Group #15780393 — subgroups

Subgroups — #15780393

Order 3328.

486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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	#13124484	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718108	C₂	1	2	yes	maximal, complemented
3	#13114886	C₂	1	1	yes	maximal, characteristic, complemented
4	#13112951	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
7	#11719535	—	2	1	no	—
8	C₂²×D₁₀₄	C₂²	1	1	yes	characteristic
9	C₁₃×#504	—	2	4	no	—
10	C₂×C₁₃×M₃₂	—	2	2	no	—
11	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
12	#11718898	—	2	1	no	—
13	#11718796	C₄	1	4	yes	—
14	#11718792	—	2	1	no	—
15	#11718776	—	2	2	no	—
16	C₂×#88059	C₂²	1	2	yes	—
17	#11718767	C₂²	1	1	yes	characteristic
18	#11718152	—	2	1	no	—
19	#11718108	—	2	4	no	—
20	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
21	C₂²×D₅₂	—	2	1	no	—
22	C₁₃×#131	—	2	2	no	—
23	C₁₃×#131	—	2	2	no	—
24	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
25	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	D₄	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	#88201	—	4	1	no	—
29	#88194	—	4	1	no	—
30	#88191	—	4	2	no	—
31	#88184	—	2	4	no	—
32	#88180	—	2	1	no	—
33	C₂×#6099	—	2	2	no	—
34	C₂×D₁₀₄	—	2	2	no	—
35	C₂×D₁₀₄	—	2	2	no	—
36	C₂×D₁₀₄	—	2	1	no	—
37	C₂×D₁₀₄	C₂×C₄	1	2	yes	—
38	C₁₃×M₃₂	—	2	4	no	—
39	C₁₃×M₃₂	—	2	2	no	—
40	C₁₃×M₃₂	D₄	1	4	yes	complemented
41	C₂×C₁₃×C₁₆	—	2	4	no	—
42	C₂×C₁₃×C₁₆	—	2	2	no	—
43	#88076	—	4	1	no	—
44	#88073	—	4	1	no	—
45	#88061	—	2	4	no	—
46	#88059	—	2	2	no	—
47	#88059	—	2	2	no	—
48	#88058	—	2	1	no	—
49	#88057	C₂×C₄	1	2	yes	—
50	#13079	—	13	1	no	maximal, Sylow
51	C₂³×D₁₃	—	4	1	no	—
52	C₁₃×#41	—	2	2	no	—
53	C₁₃×#41	—	2	2	no	—
54	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
55	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
56	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₂²⋊D₁₃	—	4	4	no	—
60	C₂×D₅₂	—	2	2	no	—
61	C₂×D₅₂	—	4	2	no	—
62	C₂×D₅₂	—	4	2	no	—
63	C₂×D₅₂	—	4	1	no	—
64	C₁₃×M₁₆	—	2	2	no	—
65	C₁₃×M₁₆	—	2	4	no	—
66	C₂×C₈×C₁₃	—	2	2	no	—
67	C₂×C₈×C₁₃	—	2	2	no	—
68	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
71	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₁₃	#41	1	2	yes	—
73	C₂²⋊Dic₁₃	—	4	1	no	—
74	#6103	—	4	4	no	—
75	C₄⋊Dic₁₃	—	2	2	no	—
76	C₄×Dic₁₃	—	4	1	no	—
77	#6099	—	4	2	no	—
78	#6099	—	4	2	no	—
79	C₂×#1055	—	4	2	no	—
