Group #15756145 — subgroups

Subgroups — #15756145

Order 3328.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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	#13123770	C₂	1	1	yes	maximal, characteristic
2	#13113584	C₂	1	1	yes	maximal, characteristic
3	#13113399	C₂	1	2	yes	maximal
4	#13112694	C₂	1	2	yes	maximal
5	C₁₃×#1835	C₂	1	1	yes	maximal, characteristic
6	#11719175	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#382	C₂²	1	2	yes	—
9	#11718763	—	2	1	no	—
10	#11718762	—	2	1	no	—
11	#11718586	C₂²	1	2	yes	—
12	#11718585	C₂²	1	1	yes	characteristic
13	#11718340	—	2	1	no	—
14	#11718340	C₄	1	2	yes	complemented
15	C₈×Dic₂₆	—	2	1	no	—
16	C₈×Dic₂₆	C₄	1	2	yes	complemented
17	C₁₃×#340	—	2	1	no	—
18	C₁₃×#340	—	2	1	no	—
19	#11718050	—	2	1	no	—
20	#11718049	—	2	1	no	—
21	#11718044	—	2	4	no	—
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	#88180	—	2	1	no	—
27	#88178	—	2	1	no	—
28	#88178	D₄	1	2	yes	—
29	C₂×#6099	—	2	1	no	—
30	#88124	—	2	1	no	—
31	#88123	Q₈	1	1	yes	characteristic
32	#88123	Q₈	1	1	yes	characteristic
33	C₄×Dic₂₆	—	2	1	no	—
34	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
38	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
39	C₁₃×#95	—	2	2	no	—
40	C₁₃×#95	—	2	2	no	—
41	C₂²⋊#1055	—	2	2	no	—
42	#88055	—	2	2	no	—
43	#88054	—	2	2	no	—
44	#88054	—	2	2	no	—
45	C₈×Dic₁₃	—	2	2	no	—
46	C₄⋊#1055	—	2	1	no	—
47	C₄⋊#1055	—	2	2	no	—
48	C₄⋊#1055	C₂×C₄	1	2	yes	—
49	C₄×#1055	—	2	2	no	—
50	#8679	—	13	1	no	maximal, Sylow
51	C₂²×C₄×C₁₃	—	4	2	no	—
52	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
55	C₂×Dic₂₆	—	2	1	no	—
56	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	—	2	2	no	—
59	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
68	C₄²×C₁₃	#41	1	1	yes	characteristic
69	C₂²⋊Dic₁₃	—	2	2	no	—
70	C₄⋊Dic₁₃	—	2	1	no	—
71	C₄⋊Dic₁₃	—	2	1	no	—
72	C₄⋊Dic₁₃	—	2	1	no	—
73	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
74	#6101	—	2	2	no	—
75	#6101	—	2	2	no	—
76	C₄×Dic₁₃	—	2	2	no	—
77	#6099	—	4	2	no	—
78	C₂×#1055	—	2	2	no	—
79	C₂×#1055	—	4	2	no	—
80	#2960	—	13	1	no	—
81	#1835	D₁₃	1	1	yes	characteristic
82	#1564	—	13	1	no	—
83	#1518	—	13	2	no	—
84	#1286	—	13	2	no	—
85	C₂³×C₁₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₁₃	—	4	1	no	—
87	C₂×C₄×C₁₃	—	4	1	no	—
88	C₂×C₄×C₁₃	—	8	2	no	—
89	C₂×C₄×C₁₃	—	8	2	no	—
90	C₂×C₄×C₁₃	—	8	2	no	—
91	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₁₃	#135	1	2	yes	—
98	C₂×C₄×C₁₃	#137	1	2	yes	—
99	C₂×Dic₁₃	—	2	2	no	—
100	C₂×Dic₁₃	—	2	2	no	—
101	Dic₂₆	—	4	2	no	—
102	Dic₂₆	—	4	2	no	—
103	C₈×C₁₃	—	2	1	no	—
104	C₈×C₁₃	—	2	1	no	—
105	C₈×C₁₃	—	2	1	no	—
106	C₈×C₁₃	—	2	1	no	—
107	#1055	—	4	2	no	—
108	#1055	—	8	2	no	—
109	#533	—	13	1	no	—
110	#446	—	13	2	no	—
111	#446	—	26	1	no	—
112	C₈×Q₈	—	13	2	no	—
113	C₈×Q₈	—	26	1	no	—
114	#431	—	13	2	no	—
115	#424	—	26	1	no	—
116	#423	—	13	1	no	—
117	#405	—	26	1	no	—
118	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
119	#382	C₂×D₁₃	1	2	yes	—
120	#340	—	2	1	no	—
121	#340	—	2	1	no	—
122	#335	—	26	1	no	—
123	#334	—	26	1	no	—
124	#328	—	26	4	no	—
125	C₂²×C₁₃	—	2	1	no	—
126	C₂²×C₁₃	—	2	1	no	—
127	C₂²×C₁₃	#380	1	1	yes	characteristic
128	C₂²×C₁₃	#464	1	2	yes	—
129	C₄×C₁₃	—	2	1	no	—
130	C₄×C₁₃	—	2	1	no	—
