Group #34187956 — subgroups

Subgroups — #34187956

Order 20224.

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

normal subgroups only

This group has 602 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	C₂×#19098940	C₂	1	1	yes	maximal, characteristic
2	#23764239	C₂	1	2	yes	maximal, complemented
3	#23762069	C₂	1	2	yes	maximal, complemented
4	#23761689	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₆₃₂	C₄	1	4	yes	—
7	C₂×#14579158	C₂²	1	2	yes	—
8	#19098940	—	2	2	no	—
9	#19098940	—	2	1	no	—
10	#19098940	—	2	1	no	—
11	#19098616	C₂²	1	1	yes	characteristic
12	C₂×#14579077	—	2	4	no	—
13	C₄×#11929608	C₂²	1	1	yes	characteristic
14	#19098306	—	2	4	no	—
15	#19098285	—	2	1	no	—
16	#19098284	—	2	1	no	—
17	#423×C₇₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	#334×C₇₉	—	2	2	no	—
20	C₂²×D₃₁₆	—	2	2	no	—
21	C₂²×D₃₁₆	—	2	2	no	—
22	C₂²×D₃₁₆	C₂×C₄	1	4	yes	—
23	C₂×D₆₃₂	—	2	4	no	—
24	C₂×D₆₃₂	—	2	4	no	—
25	C₂×D₆₃₂	—	4	8	no	—
26	C₂×#11929608	D₄	1	2	yes	—
27	#14579158	—	2	2	no	—
28	#14579158	—	2	2	no	—
29	#14579158	—	2	2	no	—
30	#14579158	—	2	2	no	—
31	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
32	#14579077	—	4	8	no	—
33	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
34	#14579072	—	2	1	no	—
35	C₄×C₇₉⋊C₈	—	2	1	no	—
36	C₄×C₇₉⋊C₈	—	2	1	no	—
37	C₂×M₁₆×C₇₉	—	2	2	no	—
38	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₇₉	—	2	2	no	—
41	C₄⋊C₈×C₇₉	—	2	2	no	—
42	C₄×C₈×C₇₉	D₄	1	2	yes	—
43	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
45	C₂³×D₇₉	—	2	4	no	—
46	C₂×D₃₁₆	—	2	4	no	—
47	C₂×D₃₁₆	—	2	4	no	—
48	C₂×D₃₁₆	—	4	8	no	—
49	C₂×D₃₁₆	—	4	2	no	—
50	C₂×D₃₁₆	—	4	2	no	—
51	C₂×D₃₁₆	—	4	2	no	—
52	C₂×D₃₁₆	—	4	2	no	—
53	C₂×D₃₁₆	—	4	4	no	—
54	C₂×D₃₁₆	—	4	4	no	—
55	C₂×D₃₁₆	—	8	4	no	—
56	D₆₃₂	—	4	8	no	—
57	D₆₃₂	—	4	8	no	—
58	#11929608	—	2	4	no	—
59	C₂×C₇₉⋊C₈	—	2	2	no	—
60	C₂×C₇₉⋊C₈	—	2	2	no	—
61	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
64	M₁₆×C₇₉	—	4	4	no	—
65	C₂×C₈×C₇₉	—	2	4	no	—
66	C₂×C₈×C₇₉	—	4	2	no	—
67	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₇₉	#41	1	1	yes	characteristic
73	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
74	C₂²×D₇₉	—	4	4	no	—
75	C₂²×D₇₉	—	4	8	no	—
76	C₂²×D₇₉	—	8	4	no	—
77	C₂²×D₇₉	—	8	4	no	—
78	C₂×C₄×C₇₉	—	2	2	no	—
79	C₂×C₄×C₇₉	—	2	2	no	—
80	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
83	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
86	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
87	D₃₁₆	—	4	8	no	—
88	D₃₁₆	—	8	4	no	—
89	D₃₁₆	—	8	4	no	—
90	D₃₁₆	—	8	4	no	—
91	D₃₁₆	—	8	4	no	—
92	D₃₁₆	—	8	2	no	—
93	D₃₁₆	—	8	2	no	—
94	C₈×C₇₉	—	2	2	no	—
95	C₈×C₇₉	—	8	2	no	—
96	C₈×C₇₉	#100	1	4	yes	complemented
97	C₇₉⋊C₈	—	4	2	no	—
98	C₇₉⋊C₈	—	4	2	no	—
99	C₂²×C₇₉	—	2	1	no	—
100	C₂²×C₇₉	—	2	1	no	—
101	C₂²×C₇₉	#390	1	1	yes	characteristic
102	C₂²×C₇₉	#442	1	2	yes	—
103	C₂×D₇₉	—	8	4	no	—
104	C₂×D₇₉	—	8	4	no	—
105	C₂×D₇₉	—	8	4	no	—
106	C₂×D₇₉	—	16	8	no	—
107	C₄×C₇₉	—	2	1	no	—
108	C₄×C₇₉	—	2	1	no	—
109	C₄×C₇₉	C₂×#100	1	2	yes	—
110	C₄×C₇₉	#469	1	2	yes	—
111	C₄×C₇₉	#472	1	2	yes	—
112	C₄×C₇₉	#496	1	2	yes	—
113	#9811	—	79	1	no	maximal, Sylow
114	C₂×C₇₉	—	2	2	no	—
115	C₂×C₇₉	#1965	1	1	yes	characteristic
116	C₂×C₇₉	#1972	1	1	yes	characteristic
117	C₂×C₇₉	#1978	1	1	yes	characteristic
118	D₇₉	—	16	4	no	—
119	C₂×#493	—	79	1	no	—