80	D₁₀₄	—	2	4	no	—
81	D₁₀₄	—	4	1	no	—
82	D₁₀₄	—	4	1	no	—
83	C₁₃×C₁₆	—	2	4	no	—
84	#3407	D₁₃	1	1	yes	characteristic, complemented
85	#3058	—	13	1	no	—
86	C₂×#361	—	13	2	no	—
87	#1813	—	13	1	no	—
88	#1389	—	13	2	no	—
89	C₂³×C₁₃	#102	1	2	yes	—
90	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
91	C₂²×D₁₃	—	4	2	no	—
92	C₂²×D₁₃	—	8	2	no	—
93	C₂²×D₁₃	—	16	2	no	—
94	Q₈×C₁₃	—	2	2	no	—
95	D₄×C₁₃	—	2	4	no	—
96	D₄×C₁₃	—	2	2	no	—
97	C₂×C₄×C₁₃	—	2	2	no	—
98	C₂×C₄×C₁₃	—	2	2	no	—
99	C₂×C₄×C₁₃	#102	1	2	yes	—
100	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₃	#121	1	2	yes	—
102	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
103	C₂×C₄×C₁₃	#135	1	2	yes	—
104	C₂²⋊D₁₃	—	16	4	no	—
105	C₂×Dic₁₃	—	4	2	no	—
106	D₅₂	—	4	2	no	—
107	D₅₂	—	4	2	no	—
108	D₅₂	—	8	2	no	—
109	C₈×C₁₃	—	2	2	no	—
110	C₈×C₁₃	C₄×D₄	1	2	yes	—
111	C₈×C₁₃	#120	1	1	yes	characteristic
112	C₈×C₁₃	#123	1	1	yes	characteristic
113	#1055	—	8	2	no	—
114	C₂²×D₈	—	13	1	no	—
115	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
116	#535	—	26	1	no	—
117	#504	—	2	4	no	—
118	C₂×M₃₂	—	2	2	no	—
119	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
120	#469	—	13	4	no	—
121	#466	—	26	2	no	—
122	C₂×#108	—	13	2	no	—
123	#427	—	13	1	no	—
124	#418	—	26	1	no	—
125	#413	—	26	1	no	—
126	#361	—	26	4	no	—
127	#338	—	26	1	no	—
128	C₂²×C₁₃	—	2	2	no	—
129	C₂²×C₁₃	—	4	1	no	—
130	C₂²×C₁₃	—	4	2	no	—
131	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
132	C₂²×C₁₃	#465	1	2	yes	—
133	C₂×D₁₃	—	8	4	no	—
134	C₂×D₁₃	—	8	2	no	—
135	C₂×D₁₃	—	16	4	no	—
136	C₄×C₁₃	—	2	2	no	—
137	C₄×C₁₃	#386	1	1	yes	characteristic
138	C₄×C₁₃	#416	1	1	yes	characteristic
139	C₄×C₁₃	#466	1	2	yes	—
140	Dic₁₃	—	8	2	no	—
141	C₂×#41	D₅₂	1	1	yes	characteristic
142	C₂²×D₄	—	26	1	no	—
143	C₂×D₈	—	13	2	no	—
144	C₂×D₈	—	26	2	no	—
145	C₂×D₈	—	26	2	no	—
146	C₂×D₈	—	26	1	no	—
147	#131	—	2	2	no	—
148	#131	—	2	2	no	—
149	C₂×M₁₆	—	26	2	no	—
150	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
151	C₂×M₁₆	D₅₂	1	1	yes	characteristic
152	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
153	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
154	#127	—	52	1	no	—
155	#124	—	52	1	no	—
156	#121	—	26	4	no	—
157	#120	—	52	2	no	—
158	#117	—	26	1	no	—
159	M₃₂	—	2	4	no	—
160	M₃₂	—	2	2	no	—
161	M₃₂	C₂²⋊D₁₃	1	4	yes	complemented
162	C₂×C₁₆	—	2	4	no	—
163	C₂×C₁₆	—	2	2	no	—
164	#108	—	26	2	no	—
165	#108	—	26	2	no	—
