Group #15765696 — subgroups

Subgroups — #15765696

Order 3328.

670 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11718749	C₂	1	2	yes	maximal
2	#13115798	C₂	1	2	yes	maximal, complemented
3	#13115642	C₂	1	1	yes	maximal, characteristic
4	#13112663	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×Q₁₆	—	2	2	no	—
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×#88128	C₂²	1	1	yes	characteristic
9	C₁₃×#494	—	2	4	no	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88061	—	2	2	no	—
12	#11718749	—	2	4	no	—
13	#11718749	—	2	4	no	—
14	C₂×#88049	—	2	4	no	—
15	#11718596	C₂²	1	1	yes	characteristic
16	C₂×C₄×#1055	C₂²	1	2	yes	—
17	#11718121	—	2	4	no	—
18	C₂²×Q₈×C₁₃	—	2	2	no	—
19	C₂²×D₅₂	—	2	1	no	—
20	C₂²×D₅₂	—	2	2	no	—
21	C₂×C₁₃×Q₁₆	—	2	8	no	—
22	C₂×C₁₃×Q₁₆	—	4	4	no	—
23	C₂×C₁₃×Q₁₆	—	4	4	no	—
24	C₂²×C₈×C₁₃	D₄	1	2	yes	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₁₃×C₄⋊Q₈	—	2	2	no	—
28	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₃	—	2	1	no	—
33	C₂×C₄⋊Dic₁₃	—	2	2	no	—
34	C₂²×#1055	D₄	1	4	yes	—
35	#88128	—	2	2	no	—
36	#88128	—	2	1	no	—
37	#88128	D₄	1	2	yes	—
38	C₄×C₈×C₁₃	—	2	2	no	—
39	#88061	—	4	4	no	—
40	#88049	—	2	16	no	—
41	C₄×#1055	—	2	2	no	—
42	C₄×#1055	—	2	2	no	—
43	#10306	—	13	1	no	maximal, Sylow
44	C₂³×D₁₃	—	4	1	no	—
45	C₂×Q₈×C₁₃	—	2	4	no	—
46	C₂×Q₈×C₁₃	—	4	2	no	—
47	C₂×Q₈×C₁₃	—	4	4	no	—
48	C₂×Q₈×C₁₃	—	4	4	no	—
49	C₂²×C₄×C₁₃	—	4	2	no	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₁₃	—	4	1	no	—
53	C₂×D₅₂	—	2	4	no	—
54	C₂×D₅₂	—	2	2	no	—
55	C₂×D₅₂	—	4	2	no	—
56	C₂×D₅₂	—	4	4	no	—
57	C₂×D₅₂	—	4	2	no	—
58	C₂×D₅₂	—	4	4	no	—
59	C₂×D₅₂	—	4	1	no	—
60	C₂×D₅₂	—	4	2	no	—
61	C₁₃×Q₁₆	—	4	16	no	—
62	C₂×C₈×C₁₃	—	2	2	no	—
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₂×C₈×C₁₃	D₈	1	4	yes	—
65	C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₁₃×C₄⋊C₄	—	4	2	no	—
68	C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₃	C₂×D₄	1	2	yes	—
71	C₄²×C₁₃	#41	1	1	yes	characteristic
72	C₄⋊Dic₁₃	—	4	2	no	—
73	C₄⋊Dic₁₃	—	4	4	no	—
74	C₂×#1055	—	2	4	no	—
75	C₂×#1055	—	2	4	no	—
76	C₂×#1055	—	2	4	no	—
77	C₂×#494	D₁₃	1	1	yes	characteristic, complemented
78	C₂×#486	—	13	2	no	—
79	#1990	—	13	2	no	—
80	#1957	—	13	1	no	—
81	#1273	—	13	1	no	—
82	C₂³×C₁₃	#127	1	1	yes	characteristic
83	C₂²×D₁₃	—	4	2	no	—