131	C₄×C₁₃	—	2	1	no	—
132	C₄×C₁₃	—	2	1	no	—
133	C₄×C₁₃	—	16	2	no	—
134	C₄×C₁₃	#416	1	1	yes	characteristic
135	C₄×C₁₃	#419	1	1	yes	characteristic
136	C₄×C₁₃	#479	1	2	yes	—
137	Dic₁₃	—	4	2	no	—
138	Dic₁₃	—	4	2	no	—
139	C₂×M₁₆	—	26	1	no	—
140	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
141	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
142	C₄⋊Q₈	—	13	1	no	—
143	C₄⋊Q₈	—	13	1	no	—
144	#125	—	26	1	no	—
145	C₂²⋊Q₈	—	13	2	no	—
146	C₂²⋊Q₈	—	26	1	no	—
147	C₄×Q₈	—	13	2	no	—
148	C₄×Q₈	—	26	1	no	—
149	#117	—	26	1	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
152	C₄⋊C₈	—	13	2	no	—
153	C₄⋊C₈	—	26	2	no	—
154	C₄⋊C₈	—	26	2	no	—
155	C₄⋊C₈	—	26	1	no	—
156	C₄⋊C₈	—	26	2	no	—
157	C₂²⋊C₈	—	26	2	no	—
158	#97	—	26	2	no	—
159	C₄×C₈	—	26	2	no	—
160	C₄×C₈	—	26	2	no	—
161	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
162	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
163	C₄×C₈	D₅₂	1	1	yes	characteristic
164	C₄×C₈	D₅₂	1	1	yes	characteristic
165	#95	—	2	2	no	—
166	#95	—	2	2	no	—
167	C₂×C₁₃	—	2	2	no	—
168	C₂×C₁₃	#1805	1	1	yes	characteristic
169	C₂×C₁₃	#1812	1	1	yes	characteristic
170	C₂×C₁₃	#1814	1	1	yes	characteristic
171	C₂×Q₈	—	13	2	no	—
172	C₂×Q₈	—	26	1	no	—
173	C₂²×C₄	—	4	2	no	—
174	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
175	C₂²×C₄	#6129	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
177	M₁₆	—	52	2	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	26	2	no	—
181	C₂×C₈	—	52	2	no	—
182	C₂×C₈	#6103	1	1	yes	characteristic
183	C₂×C₈	#6103	1	1	yes	characteristic
184	C₂×C₈	#6103	1	1	yes	characteristic
185	C₂×C₈	#6103	1	1	yes	characteristic
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	13	2	no	—
189	C₄⋊C₄	—	26	2	no	—
190	C₄⋊C₄	—	26	2	no	—
191	C₄⋊C₄	—	26	1	no	—
192	C₄⋊C₄	—	26	1	no	—
193	C₄⋊C₄	—	26	1	no	—
194	C₂²⋊C₄	—	26	2	no	—
195	C₄²	—	26	2	no	—
196	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
197	C₄²	C₂×D₅₂	1	1	yes	characteristic
198	C₄²	Q₈×D₁₃	1	1	yes	characteristic
199	C₄²	#6131	1	1	yes	characteristic
200	C₁₃	#8679	1	1	yes	characteristic, complemented, Sylow
201	C₂³	#88192	1	1	yes	characteristic
202	Q₈	—	52	2	no	—
203	Q₈	—	52	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	8	2	no	—
207	C₂×C₄	—	8	2	no	—
208	C₂×C₄	—	8	2	no	—
209	C₂×C₄	—	26	2	no	—
210	C₂×C₄	—	26	2	no	—
211	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
212	C₂×C₄	#88146	1	1	yes	characteristic
213	C₂×C₄	#88149	1	1	yes	characteristic
214	C₂×C₄	#88151	1	1	yes	characteristic
215	C₂×C₄	C₂×#6103	1	1	yes	characteristic
216	C₂×C₄	#88200	1	1	yes	characteristic
217	C₂×C₄	#88204	1	2	yes	—
218	C₂×C₄	#88205	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	52	2	no	—
224	C₈	—	104	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#11718648	1	1	yes	characteristic
228	C₂²	#11718715	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	16	2	no	—
234	C₄	—	52	2	no	—
235	C₄	—	52	2	no	—
236	C₄	#11718663	1	1	yes	characteristic
237	C₄	#11718665	1	1	yes	characteristic
238	C₄	#11718724	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#13114848	1	1	yes	characteristic
241	C₂	#13114879	1	1	yes	characteristic
242	C₂	#13114887	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13123770

