Group #20303970 — subgroups

Subgroups — C₂₉×#9070 #20303970

Order 7424.

426 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 126 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	C₂₉×#3131	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2986	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#1526	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1484	C₂	1	2	yes	maximal
5	C₂₉×#1278	C₂	1	2	yes	maximal, complemented
6	C₂₉×#533	C₂²	1	1	yes	characteristic
7	C₂₉×#532	C₂²	1	1	yes	characteristic
8	C₂₉×#488	—	2	2	no	—
9	C₂₉×#487	C₄	1	2	yes	—
10	C₂₉×#486	C₄	1	2	yes	—
11	C₂₉×#446	—	2	2	no	—
12	C₈×Q₈×C₂₉	—	2	2	no	—
13	C₂₉×#433	—	2	2	no	—
14	C₂₉×#431	C₂²	1	2	yes	—
15	C₂₉×#416	—	2	2	no	—
16	C₄×M₁₆×C₂₉	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#330	—	2	2	no	—
19	C₂₉×D₄⋊C₈	—	2	2	no	—
20	C₂₉×D₄⋊C₈	—	2	2	no	—
21	C₂×#41×C₂₉	—	2	1	no	—
22	C₂×M₁₆×C₂₉	—	2	2	no	—
23	C₂²×C₈×C₂₉	—	2	1	no	—
24	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
25	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
26	C₂₉×#127	C₂×C₄	1	1	yes	characteristic
27	C₂₉×#125	D₄	1	2	yes	—
28	C₂₉×#124	—	2	1	no	—
29	C₂₉×C₂²⋊Q₈	—	2	2	no	—
30	C₂₉×#121	—	2	2	no	—
31	C₄×Q₈×C₂₉	—	2	2	no	—
32	C₄×D₄×C₂₉	—	2	2	no	—
33	C₂₉×#117	D₄	1	2	yes	—
34	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
35	C₂₉×C₄⋊C₈	—	2	4	no	—
36	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
37	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
38	C₂₉×#103	—	2	4	no	—
39	C₂₉×#102	—	2	4	no	—
40	C₂₉×C₂²⋊C₈	—	2	2	no	—
41	C₂₉×#97	—	2	2	no	—
42	C₂₉×#97	—	2	2	no	—
43	C₄×C₈×C₂₉	—	2	2	no	—
44	C₄×C₈×C₂₉	—	2	2	no	—
45	C₄×C₈×C₂₉	—	2	1	no	—
46	C₄×C₈×C₂₉	—	2	2	no	—
47	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
48	#41×C₂₉	—	4	4	no	—
49	C₂×Q₈×C₂₉	—	2	2	no	—
50	C₂×Q₈×C₂₉	—	2	1	no	—
51	C₂×D₄×C₂₉	—	2	1	no	—
52	C₂×D₄×C₂₉	—	2	2	no	—
53	C₂×D₄×C₂₉	—	4	1	no	—
54	C₂²×C₄×C₂₉	—	4	1	no	—
55	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₂₉	#41	1	2	yes	—
57	M₁₆×C₂₉	—	2	4	no	—
58	M₁₆×C₂₉	—	4	2	no	—
59	C₂×C₈×C₂₉	—	2	2	no	—
60	C₂×C₈×C₂₉	—	2	2	no	—
61	C₂×C₈×C₂₉	—	2	2	no	—
62	C₂×C₈×C₂₉	—	4	2	no	—
63	C₂×C₈×C₂₉	—	4	2	no	—
64	C₄⋊C₄×C₂₉	—	2	2	no	—
65	C₄⋊C₄×C₂₉	—	2	4	no	—
66	C₄⋊C₄×C₂₉	—	2	2	no	—
67	C₄⋊C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
68	C₂²⋊C₄×C₂₉	—	2	2	no	—
69	C₂²⋊C₄×C₂₉	—	4	2	no	—
70	C₄²×C₂₉	—	2	2	no	—
71	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₂₉	C₂×D₄	1	2	yes	—
74	#9070	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂³×C₂₉	—	4	1	no	—
76	C₂³×C₂₉	#123	1	1	yes	characteristic
77	Q₈×C₂₉	—	4	2	no	—
78	Q₈×C₂₉	—	4	2	no	—
79	Q₈×C₂₉	—	4	2	no	—
80	D₄×C₂₉	—	4	2	no	—
81	D₄×C₂₉	—	4	2	no	—
82	D₄×C₂₉	—	4	2	no	—
83	D₄×C₂₉	—	8	2	no	—
84	C₂×C₄×C₂₉	—	2	2	no	—
85	C₂×C₄×C₂₉	—	2	2	no	—
86	C₂×C₄×C₂₉	—	2	2	no	—
87	C₂×C₄×C₂₉	—	2	4	no	—
88	C₂×C₄×C₂₉	—	4	1	no	—
89	C₂×C₄×C₂₉	—	8	2	no	—
90	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
93	C₂×C₄×C₂₉	#121	1	2	yes	—
94	C₈×C₂₉	—	4	2	no	—
95	C₈×C₂₉	—	4	4	no	—
96	C₈×C₂₉	—	4	2	no	—
97	C₈×C₂₉	—	4	2	no	—
98	#3131	C₂×C₂₉	1	1	yes	characteristic
99	#2986	C₂×C₂₉	1	1	yes	characteristic, complemented
100	#1526	C₂×C₂₉	1	1	yes	characteristic, complemented
101	#1484	C₂×C₂₉	1	2	yes	—
102	#1278	C₂×C₂₉	1	2	yes	complemented