84	C₂²×D₁₃	—	8	1	no	—
85	C₂²×D₁₃	—	8	2	no	—
86	C₂²×D₁₃	—	8	1	no	—
87	C₂²×D₁₃	—	8	2	no	—
88	Q₈×C₁₃	—	4	8	no	—
89	Q₈×C₁₃	—	8	4	no	—
90	C₂×C₄×C₁₃	—	4	4	no	—
91	C₂×C₄×C₁₃	—	8	2	no	—
92	C₂×C₄×C₁₃	—	8	2	no	—
93	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#120	1	2	yes	—
95	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#121	1	2	yes	—
97	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
98	C₂×C₄×C₁₃	#135	1	4	yes	—
99	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
100	C₂×C₄×C₁₃	#137	1	4	yes	—
101	C₂×Dic₁₃	—	8	1	no	—
102	C₂×Dic₁₃	—	8	2	no	—
103	D₅₂	—	4	8	no	—
104	D₅₂	—	4	4	no	—
105	D₅₂	—	8	2	no	—
106	D₅₂	—	8	4	no	—
107	C₈×C₁₃	—	2	4	no	—
108	#1055	—	4	4	no	—
109	C₂²×Q₁₆	—	2	2	no	—
110	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
111	C₂×#127	—	13	1	no	—
112	#494	—	2	4	no	—
113	#486	—	26	4	no	—
114	#486	—	26	4	no	—
115	C₂×#102	—	26	4	no	—
116	C₂×#102	—	26	2	no	—
117	C₂×C₄×C₈	—	13	2	no	—
118	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
119	#384	—	13	1	no	—
120	#340	—	26	4	no	—
121	C₂²×C₁₃	#392	1	1	yes	characteristic
122	C₂²×C₁₃	#493	1	1	yes	characteristic
123	C₂²×C₁₃	#495	1	2	yes	—
124	C₂²×C₁₃	#496	1	1	yes	characteristic
125	C₂²×C₁₃	#497	1	2	yes	—
126	C₂×D₁₃	—	8	2	no	—
127	C₂×D₁₃	—	8	4	no	—
128	C₂×D₁₃	—	16	1	no	—
129	C₂×D₁₃	—	16	2	no	—
130	C₂×D₁₃	—	16	1	no	—
131	C₄×C₁₃	—	8	4	no	—
132	C₄×C₁₃	#447	1	2	yes	—
133	C₄×C₁₃	#452	1	4	yes	—
134	C₄×C₁₃	#459	1	2	yes	—
135	C₄×C₁₃	#464	1	4	yes	—
136	Dic₁₃	—	16	1	no	—
137	C₂²×Q₈	—	2	2	no	—
138	C₂²×D₄	—	26	2	no	—
139	C₂²×D₄	—	26	1	no	—
140	C₂×Q₁₆	—	2	8	no	—
141	C₂×Q₁₆	—	4	4	no	—
142	C₂×Q₁₆	—	4	4	no	—
143	C₂²×C₈	—	13	4	no	—
144	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	C₂²⋊D₁₃	1	4	yes	—
149	#127	—	13	2	no	—
150	#127	—	26	1	no	—
151	#127	—	26	2	no	—
152	C₂×C₄⋊C₄	—	2	2	no	—
153	C₂×C₄⋊C₄	—	2	2	no	—
154	C₂×C₄⋊C₄	—	26	2	no	—
155	C₂×C₄⋊C₄	—	26	1	no	—
156	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
157	#102	—	26	16	no	—
158	#102	—	52	4	no	—
159	C₄×C₈	—	2	2	no	—
160	C₄×C₈	—	26	2	no	—
161	C₄×C₈	—	26	2	no	—
162	C₂×C₁₃	#1709	1	1	yes	characteristic
163	C₂×C₁₃	#1720	1	2	yes	—
164	C₂×C₁₃	#1722	1	1	yes	characteristic
165	C₂×C₁₃	#2011	1	1	yes	characteristic
166	C₂×C₁₃	#2015	1	2	yes	—
167	D₁₃	—	16	2	no	—
168	C₂⁴	—	52	1	no	—
169	C₂×Q₈	—	2	4	no	—
