Group #15762729 — subgroups

Subgroups — #15762729

Order 3328.

694 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11718356	C₂	1	1	yes	maximal, characteristic
2	#13115641	C₂	1	2	yes	maximal, complemented
3	#13115641	C₂	1	2	yes	maximal, complemented
4	C₂×#11718046	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₀₄	—	2	2	no	—
7	C₂×#88128	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#384	C₂²	1	2	yes	—
10	C₂×#88049	—	2	4	no	—
11	C₂×#88049	—	2	4	no	—
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
14	#11718356	—	2	2	no	—
15	#11718356	C₄	1	4	yes	complemented
16	C₁₃×#340	—	2	2	no	—
17	#11718046	—	2	2	no	—
18	C₂²×D₅₂	—	2	2	no	—
19	C₂²×D₅₂	—	2	2	no	—
20	C₂²×D₅₂	—	2	2	no	—
21	C₂²×C₈×C₁₃	D₄	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₂²×#1055	D₄	1	2	yes	—
27	C₂²×#1055	D₄	1	2	yes	—
28	C₂×D₁₀₄	—	2	8	no	—
29	C₂×D₁₀₄	—	4	8	no	—
30	#88128	—	2	2	no	—
31	#88128	—	2	2	no	—
32	#88128	—	2	2	no	—
33	#88128	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₃	D₄	1	2	yes	—
36	#88049	—	4	8	no	—
37	#88049	—	4	8	no	—
38	C₄×#1055	—	2	1	no	—
39	C₄×#1055	—	2	1	no	—
40	C₄×#1055	—	2	1	no	—
41	C₄×#1055	—	2	1	no	—
42	#9832	—	13	1	no	maximal, Sylow
43	C₂³×D₁₃	—	4	2	no	—
44	C₂²×C₄×C₁₃	—	4	2	no	—
45	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×D₅₂	—	2	4	no	—
49	C₂×D₅₂	—	2	4	no	—
50	C₂×D₅₂	—	2	4	no	—
51	C₂×D₅₂	—	4	4	no	—
52	C₂×D₅₂	—	4	4	no	—
53	C₂×D₅₂	—	4	4	no	—
54	C₂×D₅₂	—	4	4	no	—
55	C₂×D₅₂	—	4	4	no	—
56	C₂×D₅₂	—	4	4	no	—
57	C₂×D₅₂	—	4	2	no	—
58	C₂×D₅₂	—	4	2	no	—
59	C₂×D₅₂	—	4	2	no	—
60	C₂×C₈×C₁₃	—	2	4	no	—
61	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
62	C₁₃×C₄⋊C₄	—	4	4	no	—
63	C₁₃×C₄⋊C₄	—	4	4	no	—
64	C₁₃×C₄⋊C₄	—	4	4	no	—
65	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₃	#41	1	1	yes	characteristic
68	C₄²×C₁₃	#41	1	1	yes	characteristic
69	C₂×#1055	—	2	2	no	—
70	C₂×#1055	—	2	2	no	—
71	C₂×#1055	—	2	2	no	—
72	C₂×#1055	—	2	4	no	—
73	C₂×#1055	D₈	1	4	yes	complemented
74	D₁₀₄	—	4	16	no	—
75	C₂×#493	—	13	1	no	—
76	#1957	—	13	2	no	—
77	#1957	—	13	2	no	—
78	#1834	D₁₃	1	1	yes	characteristic, complemented
79	C₂×#322	—	13	1	no	—
80	C₂³×C₁₃	#127	1	1	yes	characteristic
81	C₂²×D₁₃	—	4	4	no	—
82	C₂²×D₁₃	—	8	2	no	—
83	C₂²×D₁₃	—	8	2	no	—
84	C₂²×D₁₃	—	8	2	no	—
85	C₂²×D₁₃	—	8	2	no	—
86	C₂²×D₁₃	—	8	2	no	—
87	C₂²×D₁₃	—	8	2	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	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
98	C₂×C₄×C₁₃	#135	1	2	yes	—
99	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
100	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
101	D₅₂	—	4	8	no	—
102	D₅₂	—	4	8	no	—
103	D₅₂	—	4	8	no	—
104	D₅₂	—	8	4	no	—
105	D₅₂	—	8	4	no	—
106	D₅₂	—	8	4	no	—
107	C₈×C₁₃	—	2	4	no	—
108	#1055	—	2	4	no	—
109	#1055	—	4	2	no	—
110	C₂²×D₈	—	26	2	no	—
111	C₂×#127	—	13	2	no	—
112	#493	—	13	4	no	—
113	#493	—	26	2	no	—
114	C₂×#102	—	26	4	no	—
115	C₂×#102	—	26	4	no	—
116	C₂×C₄×C₈	—	13	1	no	—
117	C₂×C₄×C₈	—	13	1	no	—
118	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
119	#384	C₂×D₁₃	1	2	yes	—
120	#340	—	2	2	no	—
121	#322	—	26	2	no	—
122	C₂²×C₁₃	#390	1	1	yes	characteristic
123	C₂²×C₁₃	#493	1	1	yes	characteristic
124	C₂²×C₁₃	#495	1	1	yes	characteristic
125	C₂²×C₁₃	#496	1	2	yes	—
126	C₂²×C₁₃	#496	1	2	yes	—
127	C₂×D₁₃	—	8	4	no	—
128	C₂×D₁₃	—	8	4	no	—
129	C₂×D₁₃	—	8	4	no	—
130	C₂×D₁₃	—	16	2	no	—
131	C₂×D₁₃	—	16	2	no	—
132	C₂×D₁₃	—	16	2	no	—