120	#1965	—	79	2	no	—
121	#1566	D₇₉	1	1	yes	characteristic, complemented
122	#1545	—	79	2	no	—
123	#1451	—	79	1	no	—
124	C₇₉	#9811	1	1	yes	characteristic, complemented, Sylow
125	C₂²×D₈	—	79	4	no	—
126	C₂×#127	—	79	2	no	—
127	#493	—	158	2	no	—
128	#493	—	158	1	no	—
129	#493	—	158	1	no	—
130	#431	—	79	1	no	—
131	#423	C₂×D₇₉	1	2	yes	—
132	C₂×#100	—	158	4	no	—
133	C₄×M₁₆	—	79	1	no	—
134	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
135	#334	—	2	2	no	—
136	#331	—	158	4	no	—
137	#322	—	158	1	no	—
138	#322	—	158	1	no	—
139	C₂²×D₄	—	79	4	no	—
140	C₂²×D₄	—	158	2	no	—
141	C₂²×D₄	—	158	2	no	—
142	C₂×D₈	—	316	8	no	—
143	C₂×D₈	—	158	4	no	—
144	C₂×D₈	—	158	4	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	79	2	no	—
147	C₂²×C₈	C₄×D₇₉	1	2	yes	—
148	#127	—	158	2	no	—
149	#127	—	158	2	no	—
150	#127	—	158	2	no	—
151	#127	—	158	2	no	—
152	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	2	2	no	—
155	C₄⋊C₈	—	79	2	no	—
156	#100	—	316	8	no	—
157	C₂²⋊C₈	—	158	1	no	—
158	#97	—	158	1	no	—
159	C₄×C₈	—	158	1	no	—
160	C₄×C₈	—	158	1	no	—
161	C₄×C₈	D₃₁₆	1	1	yes	characteristic
162	C₄×C₈	D₃₁₆	1	1	yes	characteristic
163	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
164	C₂⁴	—	158	4	no	—
165	C₂×D₄	—	316	8	no	—
166	C₂×D₄	—	316	2	no	—
167	C₂×D₄	—	316	2	no	—
168	C₂×D₄	—	316	2	no	—
169	C₂×D₄	—	316	2	no	—
170	C₂×D₄	—	316	4	no	—
171	C₂×D₄	—	316	4	no	—
172	C₂×D₄	—	632	4	no	—
173	C₂×D₄	—	158	4	no	—
174	C₂×D₄	—	158	4	no	—
175	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
177	C₂²×C₄	#11929625	1	1	yes	characteristic
178	D₈	—	316	8	no	—
179	D₈	—	316	8	no	—
180	M₁₆	—	4	4	no	—
181	M₁₆	—	158	4	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	158	2	no	—
185	C₂×C₈	—	158	2	no	—
186	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
187	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
188	C₄²	D₄×D₇₉	1	1	yes	characteristic
189	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
190	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
191	C₄²	#11929625	1	1	yes	characteristic
192	C₂³	—	316	4	no	—
193	C₂³	—	316	8	no	—
194	C₂³	—	632	4	no	—
195	C₂³	—	632	4	no	—
196	C₂³	#14579123	1	1	yes	characteristic
197	D₄	—	316	8	no	—
198	D₄	—	632	4	no	—
199	D₄	—	632	4	no	—
200	D₄	—	632	2	no	—
201	D₄	—	632	2	no	—
202	D₄	—	632	4	no	—
203	D₄	—	632	4	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₄	#14579123	1	1	yes	characteristic
208	C₂×C₄	#14579136	1	1	yes	characteristic
209	C₂×C₄	#14579136	1	1	yes	characteristic
210	C₂×C₄	#14579150	1	1	yes	characteristic
211	C₂×C₄	#14579157	1	1	yes	characteristic
212	C₂×C₄	#14579188	1	4	yes	—
213	C₈	—	2	2	no	—
214	C₈	—	8	2	no	—
215	C₈	—	316	2	no	—
216	C₈	—	316	2	no	—
217	C₈	#14579077	1	4	yes	complemented
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	632	4	no	—
221	C₂²	—	632	4	no	—
222	C₂²	—	632	4	no	—
223	C₂²	—	1264	8	no	—
224	C₂²	#19098464	1	1	yes	characteristic
225	C₂²	#19098674	1	2	yes	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	C₂×#14579077	1	2	yes	—
229	C₄	#19098817	1	2	yes	—
230	C₄	#19098834	1	2	yes	—
231	C₄	#19098949	1	2	yes	—
232	C₂	—	2	2	no	—
233	C₂	—	1264	4	no	—
234	C₂	#23764239	1	1	yes	characteristic
235	C₂	#23764274	1	1	yes	characteristic
236	C₂	#23764308	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098940

