Group #15699874 — subgroups

Subgroups — C₁₃×#13535 #15699874

Order 3328.

354 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 114 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×C₁₃×#365	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#361	C₂	1	2	yes	maximal
3	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1849	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
8	C₂×C₁₃×#108	—	2	1	no	—
9	C₂×C₁₃×#108	C₂²	1	2	yes	—
10	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
11	C₁₃×#423	—	2	1	no	—
12	C₂×C₁₃×#102	—	2	1	no	—
13	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
14	C₁₃×#390	—	2	1	no	—
15	C₁₃×#365	—	2	4	no	—
16	C₁₃×#361	—	2	4	no	—
17	C₂²×D₄×C₁₃	—	2	1	no	—
18	C₂×C₁₃×D₈	—	2	2	no	—
19	C₂×C₁₃×D₈	—	2	2	no	—
20	C₂×C₁₃×D₈	—	2	1	no	—
21	C₂×C₁₃×D₈	Q₈	1	2	yes	—
22	C₂×C₁₃×M₁₆	—	2	2	no	—
23	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
27	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
28	C₁₃×M₃₂	—	2	2	no	—
29	C₁₃×M₃₂	D₄	1	4	yes	—
30	C₂×C₁₃×C₁₆	—	2	2	no	—
31	C₁₃×#108	—	2	2	no	—
32	C₁₃×#108	—	2	2	no	—
33	C₁₃×#108	—	4	2	no	—
34	C₁₃×#106	—	2	2	no	—
35	C₁₃×C₄⋊C₈	—	4	2	no	—
36	C₁₃×#102	—	4	2	no	—
37	C₁₃×#97	—	2	2	no	—
38	#13535	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂⁴×C₁₃	—	4	1	no	—
40	C₂×D₄×C₁₃	—	2	2	no	—
41	C₂×D₄×C₁₃	—	4	1	no	—
42	C₂×D₄×C₁₃	—	4	1	no	—
43	C₂×D₄×C₁₃	—	4	1	no	—
44	C₂×D₄×C₁₃	—	4	1	no	—
45	C₂×D₄×C₁₃	—	4	1	no	—
46	C₂²×C₄×C₁₃	—	4	1	no	—
47	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₁₃×D₈	—	2	4	no	—
50	C₁₃×D₈	—	4	2	no	—
51	C₁₃×M₁₆	—	4	2	no	—
52	C₁₃×M₁₆	—	4	2	no	—
53	C₂×C₈×C₁₃	—	2	1	no	—
54	C₂×C₈×C₁₃	—	2	1	no	—
55	C₂×C₈×C₁₃	—	4	2	no	—
56	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
57	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
58	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₈×C₁₃	#41	1	2	yes	—
60	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
61	C₁₃×C₄⋊C₄	—	4	1	no	—
62	C₁₃×C₄⋊C₄	—	4	1	no	—
63	C₁₃×C₂²⋊C₄	—	8	4	no	—
64	C₄²×C₁₃	—	2	1	no	—
65	C₄²×C₁₃	—	2	1	no	—
66	C₁₃×C₁₆	—	2	4	no	—
67	C₂×#365	C₂×C₁₃	1	2	yes	complemented
68	C₂×#361	C₂×C₁₃	1	2	yes	—
69	#1972	C₂×C₁₃	1	1	yes	characteristic
70	#1849	C₂×C₁₃	1	1	yes	characteristic, complemented
71	#1377	C₂×C₁₃	1	1	yes	characteristic, complemented
72	C₂³×C₁₃	—	4	2	no	—
73	C₂³×C₁₃	—	8	2	no	—
74	C₂³×C₁₃	—	8	2	no	—
75	C₂³×C₁₃	—	8	1	no	—
76	C₂³×C₁₃	—	8	1	no	—
77	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
78	D₄×C₁₃	—	4	2	no	—
79	D₄×C₁₃	—	4	2	no	—
80	D₄×C₁₃	—	8	1	no	—
81	D₄×C₁₃	—	8	1	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	—	4	2	no	—
84	C₂×C₄×C₁₃	—	8	2	no	—
85	C₂×C₄×C₁₃	—	8	1	no	—
86	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
88	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₈×C₁₃	—	2	2	no	—
93	C₈×C₁₃	—	8	2	no	—
94	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
95	C₈×C₁₃	#123	1	2	yes	—
96	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
97	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
98	C₂×#108	—	2	1	no	—
99	C₂×#108	C₂²×C₁₃	1	2	yes	—
100	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
101	#423	—	2	1	no	—
102	C₂×#102	—	2	1	no	—
103	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
104	#390	—	2	1	no	—
105	#365	—	2	4	no	—
106	#361	—	2	4	no	—
107	C₂²×C₁₃	—	2	2	no	—