133	C₂×D₁₃	—	16	2	no	—
134	C₄×C₁₃	—	16	2	no	—
135	C₄×C₁₃	#418	1	2	yes	—
136	C₄×C₁₃	C₄×D₈	1	2	yes	—
137	C₄×C₁₃	#442	1	2	yes	—
138	C₄×C₁₃	#466	1	2	yes	—
139	C₄×C₁₃	#469	1	2	yes	—
140	C₄×C₁₃	#490	1	2	yes	—
141	C₂²×D₄	—	26	2	no	—
142	C₂²×D₄	—	26	2	no	—
143	C₂²×D₄	—	26	2	no	—
144	C₂×D₈	—	26	8	no	—
145	C₂×D₈	—	52	8	no	—
146	C₂²×C₈	—	13	2	no	—
147	C₂²×C₈	—	13	2	no	—
148	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
149	#127	—	13	4	no	—
150	#127	—	26	2	no	—
151	#127	—	26	2	no	—
152	#127	—	26	2	no	—
153	C₂×C₄⋊C₄	—	2	2	no	—
154	C₂×C₄⋊C₄	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
157	#102	—	52	8	no	—
158	#102	—	52	8	no	—
159	C₄×C₈	—	26	1	no	—
160	C₄×C₈	—	26	1	no	—
161	C₄×C₈	—	26	1	no	—
162	C₄×C₈	—	26	1	no	—
163	C₄×C₈	C₄×D₁₃	1	2	yes	—
164	C₄×C₈	D₅₂	1	2	yes	—
165	C₂×C₁₃	#1717	1	2	yes	—
166	C₂×C₁₃	#1721	1	2	yes	—
167	C₂×C₁₃	#1961	1	1	yes	characteristic
168	C₂×C₁₃	#1970	1	1	yes	characteristic
169	C₂×C₁₃	#1972	1	1	yes	characteristic
170	D₁₃	—	16	4	no	—
171	C₂⁴	—	52	2	no	—
172	C₂×D₄	—	26	4	no	—
173	C₂×D₄	—	26	4	no	—
174	C₂×D₄	—	26	4	no	—
175	C₂×D₄	—	52	2	no	—
176	C₂×D₄	—	52	2	no	—
177	C₂×D₄	—	52	4	no	—
178	C₂×D₄	—	52	4	no	—
179	C₂×D₄	—	52	4	no	—
180	C₂×D₄	—	52	4	no	—
181	C₂×D₄	—	52	2	no	—
182	C₂×D₄	—	52	4	no	—
183	C₂×D₄	—	52	4	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
186	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
188	D₈	—	52	16	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	13	4	no	—
191	C₂×C₈	—	26	2	no	—
192	C₂×C₈	—	26	2	no	—
193	C₂×C₈	—	26	2	no	—
194	C₂×C₈	—	26	4	no	—
195	C₂×C₈	#6103	1	4	yes	—
196	C₄⋊C₄	—	4	4	no	—
197	C₄⋊C₄	—	4	4	no	—
198	C₄⋊C₄	—	4	4	no	—
199	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
200	C₄²	C₂×D₅₂	1	1	yes	characteristic
201	C₄²	#6131	1	1	yes	characteristic
202	C₄²	#6131	1	1	yes	characteristic
203	C₁₃	#9832	1	1	yes	characteristic, complemented, Sylow
204	C₂³	—	52	4	no	—
205	C₂³	—	104	2	no	—
206	C₂³	—	104	2	no	—
207	C₂³	—	104	2	no	—
208	C₂³	—	104	2	no	—
209	C₂³	—	104	2	no	—
210	C₂³	—	104	2	no	—
211	C₂³	#88194	1	1	yes	characteristic
212	D₄	—	52	8	no	—
213	D₄	—	52	8	no	—
214	D₄	—	52	8	no	—
215	D₄	—	104	4	no	—
216	D₄	—	104	4	no	—
217	D₄	—	104	4	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	#88147	1	1	yes	characteristic
222	C₂×C₄	#88147	1	1	yes	characteristic
223	C₂×C₄	#88149	1	1	yes	characteristic
224	C₂×C₄	#88149	1	1	yes	characteristic
225	C₂×C₄	D₈×D₁₃	1	2	yes	—
226	C₂×C₄	#88168	1	4	yes	—
227	C₂×C₄	#88173	1	2	yes	—
228	C₂×C₄	C₂×#6103	1	1	yes	characteristic
229	C₂×C₄	#88201	1	1	yes	characteristic
230	C₂×C₄	#88203	1	4	yes	—
231	C₈	—	2	4	no	—
232	C₈	—	26	4	no	—
233	C₈	—	52	2	no	—
234	C₂²	—	104	4	no	—
235	C₂²	—	104	4	no	—
236	C₂²	—	104	4	no	—
237	C₂²	—	208	2	no	—
238	C₂²	—	208	2	no	—
239	C₂²	—	208	2	no	—
240	C₂²	—	208	2	no	—
241	C₂²	#11718649	1	1	yes	characteristic
242	C₂²	#11718719	1	2	yes	—
243	C₂²	#11718812	1	1	yes	characteristic
244	C₂²	#11718837	1	2	yes	—
245	C₂²	#11718852	1	1	yes	characteristic
246	C₄	—	16	2	no	—
247	C₄	#11718526	1	2	yes	—
248	C₄	#11718530	1	2	yes	—
249	C₄	#11718533	1	2	yes	—
250	C₄	#11718544	1	2	yes	—
251	C₄	#11718662	1	2	yes	—
252	C₄	#11718728	1	2	yes	—
253	C₂	—	208	4	no	—
254	C₂	#13114478	1	2	yes	—
255	C₂	#13114504	1	2	yes	—
256	C₂	#13115659	1	1	yes	characteristic
257	C₂	#13115700	1	1	yes	characteristic
258	C₂	#13115710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718356