C₂

yes

maximal, characteristic

#23764239

C₂

yes

maximal, complemented

#23762069

C₂

yes

maximal, complemented

#23761689

C₂

yes

maximal, characteristic, complemented

C₇₉×#1566

C₂

yes

maximal, characteristic, complemented

C₂²×D₆₃₂

C₄

yes

—

C₂×#14579158

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×#14579077

—

C₄×#11929608

C₂²

yes

—

—

—

#423×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#334×C₇₉

—

C₂²×D₃₁₆

—

C₂²×D₃₁₆

—

C₂²×D₃₁₆

C₂×C₄

yes

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×#11929608

D₄

yes

—

—

—

—

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579077

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

C₂×C₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₂³×D₇₉

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

D₆₃₂

—

D₆₃₂

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

#41

yes

characteristic

C₂³×C₇₉

C₄×D₄

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

#100

yes

complemented

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

#390

yes

characteristic

102

C₂²×C₇₉

#442

yes

—

103

C₂×D₇₉

—

104

C₂×D₇₉

—

105

C₂×D₇₉

—

106

C₂×D₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

C₂×#100

yes

—

110

C₄×C₇₉

#469

yes

—

111

C₄×C₇₉

#472

yes

—

112

C₄×C₇₉

#496

yes

—

113

#9811

—

maximal, Sylow

114

C₂×C₇₉

—

115

C₂×C₇₉

#1965

yes

characteristic

116

C₂×C₇₉

#1972

yes

characteristic

117

C₂×C₇₉

#1978

yes

characteristic

118

D₇₉

—

119

C₂×#493

—

120

#1965

—

121

#1566

D₇₉

yes

characteristic, complemented

122

#1545

—

123

#1451

—

124

C₇₉

#9811

yes

characteristic, complemented, Sylow

125

C₂²×D₈

—

126

C₂×#127

—

127

#493

—

158

—

128

#493

—

158

—

129

#493

—

158

—

130

#431

—

131

#423

C₂×D₇₉

yes

—

132

C₂×#100

—

158

—

133

C₄×M₁₆

—

134

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

135

#334

—

136

#331

—

158

—

137

#322

—

158

—

138

#322

—

158

—

139

C₂²×D₄

—

140

C₂²×D₄

—

158

—

141

C₂²×D₄

—

158

—

142

C₂×D₈

—

316

—

143

C₂×D₈

—

158

—

144

C₂×D₈

—

158

—

145

C₂×M₁₆

—

146

C₂×M₁₆

—

147

C₂²×C₈

C₄×D₇₉

yes

—

148

#127

—

158

—

149

#127

—

158

—

150

#127

—

158

—

151

#127

—

158

—

152

C₂×C₄²

C₂²×D₇₉

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#100

—

316

—

157

C₂²⋊C₈

—

158

—

158

#97

—

158

—

159

C₄×C₈

—

158

—

160

C₄×C₈

—

158

—

161

C₄×C₈

D₃₁₆

yes

characteristic

162

C₄×C₈

D₃₁₆

yes

characteristic

163

C₄×C₈

C₂²⋊D₇₉

yes

—

164

C₂⁴

—

158

—

165

C₂×D₄

—

316

—

166

C₂×D₄

—

316

—

167

C₂×D₄

—

316

—

168

C₂×D₄

—

316

—

169

C₂×D₄

—

316

—

170

C₂×D₄

—

316

—

171

C₂×D₄

—

316

—

172

C₂×D₄

—

632

—

173

C₂×D₄

—

158

—

174

C₂×D₄

—

158

—

175

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