108	C₂²×C₁₃	—	8	4	no	—
109	C₂²×C₁₃	—	8	2	no	—
110	C₂²×C₁₃	—	16	1	no	—
111	C₂²×C₁₃	—	16	1	no	—
112	C₂²×C₁₃	—	16	2	no	—
113	C₂²×C₁₃	#476	1	1	yes	characteristic
114	C₂²×C₁₃	#481	1	1	yes	characteristic
115	C₂²×C₁₃	#492	1	1	yes	characteristic
116	C₄×C₁₃	—	4	2	no	—
117	C₄×C₁₃	—	16	1	no	—
118	C₄×C₁₃	#399	1	1	yes	characteristic
119	C₄×C₁₃	#476	1	1	yes	characteristic
120	C₄×C₁₃	#481	1	1	yes	characteristic
121	C₄×C₁₃	#496	1	1	yes	characteristic
122	C₂²×D₄	—	2	1	no	—
123	C₂×D₈	—	2	2	no	—
124	C₂×D₈	—	2	2	no	—
125	C₂×D₈	—	2	1	no	—
126	C₂×D₈	Q₈×C₁₃	1	2	yes	—
127	C₂×M₁₆	—	2	2	no	—
128	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
129	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
130	C₂×C₄⋊C₄	—	2	1	no	—
131	C₂×C₂²⋊C₄	—	4	2	no	—
132	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
133	M₃₂	—	2	2	no	—
134	M₃₂	D₄×C₁₃	1	4	yes	—
135	C₂×C₁₆	—	2	2	no	—
136	#108	—	2	2	no	—
137	#108	—	2	2	no	—
138	#108	—	4	2	no	—
139	#106	—	2	2	no	—
140	C₄⋊C₈	—	4	2	no	—
141	#102	—	4	2	no	—
142	#97	—	2	2	no	—
143	C₂×C₁₃	—	2	1	no	—
144	C₂×C₁₃	—	2	1	no	—
145	C₂×C₁₃	—	16	2	no	—
146	C₂×C₁₃	#2094	1	1	yes	characteristic
147	C₂×C₁₃	#2238	1	2	yes	—
148	C₂⁴	—	4	1	no	—
149	C₂×D₄	—	2	2	no	—
150	C₂×D₄	—	4	1	no	—
151	C₂×D₄	—	4	1	no	—
152	C₂×D₄	—	4	1	no	—
153	C₂×D₄	—	4	1	no	—
154	C₂×D₄	—	4	1	no	—
155	C₂²×C₄	—	4	1	no	—
156	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
157	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
158	D₈	—	2	4	no	—
159	D₈	—	4	2	no	—
160	M₁₆	—	4	2	no	—
161	M₁₆	—	4	2	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	2	1	no	—
164	C₂×C₈	—	4	2	no	—
165	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
166	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
167	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
168	C₂×C₈	C₁₃×#41	1	2	yes	—
169	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
170	C₄⋊C₄	—	4	1	no	—
171	C₄⋊C₄	—	4	1	no	—
172	C₂²⋊C₄	—	8	4	no	—
173	C₄²	—	2	1	no	—
174	C₄²	—	2	1	no	—
175	C₁₆	—	2	4	no	—
176	C₁₃	#13535	1	1	yes	characteristic, direct product factor, Sylow
177	C₂³	—	4	2	no	—
178	C₂³	—	8	2	no	—
179	C₂³	—	8	2	no	—
180	C₂³	—	8	1	no	—
181	C₂³	—	8	1	no	—
182	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
183	D₄	—	4	2	no	—
184	D₄	—	4	2	no	—
185	D₄	—	8	1	no	—
186	D₄	—	8	1	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	1	no	—
191	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
193	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
194	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
195	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₈	—	2	2	no	—
198	C₈	—	8	2	no	—
199	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
200	C₈	C₁₃×#123	1	2	yes	—
201	C₂²	—	2	2	no	—
202	C₂²	—	8	4	no	—
203	C₂²	—	8	2	no	—
204	C₂²	—	16	1	no	—
205	C₂²	—	16	1	no	—
206	C₂²	—	16	2	no	—
207	C₂²	C₁₃×#476	1	1	yes	characteristic
208	C₂²	C₁₃×#481	1	1	yes	characteristic
209	C₂²	C₁₃×#492	1	1	yes	characteristic
210	C₄	—	4	2	no	—
211	C₄	—	16	1	no	—
212	C₄	C₁₃×#399	1	1	yes	characteristic
213	C₄	C₁₃×#476	1	1	yes	characteristic
214	C₄	C₁₃×#481	1	1	yes	characteristic
215	C₄	C₁₃×#496	1	1	yes	characteristic
216	C₂	—	2	1	no	—
217	C₂	—	2	1	no	—
218	C₂	—	16	2	no	—
219	C₂	C₁₃×#2094	1	1	yes	characteristic
220	C₂	C₁₃×#2238	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#365