103	C₂²×C₂₉	—	2	2	no	—
104	C₂²×C₂₉	—	2	1	no	—
105	C₂²×C₂₉	—	8	2	no	—
106	C₂²×C₂₉	—	8	1	no	—
107	C₂²×C₂₉	#386	1	1	yes	characteristic
108	C₄×C₂₉	—	2	2	no	—
109	C₄×C₂₉	—	2	1	no	—
110	C₄×C₂₉	—	4	4	no	—
111	C₄×C₂₉	—	8	1	no	—
112	C₄×C₂₉	#443	1	2	yes	—
113	C₄×C₂₉	#444	1	2	yes	—
114	C₄×C₂₉	#454	1	2	yes	—
115	#533	C₂²×C₂₉	1	1	yes	characteristic
116	#532	C₂²×C₂₉	1	1	yes	characteristic
117	#488	—	2	2	no	—
118	#487	C₄×C₂₉	1	2	yes	—
119	#486	C₄×C₂₉	1	2	yes	—
120	#446	—	2	2	no	—
121	C₈×Q₈	—	2	2	no	—
122	#433	—	2	2	no	—
123	#431	C₂²×C₂₉	1	2	yes	—
124	#416	—	2	2	no	—
125	C₄×M₁₆	C₂²×C₂₉	1	2	yes	—
126	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
127	#330	—	2	2	no	—
128	D₄⋊C₈	—	2	2	no	—
129	D₄⋊C₈	—	2	2	no	—
130	C₂×C₂₉	—	4	1	no	—
131	C₂×C₂₉	—	16	1	no	—
132	C₂×C₂₉	#1876	1	2	yes	—
133	C₂×C₂₉	#1888	1	1	yes	characteristic
134	C₂×#41	—	2	1	no	—
135	C₂×M₁₆	—	2	2	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
138	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
139	#127	C₂×C₄×C₂₉	1	1	yes	characteristic
140	#125	D₄×C₂₉	1	2	yes	—
141	#124	—	2	1	no	—
142	C₂²⋊Q₈	—	2	2	no	—
143	#121	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×D₄	—	2	2	no	—
146	#117	D₄×C₂₉	1	2	yes	—
147	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
148	C₄⋊C₈	—	2	4	no	—
149	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
150	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
151	#103	—	2	4	no	—
152	#102	—	2	4	no	—
153	C₂²⋊C₈	—	2	2	no	—
154	#97	—	2	2	no	—
155	#97	—	2	2	no	—
156	C₄×C₈	—	2	2	no	—
157	C₄×C₈	—	2	1	no	—
158	C₄×C₈	—	2	2	no	—
159	C₄×C₈	—	2	2	no	—
160	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
161	C₂₉	#9070	1	1	yes	characteristic, direct product factor, Sylow
162	#41	—	4	4	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	1	no	—
165	C₂×D₄	—	2	1	no	—
166	C₂×D₄	—	2	2	no	—
167	C₂×D₄	—	4	1	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
170	C₂²×C₄	#41×C₂₉	1	2	yes	—
171	M₁₆	—	2	4	no	—
172	M₁₆	—	4	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	4	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	C₂²⋊C₄×C₂₉	1	4	yes	—
182	C₂²⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
186	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
187	C₄²	C₂×D₄×C₂₉	1	2	yes	—
188	C₂³	—	4	1	no	—
189	C₂³	C₂₉×#123	1	1	yes	characteristic
190	Q₈	—	4	2	no	—
191	Q₈	—	4	2	no	—
192	Q₈	—	4	2	no	—
193	D₄	—	4	2	no	—
194	D₄	—	4	2	no	—
195	D₄	—	4	2	no	—
196	D₄	—	8	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	8	2	no	—
203	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
204	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
205	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
206	C₂×C₄	C₂₉×#121	1	2	yes	—
207	C₈	—	4	2	no	—
208	C₈	—	4	4	no	—
209	C₈	—	4	2	no	—
210	C₈	—	4	2	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	1	no	—
213	C₂²	—	8	2	no	—
214	C₂²	—	8	1	no	—
215	C₂²	C₂₉×#386	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	1	no	—
218	C₄	—	4	4	no	—
219	C₄	—	8	1	no	—
220	C₄	C₂₉×#443	1	2	yes	—
221	C₄	C₂₉×#444	1	2	yes	—
222	C₄	C₂₉×#454	1	2	yes	—
223	C₂	—	4	1	no	—
224	C₂	—	16	1	no	—
225	C₂	C₂₉×#1876	1	2	yes	—
226	C₂	C₂₉×#1888	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#3131

