no	—
68	C₂×C₇×C₂₉	—	15	1	no	—
69	D₇×C₂₉	—	3	1	no	—
70	D₇×C₂₉	—	5	1	no	—
71	C₂²×C₃×C₂₉	—	105	1	no	—
72	C₂×D₃×C₂₉	—	35	1	no	—
73	C₃²×C₅×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
74	C₂×C₅×C₂₉	—	21	1	no	—
75	D₅×C₂₉	—	3	1	no	—
76	D₅×C₂₉	—	7	1	no	—
77	C₃²×C₂₉	D₅×D₇	1	1	yes	characteristic, complemented, Hall
78	C₃×D₃×D₇	—	5	1	no	Hall
79	C₇×D₁₅	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
80	C₅×D₂₁	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
81	C₃×D₃₅	—	2	1	no	—
82	C₃×D₃₅	D₃×C₂₉	1	1	yes	characteristic, complemented
83	C₃×D₃₅	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
84	C₃×C₇×D₅	—	3	1	no	—
85	C₃×C₅×D₇	—	3	1	no	—
86	C₇×C₂₉	C₃×D₃×D₅	1	1	yes	characteristic, complemented, Hall
87	C₃×D₃×D₅	—	7	1	no	Hall
88	C₂×C₃×C₂₉	—	15	1	no	—
89	C₂×C₃×C₂₉	—	21	1	no	—
90	C₂×C₃×C₂₉	—	35	1	no	—
91	C₂×C₃×C₂₉	—	35	1	no	—
92	C₂×C₃×C₂₉	—	70	1	no	—
93	D₃×C₂₉	—	5	1	no	—
94	D₃×C₂₉	—	7	1	no	—
95	C₅×C₂₉	C₃×D₃×D₇	1	1	yes	characteristic, complemented, Hall
96	D₅×D₇	—	3	1	no	Hall
97	C₃×D₂₁	D₅×C₂₉	1	1	yes	characteristic, complemented
98	C₃×D₃×C₇	—	5	1	no	—
99	C₃²×D₇	—	5	1	no	—
100	C₂²×C₂₉	—	105	1	no	Hall
101	C₃×C₅×C₇	—	2	1	no	—
102	C₃×C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
103	C₃×C₅×C₇	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented
104	C₃×D₁₅	D₇×C₂₉	1	1	yes	characteristic, complemented
105	C₃×C₅×D₃	—	7	1	no	—
106	C₃²×D₅	—	7	1	no	—
107	C₃×C₂₉	—	2	1	no	—
108	C₃×C₂₉	C₃×D₅×D₇	1	1	yes	characteristic, complemented
109	C₃×C₂₉	D₁₅⋊D₇	1	1	yes	characteristic, direct product factor
110	C₂×C₃×D₇	—	15	1	no	—
111	D₃×D₇	—	5	1	no	—
112	D₃₅	C₃×D₃×C₂₉	1	1	yes	characteristic, complemented
113	C₅×D₇	—	3	1	no	—
114	C₇×D₅	—	3	1	no	—
115	C₃²×C₇	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
116	C₂×C₃×D₅	—	21	1	no	—
117	D₃×D₅	—	7	1	no	—
118	C₂×C₂₉	—	15	1	no	—