C₂

yes

maximal, complemented

C₂×C₁₃×#361

C₂

yes

maximal

C₁₃×#1972

C₂

yes

maximal, characteristic

C₁₃×#1849

C₂

yes

maximal, characteristic, complemented

C₁₃×#1377

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₃×D₈

C₂²

yes

characteristic

C₂×C₁₃×M₃₂

C₂²

yes

—

C₂×C₁₃×#108

—

C₂×C₁₃×#108

C₂²

yes

—

C₂×C₁₃×#106

C₂²

yes

characteristic

C₁₃×#423

—

C₂×C₁₃×#102

—

C₂×C₁₃×#97

C₂²

yes

characteristic

C₁₃×#390

—

C₁₃×#365

—

C₁₃×#361

—

C₂²×D₄×C₁₃

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

Q₈

yes

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₁₃×M₃₂

—

C₁₃×M₃₂

D₄

yes

—

C₂×C₁₃×C₁₆

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×#106

—

C₁₃×C₄⋊C₈

—

C₁₃×#102

—

C₁₃×#97

—

#13535

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

SD₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×D₈

—

C₁₃×D₈

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₂×C₈×C₁₃

#41

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₁₃×C₁₆

—

C₂×#365

C₂×C₁₃

yes

complemented

C₂×#361

C₂×C₁₃

yes

—

#1972

C₂×C₁₃

yes

characteristic

#1849

C₂×C₁₃

yes

characteristic, complemented

#1377

C₂×C₁₃

yes

characteristic, complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×SD₁₆

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

C₂×SD₁₆

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

C₂²⋊Q₈

yes

—

C₈×C₁₃

#123

yes

—

C₂²×D₈

C₂²×C₁₃

yes

characteristic

C₂×M₃₂

C₂²×C₁₃

yes

—

C₂×#108

—

C₂×#108

C₂²×C₁₃

yes

—

100

C₂×#106

C₂²×C₁₃

yes

characteristic

101

#423

—

102

C₂×#102

—

103

C₂×#97

C₂²×C₁₃

yes

characteristic

104

#390

—

105

#365

—

106

#361

—

107

C₂²×C₁₃

—

108

C₂²×C₁₃

—

109

C₂²×C₁₃

—

110

C₂²×C₁₃

—

111

C₂²×C₁₃

—

112

C₂²×C₁₃

—

113

C₂²×C₁₃

#476

yes

characteristic

114

C₂²×C₁₃

#481

yes

characteristic

115

C₂²×C₁₃

#492

yes

characteristic

116

C₄×C₁₃

—

117

C₄×C₁₃

—

118

C₄×C₁₃

#399

yes

characteristic

119

C₄×C₁₃

#476

yes

characteristic

120

C₄×C₁₃

#481

yes

characteristic

121

C₄×C₁₃

#496

yes

characteristic

122

C₂²×D₄

—

123

C₂×D₈

—

124

C₂×D₈

—

125

C₂×D₈

—

126

C₂×D₈

Q₈×C₁₃

yes

—

127

C₂×M₁₆

—

128

C₂²×C₈

D₄×C₁₃

yes

characteristic

129

C₂²×C₈

C₂³×C₁₃

yes

characteristic

130

C₂×C₄⋊C₄

—

131

C₂×C₂²⋊C₄

—

132

C₂×C₄²

D₄×C₁₃

yes

characteristic

133

M₃₂

—

134

M₃₂

D₄×C₁₃

yes

—

135

C₂×C₁₆

—

136

#108

—

137

#108

—

138

#108

—

139

#106

—

140

C₄⋊C₈

—

141

#102

—

142

#97

—

143

C₂×C₁₃

—

144

C₂×C₁₃

—

145

C₂×C₁₃

—

146

C₂×C₁₃

#2094

yes

characteristic

147

C₂×C₁₃

#2238

yes

—

148

C₂⁴

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂²×C₄

—

156