C₂

yes

maximal, characteristic

C₂₉×#2986

C₂

yes

maximal, characteristic, complemented

C₂₉×#1526

C₂

yes

maximal, characteristic, complemented

C₂₉×#1484

C₂

yes

maximal

C₂₉×#1278

C₂

yes

maximal, complemented

C₂₉×#533

C₂²

yes

characteristic

C₂₉×#532

C₂²

yes

characteristic

C₂₉×#488

—

C₂₉×#487

C₄

yes

—

C₂₉×#486

C₄

yes

—

C₂₉×#446

—

C₈×Q₈×C₂₉

—

C₂₉×#433

—

C₂₉×#431

C₂²

yes

—

C₂₉×#416

—

C₄×M₁₆×C₂₉

C₂²

yes

—

C₂×C₄×C₈×C₂₉

C₂²

yes

characteristic

C₂₉×#330

—

C₂₉×D₄⋊C₈

—

C₂₉×D₄⋊C₈

—

C₂×#41×C₂₉

—

C₂×M₁₆×C₂₉

—

C₂²×C₈×C₂₉

—

C₂₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₂₉×C₄⋊Q₈

C₂×C₄

yes

—

C₂₉×#127

C₂×C₄

yes

characteristic

C₂₉×#125

D₄

yes

—

C₂₉×#124

—

C₂₉×C₂²⋊Q₈

—

C₂₉×#121

—

C₄×Q₈×C₂₉

—

C₄×D₄×C₂₉

—

C₂₉×#117

D₄

yes

—

C₂×C₄²×C₂₉

C₂³

yes

characteristic

C₂₉×C₄⋊C₈

—

C₂₉×C₄⋊C₈

D₄

yes

—

C₂₉×C₄⋊C₈

D₄

yes

—

C₂₉×#103

—

C₂₉×#102

—

C₂₉×C₂²⋊C₈

—

C₂₉×#97

—

C₂₉×#97

—

C₄×C₈×C₂₉

—

C₄×C₈×C₂₉

—

C₄×C₈×C₂₉

—

C₄×C₈×C₂₉

—

C₄×C₈×C₂₉

C₂×C₄

yes

—

#41×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₉

#41

yes

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

C₂²×C₄

yes

characteristic

C₄²×C₂₉

C₂×D₄

yes

characteristic

C₄²×C₂₉

C₂×D₄

yes

—

#9070

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₉

—

C₂³×C₂₉

#123

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄×D₄

yes

—

C₂×C₄×C₂₉

#120

yes

characteristic

C₂×C₄×C₂₉

#121

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

#3131

C₂×C₂₉

yes

characteristic

#2986

C₂×C₂₉

yes

characteristic, complemented

100

#1526

C₂×C₂₉

yes

characteristic, complemented

101

#1484

C₂×C₂₉

yes

—

102

#1278

C₂×C₂₉

yes

complemented

103

C₂²×C₂₉

—

104

C₂²×C₂₉

—

105

C₂²×C₂₉

—

106

C₂²×C₂₉

—

107

C₂²×C₂₉

#386

yes

characteristic

108

C₄×C₂₉

—

109

C₄×C₂₉

—

110

C₄×C₂₉

—

111

C₄×C₂₉

—

112

C₄×C₂₉

#443

yes

—

113

C₄×C₂₉

#444

yes

—

114

C₄×C₂₉

#454

yes

—

115

#533

C₂²×C₂₉

yes

characteristic

116

#532

C₂²×C₂₉

yes

characteristic

117

#488

—

118

#487

C₄×C₂₉

yes

—

119

#486

C₄×C₂₉

yes

—

120

#446

—

121

C₈×Q₈

—

122

#433

—

123

#431

C₂²×C₂₉

yes

—

124

#416

—

125

C₄×M₁₆

C₂²×C₂₉

yes

—

126

C₂×C₄×C₈

C₂²×C₂₉

yes

characteristic

127

#330

—

128

D₄⋊C₈

—

129

D₄⋊C₈

—

130

C₂×C₂₉

—

131

C₂×C₂₉

—

132

C₂×C₂₉

#1876

yes

—

133

C₂×C₂₉

#1888

yes

characteristic

134

C₂×#41

—

135

C₂×M₁₆

—

136

C₂²×C₈

—

137

C₄⋊Q₈

C₂×C₄×C₂₉

yes

characteristic

138

C₄⋊Q₈

C₂×C₄×C₂₉

yes

—

139

#127

C₂×C₄×C₂₉

yes

characteristic

140

#125

D₄×C₂₉

yes

—

141

#124

—