C₂

yes

maximal, characteristic

#13113584

C₂

yes

maximal, characteristic

#13113399

C₂

yes

maximal

#13112694

C₂

yes

maximal

C₁₃×#1835

C₂

yes

maximal, characteristic

#11719175

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#382

C₂²

yes

—

#11718763

—

#11718762

—

#11718586

C₂²

yes

—

#11718585

C₂²

yes

characteristic

#11718340

—

#11718340

C₄

yes

complemented

C₈×Dic₂₆

—

C₈×Dic₂₆

C₄

yes

complemented

C₁₃×#340

—

C₁₃×#340

—

#11718050

—

#11718049

—

#11718044

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

—

—

D₄

yes

—

C₂×#6099

—

#88124

—

#88123

Q₈

yes

characteristic

#88123

Q₈

yes

characteristic

C₄×Dic₂₆

—

C₄×Dic₂₆

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

characteristic

C₁₃×#95

—

C₁₃×#95

—

C₂²⋊#1055

—

#88055

—

#88054

—

#88054

—

C₈×Dic₁₃

—

C₄⋊#1055

—

C₄⋊#1055

—

C₄⋊#1055

C₂×C₄

yes

—

C₄×#1055

—

#8679

—

maximal, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

characteristic

C₂×Dic₂₆

—

C₂×Dic₂₆

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

characteristic

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

C₄⋊C₄

yes

—

#6101

—

#6101

—

C₄×Dic₁₃

—

—

—

—

—

D₁₃

yes

—

—

—

C₂³×C₁₃

#121

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

100

C₂×Dic₁₃

—

101

Dic₂₆

—

102

Dic₂₆

—

103

C₈×C₁₃

—

104

C₈×C₁₃

—

105

C₈×C₁₃

—

106

C₈×C₁₃

—

107

#1055

—

108

#1055

—

109

#533

—

110

#446

—

111

#446

—

112

C₈×Q₈

—

113

C₈×Q₈

—

114

#431

—

115

#424

—

116

#423

—

117

#405

—

118

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

119

#382

C₂×D₁₃

yes

—

120

#340

—

121

#340

—

122

#335

—

123

#334

—

124

#328

—

125

C₂²×C₁₃

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

#380

yes

characteristic

128

C₂²×C₁₃

#464

yes

—

129

C₄×C₁₃

—

130

C₄×C₁₃

—

131

C₄×C₁₃

—

132

C₄×C₁₃

—

133

C₄×C₁₃

—

134

C₄×C₁₃

#416

yes

characteristic

135

C₄×C₁₃

#419

yes

characteristic

136

C₄×C₁₃

#479

yes

—

137

Dic₁₃

—

138

Dic₁₃

—

139

C₂×M₁₆

—

140

C₂²×C₈

C₂²⋊D₁₃

yes

characteristic

141

C₂²×C₈

C₂²⋊D₁₃

yes

characteristic

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#125

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

#117

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄²

C₂²×D₁₃

yes

characteristic

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₂²⋊C₈

—

158

#97

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

C₄×D₁₃

yes

characteristic

162

C₄×C₈

C₄×D₁₃

yes

characteristic

163

C₄×C₈

D₅₂

yes

characteristic

164

C₄×C₈

D₅₂

yes

characteristic