119	C₂×C₂₉	—	21	1	no	—
120	C₂×C₂₉	—	35	1	no	—
121	C₃²×C₅	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
122	C₂×C₃×C₇	—	15	1	no	—
123	D₂₁	C₃×D₅×C₂₉	1	1	yes	characteristic, complemented
124	C₃×D₇	—	3	1	no	—
125	C₃×D₇	—	5	1	no	—
126	C₃×D₇	—	5	1	no	—
127	C₃×D₇	—	10	1	no	—
128	D₃×C₇	—	5	1	no	—
129	C₂×C₃×D₃	—	35	1	no	Hall
130	C₅×C₇	C₂×C₃×D₃×C₂₉	1	1	yes	characteristic, complemented, Hall
131	C₂×C₃×C₅	—	21	1	no	—
132	D₁₅	C₃×D₇×C₂₉	1	1	yes	characteristic, complemented
133	C₃×D₅	—	3	1	no	—
134	C₃×D₅	—	7	1	no	—
135	C₃×D₅	—	7	1	no	—
136	C₃×D₅	—	14	1	no	—
137	C₅×D₃	—	7	1	no	—
138	C₂₉	C₃×D₁₅⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
139	C₂×D₇	—	15	1	no	Hall
140	C₃×C₇	—	2	1	no	—
141	C₃×C₇	D₃×D₅×C₂₉	1	1	yes	characteristic, complemented
142	C₃×C₇	C₂×C₃×D₅×C₂₉	1	1	yes	characteristic, complemented
143	C₂×D₅	—	21	1	no	Hall
144	C₂×C₃²	—	35	1	no	—
145	C₃×D₃	—	5	1	no	—
146	C₃×D₃	—	7	1	no	—
147	C₃×C₅	—	2	1	no	—
148	C₃×C₅	D₃×D₇×C₂₉	1	1	yes	characteristic, complemented
149	C₃×C₅	C₂×C₃×D₇×C₂₉	1	1	yes	characteristic, complemented
150	C₂×C₇	—	15	1	no	—
151	D₇	—	3	1	no	—
152	D₇	—	5	1	no	—
153	C₂²×C₃	—	105	1	no	—
154	C₂×D₃	—	35	1	no	—
155	C₂×C₅	—	21	1	no	—
156	D₅	—	3	1	no	—
157	D₅	—	7	1	no	—
158	C₃²	D₅×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
159	C₇	C₃×D₃×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
160	C₂×C₃	—	15	1	no	—
161	C₂×C₃	—	21	1	no	—
162	C₂×C₃	—	35	1	no	—
163	C₂×C₃	—	35	1	no	—
164	C₂×C₃	—	70	1	no	—
165	D₃	—	5	1	no	—
166	D₃	—	7	1	no	—
167	C₅	C₃×D₃×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
168	C₂²	—	105	1	no	Sylow
169	C₃	—	2	1	no	—
170	C₃	C₃×D₅×D₇×C₂₉	1	1	yes	characteristic, complemented
171	C₃	C₂₉×D₁₅⋊D₇	1	1	yes	characteristic, direct product factor
172	C₂	—	15	1	no	—
173	C₂	—	21	1	no	—
174	C₂	—	35	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₂₉×D₃₅