166	#107	—	26	1	no	—
167	#106	—	13	2	no	—
168	#102	—	26	4	no	—
169	#101	—	52	1	no	—
170	#100	—	52	1	no	—
171	C₂×C₁₃	—	2	1	no	—
172	C₂×C₁₃	—	2	2	no	—
173	C₂×C₁₃	—	4	2	no	—
174	C₂×C₁₃	#1893	1	1	yes	characteristic
175	D₁₃	—	16	2	no	—
176	C₂⁴	—	52	1	no	—
177	#41	—	2	2	no	—
178	#41	—	2	2	no	—
179	C₂×Q₈	D₁₀₄	1	1	yes	characteristic
180	C₂×D₄	—	26	2	no	—
181	C₂×D₄	—	52	4	no	—
182	C₂×D₄	—	52	1	no	—
183	C₂×D₄	—	52	2	no	—
184	C₂×D₄	—	52	2	no	—
185	C₂×D₄	#6095	1	2	yes	—
186	C₂×D₄	D₁₀₄	1	1	yes	characteristic
187	C₂²×C₄	#6103	1	2	yes	—
188	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
189	D₈	—	26	4	no	—
190	D₈	—	52	1	no	—
191	D₈	—	52	1	no	—
192	M₁₆	—	2	2	no	—
193	M₁₆	—	2	4	no	—
194	M₁₆	—	52	2	no	—
195	M₁₆	—	52	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	52	2	no	—
199	C₂×C₈	#6103	1	2	yes	—
200	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
201	C₂×C₈	#6127	1	2	yes	—
202	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
203	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
204	C₄⋊C₄	—	26	2	no	—
205	C₂²⋊C₄	—	52	1	no	—
206	C₂²⋊C₄	—	52	4	no	—
207	C₄²	—	52	1	no	—
208	C₁₆	—	2	4	no	—
209	C₁₃	#13079	1	1	yes	characteristic, complemented, Sylow
210	C₂³	—	52	2	no	—
211	C₂³	—	104	2	no	—
212	C₂³	—	208	2	no	—
213	C₂³	#88061	1	2	yes	—
214	C₂³	C₂×#6095	1	1	yes	characteristic
215	Q₈	—	2	2	no	—
216	D₄	—	2	4	no	—
217	D₄	—	2	2	no	—
218	D₄	—	52	2	no	—
219	D₄	—	52	2	no	—
220	D₄	—	104	2	no	—
221	D₄	—	208	4	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	52	2	no	—
225	C₂×C₄	#88061	1	2	yes	—
226	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
227	C₂×C₄	#88158	1	2	yes	—
228	C₂×C₄	C₂×#6103	1	1	yes	characteristic
229	C₂×C₄	#88184	1	2	yes	—
230	C₈	—	2	2	no	—
231	C₈	—	104	2	no	—
232	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
233	C₈	#88183	1	1	yes	characteristic
234	C₈	#88207	1	1	yes	characteristic
235	C₂²	—	2	2	no	—
236	C₂²	—	4	1	no	—
237	C₂²	—	4	2	no	—
238	C₂²	—	104	4	no	—
239	C₂²	—	104	2	no	—
240	C₂²	—	208	4	no	—
241	C₂²	C₂×#88061	1	1	yes	characteristic
242	C₂²	#11718775	1	2	yes	—
243	C₄	—	2	2	no	—
244	C₄	—	104	2	no	—
245	C₄	#11718774	1	1	yes	characteristic
246	C₄	#11718776	1	2	yes	—
247	C₄	#11718874	1	1	yes	characteristic
248	C₂	—	2	1	no	—
249	C₂	—	2	2	no	—
250	C₂	—	4	2	no	—
251	C₂	—	208	2	no	—
252	C₂	#13115264	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13124484