C₂

yes

maximal, characteristic

#13115641

C₂

yes

maximal, complemented

#13115641

C₂

yes

maximal, complemented

C₂×#11718046

C₂

yes

maximal, characteristic, complemented

C₁₃×#1834

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₀₄

—

C₂×#88128

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

—

C₂×#88049

—

C₂×#88049

—

C₂×C₄×#1055

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

#11718356

—

#11718356

C₄

yes

complemented

C₁₃×#340

—

#11718046

—

C₂²×D₅₂

—

C₂²×D₅₂

—

C₂²×D₅₂

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂²×#1055

D₄

yes

—

C₂²×#1055

D₄

yes

—

C₂×D₁₀₄

—

C₂×D₁₀₄

—

—

—

—

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

D₄

yes

—

—

—

—

—

—

—

—

C₂³×D₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

C₄²×C₁₃

yes

C₄²×C₁₃

yes

—

—

—

—

D₈

yes

complemented

D₁₀₄

—

—

—

—

D₁₃

yes

characteristic, complemented

C₂×#322

—

C₂³×C₁₃

#127

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄×D₄

yes

characteristic

C₂×C₄×C₁₃

C₄×D₄

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

C₂×D₈

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

100

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

101

D₅₂

—

102

D₅₂

—

103

D₅₂

—

104

D₅₂

—

105

D₅₂

—

106

D₅₂

—

107

C₈×C₁₃

—

108

#1055

—

109

#1055

—

110

C₂²×D₈

—

111

C₂×#127

—

112

#493

—

113

#493

—

114

C₂×#102

—

115

C₂×#102

—

116

C₂×C₄×C₈

—

117

C₂×C₄×C₈

—

118

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

119

#384

C₂×D₁₃

yes

—

120

#340

—

121

#322

—

122

C₂²×C₁₃

#390

yes

characteristic

123

C₂²×C₁₃

#493

yes

characteristic

124

C₂²×C₁₃

#495

yes

characteristic

125

C₂²×C₁₃

#496

yes

—

126

C₂²×C₁₃

#496

yes

—

127

C₂×D₁₃

—

128

C₂×D₁₃

—

129

C₂×D₁₃

—

130

C₂×D₁₃

—

131

C₂×D₁₃

—

132

C₂×D₁₃

—

133

C₂×D₁₃

—

134

C₄×C₁₃

—

135

C₄×C₁₃

#418

yes

—

136

C₄×C₁₃

C₄×D₈

yes

—

137

C₄×C₁₃

#442

yes

—

138

C₄×C₁₃

#466

yes

—

139

C₄×C₁₃

#469

yes

—

140

C₄×C₁₃

#490

yes

—

141

C₂²×D₄

—

142

C₂²×D₄

—

143

C₂²×D₄

—

144

C₂×D₈

—

145

C₂×D₈

—

146

C₂²×C₈

—

147

C₂²×C₈

—

148

C₂²×C₈

C₂²⋊D₁₃

yes

—

149

#127

—

150

#127

—

151

#127

—

152

#127

—

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

C₄×C₈

—

163

C₄×C₈

C₄×D₁₃

yes

—

164

C₄×C₈

D₅₂

yes

—

165

C₂×C₁₃

#1717

yes

—

166

C₂×C₁₃

#1721

yes

—

167

C₂×C₁₃

#1961

yes

characteristic

168

C₂×C₁₃

#1970

yes

characteristic

169

C₂×C₁₃

#1972

yes

characteristic

170

D₁₃

—

171

C₂⁴

—

172

C₂×D₄

—

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

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂²×C₄

—

185

C₂²×C₄

D₄×D₁₃

yes

characteristic

186

C₂²×C₄

D₄×D₁₃

yes

characteristic

187

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

188

D₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

#6103

yes

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄²

C₂×C₄×D₁₃

yes

characteristic

200

C₄²

C₂×D₅₂

yes

characteristic

201

C₄²

#6131

yes

characteristic

202

C₄²

#6131

yes

characteristic

203

C₁₃

#9832

yes

characteristic, complemented, Sylow

204

C₂³

—

205

C₂³

—

104

—

206

C₂³

—

104

—

207

C₂³

—

104

—

208

C₂³

—

104

—

209

C₂³

—

104

—

210

C₂³

—

104

—

211

C₂³

#88194

yes

characteristic

212

D₄

—

213

D₄

—

214

D₄

—

215

D₄

—

104

—

216

D₄

—

104

—

217

D₄

—

104

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

#88147

yes

characteristic

222

C₂×C₄

#88147

yes

characteristic

223

C₂×C₄

#88149

yes

characteristic

224

C₂×C₄

#88149

yes

characteristic

225

C₂×C₄

D₈×D₁₃

yes

—

226

C₂×C₄

#88168

yes

—

227

C₂×C₄

#88173

yes

—

228

C₂×C₄

C₂×#6103

yes

characteristic

229

C₂×C₄

#88201

yes

characteristic

230

C₂×C₄

#88203

yes

—

231

C₈

—

232

C₈

—

233

C₈

—

234

C₂²

—

104

—

235

C₂²

—

104

—

236

C₂²

—

104

—

237

C₂²

—

208

—

238

C₂²

—

208

—

239

C₂²

—

208

—

240

C₂²

—

208

—

241

C₂²

#11718649

yes

characteristic

242

C₂²

#11718719

yes

—

243

C₂²

#11718812

yes

characteristic

244

C₂²

#11718837

yes

—

245

C₂²

#11718852

yes

characteristic

246

C₄

—

247

C₄

#11718526

yes

—

248

C₄

#11718530

yes

—

249

C₄

#11718533

yes

—

250

C₄

#11718544

yes

—

251

C₄

#11718662

yes

—

252

C₄

#11718728

yes

—

253

C₂

—

208

—

254

C₂

#13114478

yes

—

255

C₂

#13114504

yes

—

256

C₂

#13115659

yes

characteristic

257

C₂

#13115700

yes

characteristic

258

C₂

#13115710

yes

characteristic

	subgroup	G/H
center	C₂³	#88194
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1834	C₂
socle	C₂³×C₁₃	#127
prime radical	C₂×#11718356	C₂
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1834	D₁₃
hypocenter	C₁₃	#9832
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#88194

commutator

C₄²×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1834

C₂

C₂³×C₁₃

C₂

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
2. #13115641	C₂	semidirect
3. #13115641	C₂	semidirect
4. C₂×#11718046	C₂	semidirect
5. C₁₃×#1834	C₂	semidirect
15. #11718356	C₄	semidirect
73. C₂×#1055	D₈	semidirect
78. #1834	D₁₃	semidirect
203. C₁₃	#9832	semidirect

H ≅ G/N

type

2. #13115641

C₂

semidirect

3. #13115641

C₂

semidirect

4. C₂×#11718046

C₂

semidirect

5. C₁₃×#1834

C₂

semidirect

15. #11718356

C₄

semidirect

73. C₂×#1055

D₈

semidirect

78. #1834

D₁₃

semidirect

203. C₁₃

#9832

semidirect

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

subgroup	index
C₂×#11718356	2
#13115641	2
C₂×#11718046	2
C₁₃×#1834	2
#9832	13

subgroup

index

C₁₃×#1834

Subgroups — #15762729

Conjugacy classes of subgroups

Complements

Maximal subgroups