C₂

yes

maximal, characteristic, complemented

C₃×C₅×C₂₉×D₂₁

C₂

yes

maximal, characteristic, complemented

C₃×C₇×C₂₉×D₁₅

C₂

yes

maximal, characteristic, complemented

C₂₉×D₁₅⋊D₇

C₃

yes

maximal, characteristic, direct product factor

C₃×D₅×D₇×C₂₉

—

maximal

C₃²×C₅×C₇×C₂₉

C₂²

yes

characteristic, complemented, Hall

C₃×D₃×D₇×C₂₉

—

maximal, Hall

C₇×C₂₉×D₁₅

C₂×C₃

yes

characteristic, complemented

C₅×C₂₉×D₂₁

C₂×C₃

yes

characteristic, complemented

C₃×C₂₉×D₃₅

—

C₃×C₂₉×D₃₅

D₃

yes

characteristic, complemented

C₃×C₂₉×D₃₅

C₂×C₃

yes

characteristic, complemented

C₃×C₇×D₅×C₂₉

—

C₃×C₅×D₇×C₂₉

—

C₃×D₃×D₅×C₂₉

—

maximal, Hall

D₅×D₇×C₂₉

—

Hall

C₃×C₂₉×D₂₁

D₅

yes

characteristic, complemented

C₃×D₃×C₇×C₂₉

—

C₃²×D₇×C₂₉

—

C₃×C₅×C₇×C₂₉

—

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic, complemented

C₃×C₅×C₇×C₂₉

C₂²×C₃

yes

characteristic, complemented

C₃×C₂₉×D₁₅

D₇

yes

characteristic, complemented

C₃×C₅×D₃×C₂₉

—

C₃²×D₅×C₂₉

—

C₂×C₃×D₇×C₂₉

—

D₃×D₇×C₂₉

—

C₂₉×D₃₅

C₃×D₃

yes

characteristic, complemented

C₇×D₅×C₂₉

—

C₅×D₇×C₂₉

—

C₃²×C₇×C₂₉

C₂×D₅

yes

characteristic, complemented, Hall

C₂×C₃×D₅×C₂₉

—

D₃×D₅×C₂₉

—

C₃²×C₅×C₂₉

C₂×D₇

yes

characteristic, complemented, Hall

C₃×D₁₅⋊D₇

C₂₉

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃×C₇×C₂₉

—

C₂₉×D₂₁

C₃×D₅

yes

characteristic, complemented

D₃×C₇×C₂₉

—

C₃×D₇×C₂₉

—

C₃×D₇×C₂₉

—

C₃×D₇×C₂₉

—

C₃×D₇×C₂₉

—

C₂×C₃×D₃×C₂₉

—

Hall

C₅×C₇×C₂₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₂₉

—

C₂₉×D₁₅

C₃×D₇

yes

characteristic, complemented

C₅×D₃×C₂₉

—

C₃×D₅×C₂₉

—

C₃×D₅×C₂₉

—

C₃×D₅×C₂₉

—

C₃×D₅×C₂₉

—

C₂×D₇×C₂₉

—

Hall

C₃×C₇×D₁₅

C₂×C₂₉

yes

characteristic, complemented

C₃×C₅×D₂₁

C₂×C₂₉

yes

characteristic, complemented

C₃²×D₃₅

C₂×C₂₉

yes

characteristic, complemented

C₃×C₇×C₂₉

—

C₃×C₇×C₂₉

D₃×D₅

yes

characteristic, complemented

C₃×C₇×C₂₉

C₂×C₃×D₅

yes

characteristic, complemented

C₂×D₅×C₂₉

—

Hall

C₂×C₃²×C₂₉

—

C₃×D₃×C₂₉

—

C₃×D₃×C₂₉

—

C₃×C₅×C₂₉

—

C₃×C₅×C₂₉

D₃×D₇

yes

characteristic, complemented

C₃×C₅×C₂₉

C₂×C₃×D₇

yes

characteristic, complemented

D₁₅⋊D₇

C₃×C₂₉

yes

characteristic, direct product factor

C₃×D₅×D₇

—

C₂×C₇×C₂₉

—

D₇×C₂₉

—

D₇×C₂₉

—

C₂²×C₃×C₂₉

—

105

—

C₂×D₃×C₂₉

—

C₃²×C₅×C₇

C₂²×C₂₉

yes

characteristic, complemented, Hall

C₂×C₅×C₂₉

—

D₅×C₂₉

—

D₅×C₂₉

—

C₃²×C₂₉

D₅×D₇

yes

characteristic, complemented, Hall

C₃×D₃×D₇

—

Hall

C₇×D₁₅

C₂×C₃×C₂₉

yes

characteristic, complemented

C₅×D₂₁

C₂×C₃×C₂₉

yes

characteristic, complemented

C₃×D₃₅

—

C₃×D₃₅

D₃×C₂₉

yes

characteristic, complemented

C₃×D₃₅

C₂×C₃×C₂₉