170	C₂×Q₈	—	4	2	no	—
171	C₂×Q₈	—	4	4	no	—
172	C₂×Q₈	—	4	4	no	—
173	C₂×D₄	—	26	4	no	—
174	C₂×D₄	—	26	2	no	—
175	C₂×D₄	—	52	4	no	—
176	C₂×D₄	—	52	4	no	—
177	C₂×D₄	—	52	2	no	—
178	C₂×D₄	—	52	2	no	—
179	C₂×D₄	—	52	2	no	—
180	C₂×D₄	—	52	1	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	—	52	1	no	—
183	C₂²×C₄	D₄×D₁₃	1	2	yes	—
184	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
185	Q₁₆	—	4	16	no	—
186	C₂×C₈	—	2	2	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	26	4	no	—
189	C₂×C₈	—	26	4	no	—
190	C₂×C₈	—	26	4	no	—
191	C₂×C₈	#6104	1	4	yes	—
192	C₄⋊C₄	—	2	4	no	—
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	4	2	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	52	4	no	—
197	C₄⋊C₄	—	52	2	no	—
198	C₄²	D₄×D₁₃	1	1	yes	characteristic
199	C₄²	#6129	1	1	yes	characteristic
200	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
201	C₁₃	#10306	1	1	yes	characteristic, complemented, Sylow
202	C₂³	—	52	2	no	—
203	C₂³	—	104	1	no	—
204	C₂³	—	104	1	no	—
205	C₂³	—	104	2	no	—
206	C₂³	—	104	2	no	—
207	C₂³	#88194	1	1	yes	characteristic
208	Q₈	—	4	8	no	—
209	Q₈	—	8	4	no	—
210	D₄	—	52	4	no	—
211	D₄	—	52	8	no	—
212	D₄	—	104	4	no	—
213	D₄	—	104	2	no	—
214	C₂×C₄	—	4	4	no	—
215	C₂×C₄	—	8	2	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	104	1	no	—
218	C₂×C₄	—	104	2	no	—
219	C₂×C₄	#88172	1	4	yes	—
220	C₂×C₄	#88173	1	4	yes	—
221	C₂×C₄	C₂×#6104	1	2	yes	—
222	C₂×C₄	#88186	1	2	yes	—
223	C₂×C₄	#88191	1	2	yes	—
224	C₂×C₄	#88192	1	1	yes	characteristic
225	C₂×C₄	#88193	1	2	yes	—
226	C₂×C₄	#88207	1	1	yes	characteristic
227	C₈	—	2	4	no	—
228	C₈	—	52	4	no	—
229	C₂²	—	104	2	no	—
230	C₂²	—	104	4	no	—
231	C₂²	—	208	1	no	—
232	C₂²	—	208	2	no	—
233	C₂²	—	208	1	no	—
234	C₂²	#11718734	1	1	yes	characteristic
235	C₂²	#11718735	1	1	yes	characteristic
236	C₂²	#11718851	1	2	yes	—
237	C₂²	#11718852	1	2	yes	—
238	C₂²	#11718884	1	1	yes	characteristic
239	C₄	—	8	4	no	—
240	C₄	—	208	1	no	—
241	C₄	#11718733	1	2	yes	—
242	C₄	#11718846	1	4	yes	—
243	C₄	#11718848	1	4	yes	—
244	C₄	#11718878	1	2	yes	—
245	C₂	—	208	2	no	—
246	C₂	#13114443	1	1	yes	characteristic
247	C₂	#13114499	1	2	yes	—
248	C₂	#13114508	1	1	yes	characteristic
249	C₂	#13115907	1	1	yes	characteristic
250	C₂	#13115927	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718749