142

C₂²⋊Q₈

—

143

#121

—

144

C₄×Q₈

—

145

C₄×D₄

—

146

#117

D₄×C₂₉

yes

—

147

C₂×C₄²

C₂³×C₂₉

yes

characteristic

148

C₄⋊C₈

—

149

C₄⋊C₈

D₄×C₂₉

yes

—

150

C₄⋊C₈

D₄×C₂₉

yes

—

151

#103

—

152

#102

—

153

C₂²⋊C₈

—

154

#97

—

155

#97

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

C₂×C₄×C₂₉

yes

—

161

C₂₉

#9070

yes

characteristic, direct product factor, Sylow

162

#41

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂×D₄×C₂₉

yes

characteristic

170

C₂²×C₄

#41×C₂₉

yes

—

171

M₁₆

—

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

C₂²⋊C₄×C₂₉

yes

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

C₂²×C₄×C₂₉

yes

characteristic

186

C₄²

C₂×D₄×C₂₉

yes

characteristic

187

C₄²

C₂×D₄×C₂₉

yes

—

188

C₂³

—

189

C₂³

C₂₉×#123

yes

characteristic

190

Q₈

—

191

Q₈

—

192

Q₈

—

193

D₄

—

194

D₄

—

195

D₄

—

196

D₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

C₂×C₂²⋊C₄×C₂₉

yes

characteristic

204

C₂×C₄

C₄×D₄×C₂₉

yes

—

205

C₂×C₄

C₂₉×#120

yes

characteristic

206

C₂×C₄

C₂₉×#121

yes

—

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

C₂₉×#386

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

C₂₉×#443

yes

—

221

C₄

C₂₉×#444

yes

—

222

C₄

C₂₉×#454

yes

—

223

C₂

—

224

C₂

—

225

C₂

C₂₉×#1876

yes

—

226

C₂

C₂₉×#1888

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#120
commutator	C₄²	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂²×C₂₉	#386
prime radical	C₂₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₂₉

#120

commutator

C₄²

C₂²×C₄×C₂₉

Frattini, cosocle

C₂×C₄²

C₂³×C₂₉

socle

C₂²×C₂₉

#386

prime radical

C₂₉×#532

C₂²

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

N	H ≅ G/N	type
2. C₂₉×#2986	C₂	semidirect
3. C₂₉×#1526	C₂	semidirect
5. C₂₉×#1278	C₂	semidirect
74. #9070	C₂₉	direct (N × H)
99. #2986	C₂×C₂₉	semidirect
100. #1526	C₂×C₂₉	semidirect
102. #1278	C₂×C₂₉	semidirect
161. C₂₉	#9070	direct (N × H)

H ≅ G/N

type

2. C₂₉×#2986

C₂

semidirect

3. C₂₉×#1526

C₂

semidirect

5. C₂₉×#1278

C₂

semidirect

74. #9070

C₂₉

direct (N × H)

99. #2986

C₂×C₂₉

semidirect

100. #1526

C₂×C₂₉

semidirect

102. #1278

C₂×C₂₉

semidirect

161. C₂₉

#9070

direct (N × H)

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

subgroup	index
C₂₉×#3131	2
C₂₉×#2986	2
C₂₉×#1526	2
C₂₉×#1484	2
C₂₉×#1278	2
#9070	29

subgroup

index

C₂₉×#3131

C₂₉×#2986

C₂₉×#1526

C₂₉×#1484

C₂₉×#1278

#9070

Subgroups — C₂₉×#9070 #20303970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#9070 #20303970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9070 #20303970