yes

characteristic, complemented

C₃×C₇×D₅

—

C₃×C₅×D₇

—

C₇×C₂₉

C₃×D₃×D₅

yes

characteristic, complemented, Hall

C₃×D₃×D₅

—

Hall

C₂×C₃×C₂₉

—

C₂×C₃×C₂₉

—

C₂×C₃×C₂₉

—

C₂×C₃×C₂₉

—

C₂×C₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

C₅×C₂₉

C₃×D₃×D₇

yes

characteristic, complemented, Hall

D₅×D₇

—

Hall

C₃×D₂₁

D₅×C₂₉

yes

characteristic, complemented

C₃×D₃×C₇

—

C₃²×D₇

—

100

C₂²×C₂₉

—

105

Hall

101

C₃×C₅×C₇

—

102

C₃×C₅×C₇

C₂×D₃×C₂₉

yes

characteristic, complemented

103

C₃×C₅×C₇

C₂²×C₃×C₂₉

yes

characteristic, complemented

104

C₃×D₁₅

D₇×C₂₉

yes

characteristic, complemented

105

C₃×C₅×D₃

—

106

C₃²×D₅

—

107

C₃×C₂₉

—

108

C₃×C₂₉

C₃×D₅×D₇

yes

characteristic, complemented

109

C₃×C₂₉

D₁₅⋊D₇

yes

characteristic, direct product factor

110

C₂×C₃×D₇

—

111

D₃×D₇

—

112

D₃₅

C₃×D₃×C₂₉

yes

characteristic, complemented

113

C₅×D₇

—

114

C₇×D₅

—

115

C₃²×C₇

C₂×D₅×C₂₉

yes

characteristic, complemented, Hall

116

C₂×C₃×D₅

—

117

D₃×D₅

—

118

C₂×C₂₉

—

119

C₂×C₂₉

—

120

C₂×C₂₉

—

121

C₃²×C₅

C₂×D₇×C₂₉

yes

characteristic, complemented, Hall

122

C₂×C₃×C₇

—

123

D₂₁

C₃×D₅×C₂₉

yes

characteristic, complemented

124

C₃×D₇

—

125

C₃×D₇

—

126

C₃×D₇

—

127

C₃×D₇

—

128

D₃×C₇

—

129

C₂×C₃×D₃

—

Hall

130

C₅×C₇

C₂×C₃×D₃×C₂₉

yes

characteristic, complemented, Hall

131

C₂×C₃×C₅

—

132

D₁₅

C₃×D₇×C₂₉

yes

characteristic, complemented

133

C₃×D₅

—

134

C₃×D₅

—

135

C₃×D₅

—

136

C₃×D₅

—

137

C₅×D₃

—

138

C₂₉

C₃×D₁₅⋊D₇

yes

characteristic, direct product factor, Sylow

139

C₂×D₇

—

Hall

140

C₃×C₇

—

141

C₃×C₇

D₃×D₅×C₂₉

yes

characteristic, complemented

142

C₃×C₇

C₂×C₃×D₅×C₂₉

yes

characteristic, complemented

143

C₂×D₅

—

Hall

144

C₂×C₃²

—

145

C₃×D₃

—

146

C₃×D₃

—

147

C₃×C₅

—

148

C₃×C₅

D₃×D₇×C₂₉

yes

characteristic, complemented

149

C₃×C₅

C₂×C₃×D₇×C₂₉

yes

characteristic, complemented

150

C₂×C₇

—

151

D₇

—

152

D₇

—

153

C₂²×C₃

—

105

—

154

C₂×D₃

—

155

C₂×C₅

—

156

D₅

—

157

D₅

—

158

C₃²

D₅×D₇×C₂₉

yes

characteristic, complemented, Sylow

159

C₇

C₃×D₃×D₅×C₂₉

yes

characteristic, complemented, Sylow

160

C₂×C₃

—

161

C₂×C₃

—

162

C₂×C₃

—

163

C₂×C₃

—

164

C₂×C₃

—

165

D₃

—

166

D₃

—

167

C₅

C₃×D₃×D₇×C₂₉

yes

characteristic, complemented, Sylow

168

C₂²

—

105

Sylow

169

C₃

—

170

C₃

C₃×D₅×D₇×C₂₉

yes

characteristic, complemented

171

C₃

C₂₉×D₁₅⋊D₇

yes

characteristic, direct product factor

172

C₂

—

173

C₂

—

174

C₂

—

	subgroup	G/H
center, hypercenter	C₃×C₂₉	D₁₅⋊D₇
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₃×C₂₉

