Group #34188197 — subgroups

Subgroups — #34188197

Order 20224.

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

normal subgroups only

This group has 422 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	#23764378	C₂	1	2	yes	maximal
2	#23763145	C₂	1	1	yes	maximal, characteristic
3	#23762156	C₂	1	1	yes	maximal, characteristic
4	#23761855	C₂	1	2	yes	maximal
5	C₇₉×#3170	C₂	1	1	yes	maximal, characteristic
6	#19098587	C₂²	1	2	yes	—
7	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
9	#19098322	—	2	4	no	—
10	#19098317	—	2	2	no	—
11	#19098314	—	2	2	no	—
12	Q₈⋊(C₇₉⋊C₈)	—	2	4	no	—
13	#533×C₇₉	C₂²	1	2	yes	—
14	#500×C₇₉	C₄	1	1	yes	characteristic, complemented
15	#494×C₇₉	C₄	1	1	yes	characteristic, complemented
16	#487×C₇₉	C₄	1	2	yes	complemented
17	#467×C₇₉	—	2	2	no	—
18	C₄×Q₁₆×C₇₉	—	2	2	no	—
19	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#11929608	—	2	2	no	—
21	C₂²×C₇₉⋊C₈	—	2	1	no	—
22	C₂×C₄×Dic₇₉	—	2	1	no	—
23	C₂×C₄×Dic₇₉	—	2	1	no	—
24	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
25	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
27	C₄×C₇₉⋊C₈	—	2	1	no	—
28	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
29	C₂×Q₁₆×C₇₉	—	2	2	no	—
30	C₂²×C₈×C₇₉	D₄	1	2	yes	—
31	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
32	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
33	#125×C₇₉	—	2	2	no	—
34	C₂²⋊Q₈×C₇₉	—	2	2	no	—
35	C₂²⋊Q₈×C₇₉	—	2	2	no	—
36	C₄×Q₈×C₇₉	—	2	2	no	—
37	C₄×Q₈×C₇₉	—	2	2	no	—
38	#117×C₇₉	—	2	2	no	—
39	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
40	#107×C₇₉	—	2	2	no	—
41	#103×C₇₉	—	2	4	no	—
42	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₇₉	D₄	1	2	yes	—
45	C₂²×Dic₇₉	—	2	2	no	—
46	#11929608	—	4	4	no	—
47	C₂×C₇₉⋊C₈	—	2	2	no	—
48	C₂×C₇₉⋊C₈	—	4	2	no	—
49	C₂×C₇₉⋊C₈	—	4	2	no	—
50	C₄×Dic₇₉	—	2	4	no	—
51	C₄×Dic₇₉	—	2	4	no	—
52	C₄×Dic₇₉	—	4	2	no	—
53	C₂×Q₈×C₇₉	—	2	2	no	—
54	C₂×Q₈×C₇₉	—	2	2	no	—
55	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
58	Q₁₆×C₇₉	—	4	4	no	—
59	C₂×C₈×C₇₉	—	4	2	no	—
60	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
62	C₄⋊C₄×C₇₉	—	2	2	no	—
63	C₄⋊C₄×C₇₉	—	2	2	no	—
64	C₄⋊C₄×C₇₉	—	2	2	no	—
65	C₄⋊C₄×C₇₉	—	2	2	no	—
66	C₄⋊C₄×C₇₉	—	4	2	no	—
67	C₄⋊C₄×C₇₉	—	4	2	no	—
68	C₂²⋊C₄×C₇₉	—	4	2	no	—
69	C₄²×C₇₉	—	4	2	no	—
70	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₇₉	#41	1	1	yes	characteristic
74	C₂³×C₇₉	#121	1	1	yes	characteristic
75	Q₈×C₇₉	—	4	4	no	—
76	Q₈×C₇₉	—	4	4	no	—
77	C₂×C₄×C₇₉	—	2	2	no	—
78	C₂×C₄×C₇₉	—	2	2	no	—
79	C₂×C₄×C₇₉	—	4	2	no	—
80	C₂×C₄×C₇₉	—	4	2	no	—
81	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
87	C₂×C₄×C₇₉	#137	1	4	yes	—
88	C₂×Dic₇₉	—	2	4	no	—
89	C₂×Dic₇₉	—	4	2	no	—
90	C₂×Dic₇₉	—	4	2	no	—
91	C₈×C₇₉	—	2	2	no	—
92	C₈×C₇₉	—	2	2	no	—
93	C₇₉⋊C₈	—	4	2	no	—
94	C₇₉⋊C₈	—	8	2	no	—
95	C₂²×C₇₉	—	2	1	no	—
96	C₂²×C₇₉	—	2	1	no	—
97	C₂²×C₇₉	#390	1	1	yes	characteristic
98	C₂²×C₇₉	#470	1	2	yes	—
99	C₄×C₇₉	—	2	1	no	—
100	C₄×C₇₉	—	2	1	no	—
101	C₄×C₇₉	—	8	2	no	—
102	C₄×C₇₉	—	8	2	no	—
103	C₄×C₇₉	#421	1	2	yes	—
104	C₄×C₇₉	#441	1	2	yes	—
105	C₄×C₇₉	#443	1	2	yes	—
106	C₄×C₇₉	#497	1	2	yes	—
107	Dic₇₉	—	4	4	no	—
108	#9853	—	79	1	no	maximal, Sylow
109	C₂×C₇₉	—	2	2	no	—
110	C₂×C₇₉	#1963	1	1	yes	characteristic
111	C₂×C₇₉	#1971	1	1	yes	characteristic
112	C₂×C₇₉	#1974	1	1	yes	characteristic
113	#3170	D₇₉	1	1	yes	characteristic