C₂²×C₄

C₁₃×SD₁₆

yes

—

157

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

158

D₈

—

159

D₈

—

160

M₁₆

—

161

M₁₆

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

C₁₃×SD₁₆

yes

—

166

C₂×C₈

C₂×D₄×C₁₃

yes

—

167

C₂×C₈

C₂×Q₈×C₁₃

yes

characteristic

168

C₂×C₈

C₁₃×#41

yes

—

169

C₂×C₈

C₁₃×#41

yes

characteristic

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₂²⋊C₄

—

173

C₄²

—

174

C₄²

—

175

C₁₆

—

176

C₁₃

#13535

yes

characteristic, direct product factor, Sylow

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

C₂×C₁₃×SD₁₆

yes

characteristic

183

D₄

—

184

D₄

—

185

D₄

—

186

D₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

characteristic

192

C₂×C₄

C₁₃×#123

yes

characteristic

193

C₂×C₄

C₁₃×#127

yes

characteristic

194

C₂×C₄

C₂×C₁₃×SD₁₆

yes

characteristic

195

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

characteristic

196

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

characteristic

197

C₈

—

198

C₈

—

199

C₈

C₁₃×C₂²⋊Q₈

yes

—

200

C₈

C₁₃×#123

yes

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

C₁₃×#476

yes

characteristic

208

C₂²

C₁₃×#481

yes

characteristic

209

C₂²

C₁₃×#492

yes

characteristic

210

C₄

—

211

C₄

—

212

C₄

C₁₃×#399

yes

characteristic

213

C₄

C₁₃×#476

yes

characteristic

214

C₄

C₁₃×#481

yes

characteristic

215

C₄

C₁₃×#496

yes

characteristic

216

C₂

—

217

C₂

—

218

C₂

—

219

C₂

C₁₃×#2094

yes

characteristic

220

C₂

C₁₃×#2238

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#481
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#481

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

prime radical

C₂²×C₁₃×D₈

C₂²

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

N	H ≅ G/N	type
1. C₂×C₁₃×#365	C₂	semidirect
4. C₁₃×#1849	C₂	semidirect
5. C₁₃×#1377	C₂	semidirect
38. #13535	C₁₃	direct (N × H)
67. C₂×#365	C₂×C₁₃	semidirect
70. #1849	C₂×C₁₃	semidirect
71. #1377	C₂×C₁₃	semidirect
176. C₁₃	#13535	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₃×#365

C₂

semidirect

4. C₁₃×#1849

C₂

semidirect

5. C₁₃×#1377

C₂

semidirect

38. #13535

C₁₃

direct (N × H)

67. C₂×#365

C₂×C₁₃

semidirect

70. #1849

C₂×C₁₃

semidirect

71. #1377

C₂×C₁₃

semidirect

176. C₁₃

#13535

direct (N × H)

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

subgroup	index
C₂×C₁₃×#365	2
C₂×C₁₃×#361	2
C₁₃×#1972	2
C₁₃×#1849	2
C₁₃×#1377	2
#13535	13

subgroup

index

C₂×C₁₃×#365

C₂×C₁₃×#361

C₁₃×#1972

C₁₃×#1849

C₁₃×#1377

#13535

Subgroups — C₁₃×#13535 #15699874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#13535 #15699874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13535 #15699874