subgroup

G/H

center, hypercenter

C₃×C₂₉

D₁₅⋊D₇

commutator, cosocle, hypocenter

C₃×C₅×C₇

C₂²×C₃×C₂₉

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₂₉

C₂²

LCS

G ▷ C₃×C₅×C₇

UCS

C₁ ◁ C₃×C₂₉

N	H ≅ G/N	type
1. C₃²×C₂₉×D₃₅	C₂	semidirect
2. C₃×C₅×C₂₉×D₂₁	C₂	semidirect
3. C₃×C₇×C₂₉×D₁₅	C₂	semidirect
4. C₂₉×D₁₅⋊D₇	C₃	direct (N × H)
6. C₃²×C₅×C₇×C₂₉	C₂²	semidirect
8. C₇×C₂₉×D₁₅	C₂×C₃	semidirect
9. C₅×C₂₉×D₂₁	C₂×C₃	semidirect
11. C₃×C₂₉×D₃₅	D₃	semidirect
12. C₃×C₂₉×D₃₅	C₂×C₃	semidirect
17. C₃×C₂₉×D₂₁	D₅	semidirect
21. C₃×C₅×C₇×C₂₉	C₂×D₃	semidirect
22. C₃×C₅×C₇×C₂₉	C₂²×C₃	semidirect
23. C₃×C₂₉×D₁₅	D₇	semidirect
28. C₂₉×D₃₅	C₃×D₃	semidirect
31. C₃²×C₇×C₂₉	C₂×D₅	semidirect
34. C₃²×C₅×C₂₉	C₂×D₇	semidirect
35. C₃×D₁₅⋊D₇	C₂₉	direct (N × H)
37. C₂₉×D₂₁	C₃×D₅	semidirect
44. C₅×C₇×C₂₉	C₂×C₃×D₃	semidirect
46. C₂₉×D₁₅	C₃×D₇	semidirect
53. C₃×C₇×D₁₅	C₂×C₂₉	semidirect
54. C₃×C₅×D₂₁	C₂×C₂₉	semidirect
55. C₃²×D₃₅	C₂×C₂₉	semidirect
57. C₃×C₇×C₂₉	D₃×D₅	semidirect
58. C₃×C₇×C₂₉	C₂×C₃×D₅	semidirect
64. C₃×C₅×C₂₉	D₃×D₇	semidirect
65. C₃×C₅×C₂₉	C₂×C₃×D₇	semidirect
66. D₁₅⋊D₇	C₃×C₂₉	direct (N × H)
73. C₃²×C₅×C₇	C₂²×C₂₉	semidirect
77. C₃²×C₂₉	D₅×D₇	semidirect
79. C₇×D₁₅	C₂×C₃×C₂₉	semidirect
80. C₅×D₂₁	C₂×C₃×C₂₉	semidirect
82. C₃×D₃₅	D₃×C₂₉	semidirect
83. C₃×D₃₅	C₂×C₃×C₂₉	semidirect
86. C₇×C₂₉	C₃×D₃×D₅	semidirect
95. C₅×C₂₉	C₃×D₃×D₇	semidirect
97. C₃×D₂₁	D₅×C₂₉	semidirect
102. C₃×C₅×C₇	C₂×D₃×C₂₉	semidirect
103. C₃×C₅×C₇	C₂²×C₃×C₂₉	semidirect
104. C₃×D₁₅	D₇×C₂₉	semidirect
108. C₃×C₂₉	C₃×D₅×D₇	semidirect
109. C₃×C₂₉	D₁₅⋊D₇	direct (N × H)
112. D₃₅	C₃×D₃×C₂₉	semidirect
115. C₃²×C₇	C₂×D₅×C₂₉	semidirect
121. C₃²×C₅	C₂×D₇×C₂₉	semidirect
123. D₂₁	C₃×D₅×C₂₉	semidirect
130. C₅×C₇	C₂×C₃×D₃×C₂₉	semidirect
132. D₁₅	C₃×D₇×C₂₉	semidirect
138. C₂₉	C₃×D₁₅⋊D₇	direct (N × H)
141. C₃×C₇	D₃×D₅×C₂₉	semidirect
142. C₃×C₇	C₂×C₃×D₅×C₂₉	semidirect
148. C₃×C₅	D₃×D₇×C₂₉	semidirect
149. C₃×C₅	C₂×C₃×D₇×C₂₉	semidirect
158. C₃²	D₅×D₇×C₂₉	semidirect
159. C₇	C₃×D₃×D₅×C₂₉	semidirect
167. C₅	C₃×D₃×D₇×C₂₉	semidirect
170. C₃	C₃×D₅×D₇×C₂₉	semidirect
171. C₃	C₂₉×D₁₅⋊D₇	direct (N × H)

H ≅ G/N

type

1. C₃²×C₂₉×D₃₅

C₂

semidirect

2. C₃×C₅×C₂₉×D₂₁

C₂

semidirect

3. C₃×C₇×C₂₉×D₁₅

C₂

semidirect

4. C₂₉×D₁₅⋊D₇

C₃

direct (N × H)

6. C₃²×C₅×C₇×C₂₉

C₂²

semidirect

8. C₇×C₂₉×D₁₅

C₂×C₃

semidirect

9. C₅×C₂₉×D₂₁

C₂×C₃

semidirect

11. C₃×C₂₉×D₃₅

D₃

semidirect

12. C₃×C₂₉×D₃₅

C₂×C₃

semidirect

17. C₃×C₂₉×D₂₁

D₅

semidirect

21. C₃×C₅×C₇×C₂₉

C₂×D₃

semidirect

22. C₃×C₅×C₇×C₂₉

C₂²×C₃

semidirect

23. C₃×C₂₉×D₁₅

D₇

semidirect

28. C₂₉×D₃₅

C₃×D₃

semidirect

31. C₃²×C₇×C₂₉

C₂×D₅

semidirect

34. C₃²×C₅×C₂₉

C₂×D₇

semidirect

35. C₃×D₁₅⋊D₇

C₂₉

direct (N × H)