114	#1994	—	79	2	no	—
115	#1744	—	79	1	no	—
116	#1566	—	79	1	no	—
117	#1493	—	79	2	no	—
118	C₇₉	#9853	1	1	yes	characteristic, complemented, Sylow
119	#533	C₂×D₇₉	1	2	yes	—
120	#500	Dic₇₉	1	1	yes	characteristic, complemented
121	#494	Dic₇₉	1	1	yes	characteristic, complemented
122	#487	Dic₇₉	1	2	yes	complemented
123	#467	—	2	2	no	—
124	C₄×Q₁₆	—	2	2	no	—
125	#423	—	79	2	no	—
126	C₂×C₄×C₈	—	79	1	no	—
127	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
128	C₄³	—	79	1	no	—
129	#339	—	158	4	no	—
130	#336	—	158	2	no	—
131	#334	—	158	2	no	—
132	Q₈⋊C₈	—	158	4	no	—
133	C₂×Q₁₆	—	2	2	no	—
134	C₂×M₁₆	—	158	2	no	—
135	C₂²×C₈	—	158	1	no	—
136	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
137	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
138	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
139	#125	—	2	2	no	—
140	C₂²⋊Q₈	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	#117	—	2	2	no	—
145	C₂×C₄²	—	79	2	no	—
146	C₂×C₄²	—	158	1	no	—
147	C₂×C₄²	—	158	1	no	—
148	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
149	#107	—	2	2	no	—
150	C₄⋊C₈	—	158	2	no	—
151	C₄⋊C₈	—	158	2	no	—
152	#103	—	2	4	no	—
153	C₄×C₈	—	79	2	no	—
154	C₄×C₈	—	158	1	no	—
155	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
156	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
157	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
158	C₂×Q₈	—	2	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂²×C₄	—	158	2	no	—
161	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
162	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
163	C₂²×C₄	#11929623	1	1	yes	characteristic
164	Q₁₆	—	4	4	no	—
165	M₁₆	—	316	4	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	—	316	2	no	—
168	C₂×C₈	—	316	2	no	—
169	C₂×C₈	—	158	2	no	—
170	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
171	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₂²⋊C₄	—	4	2	no	—
179	C₄²	—	4	2	no	—
180	C₄²	—	316	2	no	—
181	C₄²	—	158	4	no	—
182	C₄²	—	158	4	no	—
183	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
184	C₄²	D₄×D₇₉	1	1	yes	characteristic
185	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
186	C₄²	#11929623	1	1	yes	characteristic
187	C₂³	#14579132	1	1	yes	characteristic
188	Q₈	—	4	4	no	—
189	Q₈	—	4	4	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	316	2	no	—
195	C₂×C₄	—	316	2	no	—
196	C₂×C₄	—	158	4	no	—
197	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
198	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
199	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
200	C₂×C₄	#14579132	1	1	yes	characteristic
201	C₂×C₄	#14579148	1	1	yes	characteristic
202	C₂×C₄	#14579157	1	1	yes	characteristic
203	C₂×C₄	#14579193	1	4	yes	—
204	C₈	—	2	2	no	—
205	C₈	—	2	2	no	—
206	C₈	—	316	2	no	—
207	C₈	—	632	2	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	#19098466	1	1	yes	characteristic
211	C₂²	#19098818	1	2	yes	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	8	2	no	—
215	C₄	—	8	2	no	—
216	C₄	—	316	4	no	—
217	C₄	#19098580	1	2	yes	—
218	C₄	#19098670	1	2	yes	—
219	C₄	#19098680	1	2	yes	—
220	C₄	#19098956	1	2	yes	—
221	C₂	—	2	2	no	—
222	C₂	#23764233	1	1	yes	characteristic
223	C₂	#23764272	1	1	yes	characteristic
224	C₂	#23764289	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764378