C₂

yes

maximal, characteristic

C₂×#11718108

C₂

yes

maximal, complemented

#13114886

C₂

yes

maximal, characteristic, complemented

#13112951

C₂

yes

maximal, complemented

C₁₃×#3407

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×#131

C₂²

yes

characteristic

#11719535

—

C₂²×D₁₀₄

C₂²

yes

characteristic

C₁₃×#504

—

C₂×C₁₃×M₃₂

—

C₂×C₁₃×M₃₂

C₂²

yes

—

#11718898

—

#11718796

C₄

yes

—

#11718792

—

#11718776

—

C₂×#88059

C₂²

yes

—

#11718767

C₂²

yes

characteristic

#11718152

—

#11718108

—

C₂×C₁₃×#41

D₄

yes

characteristic

C₂²×D₅₂

—

C₁₃×#131

—

C₁₃×#131

—

C₂×C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₁₃×M₁₆

D₄

yes

characteristic

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

—

—

—

—

—

—

C₂×D₁₀₄

—

C₂×D₁₀₄

—

C₂×D₁₀₄

—

C₂×D₁₀₄

C₂×C₄

yes

—

C₁₃×M₃₂

—

C₁₃×M₃₂

—

C₁₃×M₃₂

D₄

yes

complemented

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

—

—

—

—

—

—

—

C₂×C₄

yes

—

#13079

—

maximal, Sylow

C₂³×D₁₃

—

C₁₃×#41

—

C₁₃×#41

—

C₂×Q₈×C₁₃

D₈

yes

characteristic

C₂×D₄×C₁₃

D₈

yes

characteristic

C₂×D₄×C₁₃

SD₁₆

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₃

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₂²⋊Dic₁₃

—

#6103

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

#6099

—

#6099

—

C₂×#1055

—

D₁₀₄

—

D₁₀₄

—

D₁₀₄

—

C₁₃×C₁₆

—

#3407

D₁₃

yes

characteristic, complemented

—

—

—

—

C₂³×C₁₃

#102

yes

—

C₂³×C₁₃

C₂×SD₁₆

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#102

yes

—

100

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

101

C₂×C₄×C₁₃

#121

yes

—

102

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

103

C₂×C₄×C₁₃

#135

yes

—

104

C₂²⋊D₁₃

—

105

C₂×Dic₁₃

—

106

D₅₂

—

107

D₅₂

—

108

D₅₂

—

109

C₈×C₁₃

—

110

C₈×C₁₃

C₄×D₄

yes

—

111

C₈×C₁₃

#120

yes

characteristic

112

C₈×C₁₃

#123

yes

characteristic

113

#1055

—

114

C₂²×D₈

—

115

C₂×#131

C₂×D₁₃

yes

characteristic

116

#535

—

117

#504

—

118

C₂×M₃₂

—

119

C₂×M₃₂

C₂×D₁₃

yes

—

120

#469

—

121

#466

—

122

C₂×#108

—

123

#427

—

124

#418

—

125

#413

—

126

#361

—

127

#338

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

—

130

C₂²×C₁₃

—

131

C₂²×C₁₃

C₂×#102

yes

characteristic

132

C₂²×C₁₃

#465

yes

—

133

C₂×D₁₃

—

134

C₂×D₁₃

—

135

C₂×D₁₃

—

136

C₄×C₁₃

—

137

C₄×C₁₃

#386

yes

characteristic

138

C₄×C₁₃

#416

yes

characteristic

139

C₄×C₁₃

#466

yes

—

140

Dic₁₃

—

141

C₂×#41

D₅₂

yes

characteristic

142

C₂²×D₄

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂×D₈

—

146

C₂×D₈

—

147

#131

—

148

#131

—

149

C₂×M₁₆

—

150

C₂×M₁₆

C₄×D₁₃

yes

—

151

C₂×M₁₆

D₅₂

yes

characteristic

152

C₂²×C₈

C₂²⋊D₁₃

yes

—

153

C₂²×C₈

C₂²×D₁₃

yes

characteristic

154

#127

—

155

#124

—

156

#121

—

157

#120

—

158

#117

—

159

M₃₂

—

160

M₃₂

—

161

M₃₂

C₂²⋊D₁₃

yes

complemented

162

C₂×C₁₆

—

163

C₂×C₁₆

—

164

#108

—

165