C₂

yes

maximal

#13115798

C₂

yes

maximal, complemented

#13115642

C₂

yes

maximal, characteristic

#13112663

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×#494

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₃×Q₁₆

—

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

—

C₂×#88128

C₂²

yes

characteristic

C₁₃×#494

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

—

#11718121

—

C₂²×Q₈×C₁₃

—

C₂²×D₅₂

—

C₂²×D₅₂

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂²×C₈×C₁₃

D₄

yes

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂²×#1055

D₄

yes

—

#88128

—

#88128

—

#88128

D₄

yes

—

C₄×C₈×C₁₃

—

—

—

—

—

—

C₂³×D₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₈

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

D₁₃

yes

characteristic, complemented

—

—

—

—

C₂³×C₁₃

#127

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

characteristic

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

C₂×D₈

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

100

C₂×C₄×C₁₃

#137

yes

—

101

C₂×Dic₁₃

—

102

C₂×Dic₁₃

—

103

D₅₂

—

104

D₅₂

—

105

D₅₂

—

106

D₅₂

—

107

C₈×C₁₃

—

108

#1055

—

109

C₂²×Q₁₆

—

110

C₂×C₄⋊Q₈

C₂×D₁₃

yes

—

111

C₂×#127

—

112

#494

—

113

#486

—

114

#486

—

115

C₂×#102

—

116

C₂×#102

—

117

C₂×C₄×C₈

—

118

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

119

#384

—

120

#340

—

121

C₂²×C₁₃

#392

yes

characteristic

122

C₂²×C₁₃

#493

yes

characteristic

123

C₂²×C₁₃

#495

yes

—

124

C₂²×C₁₃

#496

yes

characteristic

125

C₂²×C₁₃

#497

yes

—

126

C₂×D₁₃

—

127

C₂×D₁₃

—

128

C₂×D₁₃

—

129

C₂×D₁₃

—

130

C₂×D₁₃

—

131

C₄×C₁₃

—

132

C₄×C₁₃

#447

yes

—

133

C₄×C₁₃

#452

yes

—

134

C₄×C₁₃

#459

yes

—

135

C₄×C₁₃

#464

yes

—

136

Dic₁₃

—

137

C₂²×Q₈

—

138

C₂²×D₄

—

139

C₂²×D₄

—

140

C₂×Q₁₆

—

141

C₂×Q₁₆

—

142

C₂×Q₁₆

—

143

C₂²×C₈

—

144

C₂²×C₈

C₂²⋊D₁₃

yes

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

C₂²⋊D₁₃

yes

—

149

#127

—

150

#127

—

151

#127

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄²

C₂²×D₁₃

yes

characteristic

157

#102

—

158

#102

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₂×C₁₃

#1709

yes

characteristic

163

C₂×C₁₃

#1720

yes

—

164

C₂×C₁₃

#1722

yes

characteristic

165

C₂×C₁₃

#2011

yes

characteristic

166

C₂×C₁₃

#2015

yes

—

167

D₁₃

—

168

C₂⁴

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

D₄×D₁₃

yes

—

184

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

185

Q₁₆

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

#6104

yes

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄²

D₄×D₁₃

yes

characteristic

199

C₄²

#6129

yes

characteristic

200

C₄²

C₂×C₂²⋊D₁₃

yes

—

201

C₁₃

#10306

yes

characteristic, complemented, Sylow

202

C₂³

—

203

C₂³

—

104

—

204

C₂³

—

104

—

205

C₂³

—

104

—

206

C₂³

—

104

—

207

C₂³

#88194

yes

characteristic

208

Q₈

—

209

Q₈

—

210

D₄

—

211

D₄

—

212

D₄

—

104

—

213

D₄

—

104

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

104

—

218

C₂×C₄

—

104

—

219

C₂×C₄

#88172

yes

—

220

C₂×C₄

#88173

yes

—

221

C₂×C₄

C₂×#6104

yes

—

222

C₂×C₄

#88186

yes

—

223

C₂×C₄

#88191

yes

—

224

C₂×C₄

#88192

yes

characteristic

225

C₂×C₄

#88193

yes

—

226

C₂×C₄

#88207

yes

characteristic

227

C₈

—

228

C₈

—

229

C₂²

—

104

—

230

C₂²

—

104

—

231

C₂²

—

208

—

232

C₂²

—

208

—

233

C₂²

—

208

—

234

C₂²

#11718734

yes

characteristic

235

C₂²

#11718735

yes

characteristic

236

C₂²

#11718851

yes

—

237

C₂²

#11718852

yes

—

238

C₂²

#11718884

yes

characteristic

239

C₄

—

240

C₄

—

208

—

241

C₄

#11718733

yes

—

242

C₄

#11718846

yes

—

243

C₄

#11718848

yes

—

244

C₄

#11718878

yes

—

245

C₂

—

208

—

246

C₂

#13114443

yes

characteristic

247

C₂

#13114499

yes

—

248

C₂

#13114508

yes

characteristic

249

C₂

#13115907

yes

characteristic

250

C₂

#13115927

yes

—

	subgroup	G/H
center	C₂³	#88194
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#494	C₂
socle	C₂³×C₁₃	#127
prime radical	C₂×#88128	C₂²
hypercenter	C₂×#494	D₁₃
hypocenter	C₁₃	#10306
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#88194

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₂×C₁₃×#494

C₂

C₂³×C₁₃

C₂²

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
2. #13115798	C₂	semidirect
4. #13112663	C₂	semidirect
5. C₂×C₁₃×#494	C₂	semidirect
77. C₂×#494	D₁₃	semidirect
201. C₁₃	#10306	semidirect

H ≅ G/N

type

2. #13115798

C₂

semidirect

4. #13112663

C₂

semidirect

5. C₂×C₁₃×#494

C₂

semidirect

77. C₂×#494

D₁₃

semidirect

201. C₁₃

#10306

semidirect

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

subgroup	index
C₂×#11718749	2
#13115798	2
#13115642	2
#13112663	2
C₂×C₁₃×#494	2
#10306	13

subgroup

index

C₂×C₁₃×#494

Subgroups — #15765696

Conjugacy classes of subgroups

Complements

Maximal subgroups