C₂

yes

maximal

#23763145

C₂

yes

maximal, characteristic

#23762156

C₂

yes

maximal, characteristic

#23761855

C₂

yes

maximal

C₇₉×#3170

C₂

yes

maximal, characteristic

#19098587

C₂²

yes

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₇₉

C₂²

yes

—

—

—

Q₈⋊(C₇₉⋊C₈)

—

#533×C₇₉

C₂²

yes

—

#500×C₇₉

C₄

yes

characteristic, complemented

#494×C₇₉

C₄

yes

characteristic, complemented

#487×C₇₉

C₄

yes

complemented

#467×C₇₉

—

C₄×Q₁₆×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

D₄

yes

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂×Q₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

#125×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

#117×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#107×C₇₉

—

#103×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

—

C₂²×Dic₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

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×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#390

yes

characteristic

C₂²×C₇₉

#470

yes

—

C₄×C₇₉

—

100

C₄×C₇₉

—

101

C₄×C₇₉

—

102

C₄×C₇₉

—

103

C₄×C₇₉

#421

yes

—

104

C₄×C₇₉

#441

yes

—

105

C₄×C₇₉

#443

yes

—

106

C₄×C₇₉

#497

yes

—

107

Dic₇₉

—

108

#9853

—

maximal, Sylow

109

C₂×C₇₉

—

110

C₂×C₇₉

#1963

yes

characteristic

111

C₂×C₇₉

#1971

yes

characteristic

112

C₂×C₇₉

#1974

yes

characteristic

113

#3170

D₇₉

yes

characteristic

114

#1994

—

115

#1744

—

116

#1566

—

117

#1493

—

118

C₇₉

#9853

yes

characteristic, complemented, Sylow

119

#533

C₂×D₇₉

yes

—

120

#500

Dic₇₉

yes

characteristic, complemented

121

#494

Dic₇₉

yes

characteristic, complemented

122

#487

Dic₇₉

yes

complemented

123

#467

—

124

C₄×Q₁₆

—

125

#423

—

126

C₂×C₄×C₈

—

127

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

128

C₄³

—

129

#339

—

158

—

130

#336

—

158

—

131

#334

—

158

—

132

Q₈⋊C₈

—

158

—

133

C₂×Q₁₆

—

134

C₂×M₁₆

—

158

—

135

C₂²×C₈

—

158

—

136

C₂²×C₈

C₂²⋊D₇₉

yes

—

137

C₄⋊Q₈

C₂×Dic₇₉

yes

—

138

C₄⋊Q₈

C₂×Dic₇₉

yes

—

139

#125

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

142

C₄×Q₈

—

143

C₄×Q₈

—

144

#117

—

145

C₂×C₄²

—

146

C₂×C₄²

—

158

—

147

C₂×C₄²

—

158

—

148

C₂×C₄²

C₂²×D₇₉

yes

characteristic

149

#107

—

150

C₄⋊C₈

—

158

—

151

C₄⋊C₈

—

158

—

152

#103

—

153

C₄×C₈

—

154

C₄×C₈

—

158

—

155

C₄×C₈

C₂×Dic₇₉

yes

characteristic

156

C₄×C₈

C₂×Dic₇₉

yes

characteristic

157

C₄×C₈

C₂²⋊D₇₉

yes

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂²×C₄