#108

—

166

#107

—

167

#106

—

168

#102

—

169

#101

—

170

#100

—

171

C₂×C₁₃

—

172

C₂×C₁₃

—

173

C₂×C₁₃

—

174

C₂×C₁₃

#1893

yes

characteristic

175

D₁₃

—

176

C₂⁴

—

177

#41

—

178

#41

—

179

C₂×Q₈

D₁₀₄

yes

characteristic

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

#6095

yes

—

186

C₂×D₄

D₁₀₄

yes

characteristic

187

C₂²×C₄

#6103

yes

—

188

C₂²×C₄

C₂×D₅₂

yes

characteristic

189

D₈

—

190

D₈

—

191

D₈

—

192

M₁₆

—

193

M₁₆

—

194

M₁₆

—

195

M₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

#6103

yes

—

200

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

201

C₂×C₈

#6127

yes

—

202

C₂×C₈

C₂×C₂²⋊D₁₃

yes

—

203

C₂×C₈

C₂×C₂²⋊D₁₃

yes

characteristic

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

—

208

C₁₆

—

209

C₁₃

#13079

yes

characteristic, complemented, Sylow

210

C₂³

—

211

C₂³

—

104

—

212

C₂³

—

208

—

213

C₂³

#88061

yes

—

214

C₂³

C₂×#6095

yes

characteristic

215

Q₈

—

216

D₄

—

217

D₄

—

218

D₄

—

219

D₄

—

220

D₄

—

104

—

221

D₄

—

208

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

#88061

yes

—

226

C₂×C₄

C₂×D₁₀₄

yes

characteristic

227

C₂×C₄

#88158

yes

—

228

C₂×C₄

C₂×#6103

yes

characteristic

229

C₂×C₄

#88184

yes

—

230

C₈

—

231

C₈

—

104

—

232

C₈

C₄×C₂²⋊D₁₃

yes

—

233

C₈

#88183

yes

characteristic

234

C₈

#88207

yes

characteristic

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

104

—

239

C₂²

—

104

—

240

C₂²

—

208

—

241

C₂²

C₂×#88061

yes

characteristic

242

C₂²

#11718775

yes

—

243

C₄

—

244

C₄

—

104

—

245

C₄

#11718774

yes

characteristic

246

C₄

#11718776

yes

—

247

C₄

#11718874

yes

characteristic

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

—

208

—

252

C₂

#13115264

yes

characteristic

	subgroup	G/H
center	C₂	#13115264
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#3407	C₂
socle	C₂×C₁₃	#1893
prime radical	#13124484	C₂
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#3407	D₁₃
hypocenter	C₁₃	#13079
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#13115264

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#3407

C₂

C₂×C₁₃

C₂

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. C₂×#11718108	C₂	semidirect
3. #13114886	C₂	semidirect
4. #13112951	C₂	semidirect
5. C₁₃×#3407	C₂	semidirect
40. C₁₃×M₃₂	D₄	semidirect
84. #3407	D₁₃	semidirect
161. M₃₂	C₂²⋊D₁₃	semidirect
209. C₁₃	#13079	semidirect

H ≅ G/N

type

2. C₂×#11718108

C₂

semidirect

3. #13114886

C₂

semidirect

4. #13112951

C₂

semidirect

5. C₁₃×#3407

C₂

semidirect

40. C₁₃×M₃₂

D₄

semidirect

84. #3407

D₁₃

semidirect

161. M₃₂

C₂²⋊D₁₃

semidirect

209. C₁₃

#13079

semidirect

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

subgroup	index
#13124484	2
C₂×#11718108	2
#13114886	2
#13112951	2
C₁₃×#3407	2
#13079	13

subgroup

index

C₁₃×#3407

Subgroups — #15780393

Conjugacy classes of subgroups

Complements

Maximal subgroups