165

#95

—

166

#95

—

167

C₂×C₁₃

—

168

C₂×C₁₃

#1805

yes

characteristic

169

C₂×C₁₃

#1812

yes

characteristic

170

C₂×C₁₃

#1814

yes

characteristic

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

—

174

C₂²×C₄

D₄×D₁₃

yes

characteristic

175

C₂²×C₄

#6129

yes

characteristic

176

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

177

M₁₆

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

#6103

yes

characteristic

183

C₂×C₈

#6103

yes

characteristic

184

C₂×C₈

#6103

yes

characteristic

185

C₂×C₈

#6103

yes

characteristic

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₂²⋊C₄

—

195

C₄²

—

196

C₄²

C₂×C₄×D₁₃

yes

characteristic

197

C₄²

C₂×D₅₂

yes

characteristic

198

C₄²

Q₈×D₁₃

yes

characteristic

199

C₄²

#6131

yes

characteristic

200

C₁₃

#8679

yes

characteristic, complemented, Sylow

201

C₂³

#88192

yes

characteristic

202

Q₈

—

203

Q₈

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

C₄⋊C₄×D₁₃

yes

characteristic

212

C₂×C₄

#88146

yes

characteristic

213

C₂×C₄

#88149

yes

characteristic

214

C₂×C₄

#88151

yes

characteristic

215

C₂×C₄

C₂×#6103

yes

characteristic

216

C₂×C₄

#88200

yes

characteristic

217

C₂×C₄

#88204

yes

—

218

C₂×C₄

#88205

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

104

—

225

C₂²

—

226

C₂²

—

227

C₂²

#11718648

yes

characteristic

228

C₂²

#11718715

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#11718663

yes

characteristic

237

C₄

#11718665

yes

characteristic

238

C₄

#11718724

yes

—

239

C₂

—

240

C₂

#13114848

yes

characteristic

241

C₂

#13114879

yes

characteristic

242

C₂

#13114887

yes

characteristic

	subgroup	G/H
center	C₂²	#11718648
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1835	C₂
socle	C₂²×C₁₃	#380
prime radical	C₂³×C₁₃	#121
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1835	D₁₃
hypocenter	C₁₃	#8679
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

subgroup

G/H

center

C₂²

#11718648

commutator

C₄²×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1835

C₂

C₂²×C₁₃

C₂³×C₁₃

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

N	H ≅ G/N	type
14. #11718340	C₄	semidirect
16. C₈×Dic₂₆	C₄	semidirect
200. C₁₃	#8679	semidirect

H ≅ G/N

type

14. #11718340

C₄

semidirect

16. C₈×Dic₂₆

C₄

semidirect

200. C₁₃

#8679

semidirect

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

subgroup	index
#13123770	2
#13113584	2
#13113399	2
#13112694	2
C₁₃×#1835	2
#8679	13

subgroup

index

C₁₃×#1835

Subgroups — #15756145

Conjugacy classes of subgroups

Complements

Maximal subgroups