—

158

—

161

C₂²×C₄

D₄×D₇₉

yes

characteristic

162

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

163

C₂²×C₄

#11929623

yes

characteristic

164

Q₁₆

—

165

M₁₆

—

316

—

166

C₂×C₈

—

167

C₂×C₈

—

316

—

168

C₂×C₈

—

316

—

169

C₂×C₈

—

158

—

170

C₂×C₈

C₂²⋊Dic₇₉

yes

—

171

C₂×C₈

C₂²⋊Dic₇₉

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₂²⋊C₄

—

179

C₄²

—

180

C₄²

—

316

—

181

C₄²

—

158

—

182

C₄²

—

158

—

183

C₄²

C₂²×Dic₇₉

yes

characteristic

184

C₄²

D₄×D₇₉

yes

characteristic

185

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

186

C₄²

#11929623

yes

characteristic

187

C₂³

#14579132

yes

characteristic

188

Q₈

—

189

Q₈

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

316

—

195

C₂×C₄

—

316

—

196

C₂×C₄

—

158

—

197

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

198

C₂×C₄

D₄×Dic₇₉

yes

characteristic

199

C₂×C₄

D₄×Dic₇₉

yes

characteristic

200

C₂×C₄

#14579132

yes

characteristic

201

C₂×C₄

#14579148

yes

characteristic

202

C₂×C₄

#14579157

yes

characteristic

203

C₂×C₄

#14579193

yes

—

204

C₈

—

205

C₈

—

206

C₈

—

316

—

207

C₈

—

632

—

208

C₂²

—

209

C₂²

—

210

C₂²

#19098466

yes

characteristic

211

C₂²

#19098818

yes

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

316

—

217

C₄

#19098580

yes

—

218

C₄

#19098670

yes

—

219

C₄

#19098680

yes

—

220

C₄

#19098956

yes

—

221

C₂

—

222

C₂

#23764233

yes

characteristic

223

C₂

#23764272

yes

characteristic

224

C₂

#23764289

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3170	C₂
socle	C₂²×C₇₉	#390
prime radical	C₂³×C₇₉	#121
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3170	D₇₉
hypocenter	C₇₉	#9853
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#14579157

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3170

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. #500×C₇₉	C₄	semidirect
15. #494×C₇₉	C₄	semidirect
16. #487×C₇₉	C₄	semidirect
118. C₇₉	#9853	semidirect
120. #500	Dic₇₉	semidirect
121. #494	Dic₇₉	semidirect
122. #487	Dic₇₉	semidirect

H ≅ G/N

type

14. #500×C₇₉

C₄

semidirect

15. #494×C₇₉

C₄

semidirect

16. #487×C₇₉

C₄

semidirect

118. C₇₉

#9853

semidirect

120. #500

Dic₇₉

semidirect

121. #494

Dic₇₉

semidirect

122. #487

Dic₇₉

semidirect

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

subgroup	index
#23764378	2
#23763145	2
#23762156	2
#23761855	2
C₇₉×#3170	2
#9853	79

subgroup

index

C₇₉×#3170

Subgroups — #34188197

Conjugacy classes of subgroups

Complements

Maximal subgroups