176

C₂²×C₄

D₄×D₇₉

yes

characteristic

177

C₂²×C₄

#11929625

yes

characteristic

178

D₈

—

316

—

179

D₈

—

316

—

180

M₁₆

—

181

M₁₆

—

158

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

158

—

185

C₂×C₈

—

158

—

186

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

187

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

188

C₄²

D₄×D₇₉

yes

characteristic

189

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

190

C₄²

C₂×D₃₁₆

yes

characteristic

191

C₄²

#11929625

yes

characteristic

192

C₂³

—

316

—

193

C₂³

—

316

—

194

C₂³

—

632

—

195

C₂³

—

632

—

196

C₂³

#14579123

yes

characteristic

197

D₄

—

316

—

198

D₄

—

632

—

199

D₄

—

632

—

200

D₄

—

632

—

201

D₄

—

632

—

202

D₄

—

632

—

203

D₄

—

632

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

207

C₂×C₄

#14579123

yes

characteristic

208

C₂×C₄

#14579136

yes

characteristic

209

C₂×C₄

#14579136

yes

characteristic

210

C₂×C₄

#14579150

yes

characteristic

211

C₂×C₄

#14579157

yes

characteristic

212

C₂×C₄

#14579188

yes

—

213

C₈

—

214

C₈

—

215

C₈

—

316

—

216

C₈

—

316

—

217

C₈

#14579077

yes

complemented

218

C₂²

—

219

C₂²

—

220

C₂²

—

632

—

221

C₂²

—

632

—

222

C₂²

—

632

—

223

C₂²

—

1264

—

224

C₂²

#19098464

yes

characteristic

225

C₂²

#19098674

yes

—

226

C₄

—

227

C₄

—

228

C₄

C₂×#14579077

yes

—

229

C₄

#19098817

yes

—

230

C₄

#19098834

yes

—

231

C₄

#19098949

yes

—

232

C₂

—

233

C₂

—

1264

—

234

C₂

#23764239

yes

characteristic

235

C₂

#23764274

yes

characteristic

236

C₂

#23764308

yes

characteristic

	subgroup	G/H
center	C₂²	#19098464
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1566	C₂
socle	C₂²×C₇₉	#390
prime radical	C₂×#19098940	C₂
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1566	D₇₉
hypocenter	C₇₉	#9811
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂²

#19098464

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1566

C₂

C₂²×C₇₉

C₂

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
2. #23764239	C₂	semidirect
3. #23762069	C₂	semidirect
4. #23761689	C₂	semidirect
5. C₇₉×#1566	C₂	semidirect
96. C₈×C₇₉	#100	semidirect
121. #1566	D₇₉	semidirect
124. C₇₉	#9811	semidirect
217. C₈	#14579077	semidirect

H ≅ G/N

type

2. #23764239

C₂

semidirect

3. #23762069

C₂

semidirect

4. #23761689

C₂

semidirect

5. C₇₉×#1566

C₂

semidirect

96. C₈×C₇₉

#100

semidirect

121. #1566

D₇₉

semidirect

124. C₇₉

#9811

semidirect

217. C₈

#14579077

semidirect

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

subgroup	index
C₂×#19098940	2
#23764239	2
#23762069	2
#23761689	2
C₇₉×#1566	2
#9811	79

subgroup

index

C₇₉×#1566

Subgroups — #34187956

Conjugacy classes of subgroups

Complements

Maximal subgroups