37. C₂₉×D₂₁

C₃×D₅

semidirect

44. C₅×C₇×C₂₉

C₂×C₃×D₃

semidirect

46. C₂₉×D₁₅

C₃×D₇

semidirect

53. C₃×C₇×D₁₅

C₂×C₂₉

semidirect

54. C₃×C₅×D₂₁

C₂×C₂₉

semidirect

55. C₃²×D₃₅

C₂×C₂₉

semidirect

57. C₃×C₇×C₂₉

D₃×D₅

semidirect

58. C₃×C₇×C₂₉

C₂×C₃×D₅

semidirect

64. C₃×C₅×C₂₉

D₃×D₇

semidirect

65. C₃×C₅×C₂₉

C₂×C₃×D₇

semidirect

66. D₁₅⋊D₇

C₃×C₂₉

direct (N × H)

73. C₃²×C₅×C₇

C₂²×C₂₉

semidirect

77. C₃²×C₂₉

D₅×D₇

semidirect

79. C₇×D₁₅

C₂×C₃×C₂₉

semidirect

80. C₅×D₂₁

C₂×C₃×C₂₉

semidirect

82. C₃×D₃₅

D₃×C₂₉

semidirect

83. C₃×D₃₅

C₂×C₃×C₂₉

semidirect

86. C₇×C₂₉

C₃×D₃×D₅

semidirect

95. C₅×C₂₉

C₃×D₃×D₇

semidirect

97. C₃×D₂₁

D₅×C₂₉

semidirect

102. C₃×C₅×C₇

C₂×D₃×C₂₉

semidirect

103. C₃×C₅×C₇

C₂²×C₃×C₂₉

semidirect

104. C₃×D₁₅

D₇×C₂₉

semidirect

108. C₃×C₂₉

C₃×D₅×D₇

semidirect

109. C₃×C₂₉

D₁₅⋊D₇

direct (N × H)

112. D₃₅

C₃×D₃×C₂₉

semidirect

115. C₃²×C₇

C₂×D₅×C₂₉

semidirect

121. C₃²×C₅

C₂×D₇×C₂₉

semidirect

123. D₂₁

C₃×D₅×C₂₉

semidirect

130. C₅×C₇

C₂×C₃×D₃×C₂₉

semidirect

132. D₁₅

C₃×D₇×C₂₉

semidirect

138. C₂₉

C₃×D₁₅⋊D₇

direct (N × H)

141. C₃×C₇

D₃×D₅×C₂₉

semidirect

142. C₃×C₇

C₂×C₃×D₅×C₂₉

semidirect

148. C₃×C₅

D₃×D₇×C₂₉

semidirect

149. C₃×C₅

C₂×C₃×D₇×C₂₉

semidirect

158. C₃²

D₅×D₇×C₂₉

semidirect

159. C₇

C₃×D₃×D₅×C₂₉

semidirect

167. C₅

C₃×D₃×D₇×C₂₉

semidirect

170. C₃

C₃×D₅×D₇×C₂₉

semidirect

171. C₃

C₂₉×D₁₅⋊D₇

direct (N × H)

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

subgroup	index
C₃²×C₂₉×D₃₅	2
C₃×C₅×C₂₉×D₂₁	2
C₃×C₇×C₂₉×D₁₅	2
C₂₉×D₁₅⋊D₇	3
C₃×D₅×D₇×C₂₉	3
C₃×D₃×D₇×C₂₉	5
C₃×D₃×D₅×C₂₉	7
C₃×D₁₅⋊D₇	29

subgroup

index

C₃²×C₂₉×D₃₅

C₃×C₅×C₂₉×D₂₁

C₃×C₇×C₂₉×D₁₅

C₂₉×D₁₅⋊D₇

C₃×D₅×D₇×C₂₉

C₃×D₃×D₇×C₂₉

C₃×D₃×D₅×C₂₉

C₃×D₁₅⋊D₇

Subgroups — C₃×C₂₉×D₁₅⋊D₇ #49141590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×C29×D15⋊D7 #49141590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₉×D₁₅⋊D₇ #49141590