Group #34180645 — subgroups

Subgroups — #34180645

Order 20224.

620 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 131 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	#23764382	C₂	1	1	yes	maximal, characteristic
2	#23762130	C₂	1	2	yes	maximal
3	#23762038	C₂	1	1	yes	maximal, characteristic
4	#23761912	C₂	1	2	yes	maximal
5	C₇₉×#3556	C₂	1	1	yes	maximal, characteristic
6	#19098620	C₂²	1	2	yes	—
7	#19098587	C₂²	1	1	yes	characteristic
8	#19098409	C₂²	1	1	yes	characteristic
9	#19098322	—	2	2	no	—
10	#19098312	—	2	2	no	—
11	#19098309	—	2	2	no	—
12	#19098305	—	2	2	no	—
13	#19098300	—	2	4	no	—
14	#564×C₇₉	—	2	2	no	—
15	#557×C₇₉	—	2	2	no	—
16	#557×C₇₉	—	2	2	no	—
17	#557×C₇₉	C₄	1	4	yes	complemented
18	#541×C₇₉	—	2	4	no	—
19	#541×C₇₉	—	2	2	no	—
20	#533×C₇₉	C₂²	1	2	yes	—
21	#533×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×#11929608	—	2	1	no	—
23	C₂×C₄×Dic₇₉	—	2	1	no	—
24	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
27	#14579072	—	2	2	no	—
28	C₇₉⋊#95	—	2	2	no	—
29	C₄⋊Q₈×C₇₉	—	2	2	no	—
30	C₄⋊Q₈×C₇₉	—	2	4	no	—
31	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
32	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
33	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
34	#126×C₇₉	—	2	8	no	—
35	#125×C₇₉	—	2	2	no	—
36	#125×C₇₉	—	2	8	no	—
37	#125×C₇₉	—	2	8	no	—
38	#125×C₇₉	—	2	4	no	—
39	#125×C₇₉	—	2	8	no	—
40	#125×C₇₉	—	2	2	no	—
41	#125×C₇₉	D₄	1	2	yes	—
42	C₂²⋊Q₈×C₇₉	—	2	2	no	—
43	C₂²⋊Q₈×C₇₉	—	2	2	no	—
44	C₂²⋊Q₈×C₇₉	D₄	1	4	yes	—
45	C₄×Q₈×C₇₉	—	2	4	no	—
46	C₄×Q₈×C₇₉	—	2	4	no	—
47	C₄×Q₈×C₇₉	—	2	4	no	—
48	C₄×Q₈×C₇₉	—	2	2	no	—
49	C₄×Q₈×C₇₉	—	2	2	no	—
50	C₄×Q₈×C₇₉	C₂×C₄	1	4	yes	—
51	#117×C₇₉	—	2	2	no	—
52	#117×C₇₉	D₄	1	2	yes	—
53	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
54	C₂²×Dic₇₉	—	4	1	no	—
55	#11929608	—	4	2	no	—
56	C₂×C₇₉⋊C₈	—	4	2	no	—
57	C₂×C₇₉⋊C₈	—	4	1	no	—
58	C₄×Dic₇₉	—	2	2	no	—
59	C₄×Dic₇₉	—	4	1	no	—
60	C₂×Q₈×C₇₉	—	2	2	no	—
61	C₂×Q₈×C₇₉	—	2	2	no	—
62	C₂×Q₈×C₇₉	C₂²⋊C₄	1	4	yes	—
63	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
65	C₄⋊C₄×C₇₉	—	2	8	no	—
66	C₄⋊C₄×C₇₉	—	2	8	no	—
67	C₄⋊C₄×C₇₉	—	2	8	no	—
68	C₄⋊C₄×C₇₉	—	2	2	no	—
69	C₄⋊C₄×C₇₉	—	2	4	no	—
70	C₄⋊C₄×C₇₉	—	2	2	no	—
71	C₄⋊C₄×C₇₉	—	2	2	no	—
72	C₄⋊C₄×C₇₉	—	2	2	no	—
73	C₄⋊C₄×C₇₉	—	2	4	no	—
74	C₄⋊C₄×C₇₉	—	2	4	no	—
75	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
76	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
77	C₂²⋊C₄×C₇₉	—	2	4	no	—
78	C₂²⋊C₄×C₇₉	—	2	2	no	—
79	C₄²×C₇₉	—	2	8	no	—
80	C₄²×C₇₉	—	2	4	no	—
81	C₄²×C₇₉	—	2	2	no	—
82	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₇₉	C₂×D₄	1	2	yes	—
84	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
85	C₂³×C₇₉	#120	1	1	yes	characteristic
86	Q₈×C₇₉	—	4	4	no	—
87	Q₈×C₇₉	—	4	4	no	—
88	Q₈×C₇₉	—	4	2	no	—
89	Q₈×C₇₉	—	4	2	no	—
90	C₂×C₄×C₇₉	—	2	1	no	—
91	C₂×C₄×C₇₉	—	2	1	no	—
92	C₂×C₄×C₇₉	—	2	4	no	—
93	C₂×C₄×C₇₉	—	2	4	no	—
94	C₂×C₄×C₇₉	—	2	4	no	—
95	C₂×C₄×C₇₉	—	4	2	no	—
96	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
97	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₇₉	#120	1	2	yes	—
99	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
100	C₂×Dic₇₉	—	4	2	no	—
101	C₂×Dic₇₉	—	8	2	no	—
102	C₇₉⋊C₈	—	8	2	no	—
103	C₇₉⋊C₈	—	8	1	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	—	2	2	no	—
106	C₂²×C₇₉	#379	1	1	yes	characteristic
107	C₄×C₇₉	—	2	1	no	—
108	C₄×C₇₉	—	2	2	no	—
109	C₄×C₇₉	—	2	2	no	—
110	C₄×C₇₉	—	4	4	no	—
111	C₄×C₇₉	—	4	4	no	—
112	C₄×C₇₉	—	4	4	no	—
113	C₄×C₇₉	#454	1	1	yes	characteristic
114	C₄×C₇₉	#456	1	1	yes	characteristic
115	Dic₇₉	—	8	2	no	—
116	#8495	—	79	1	no	maximal, Sylow
117	C₂×C₇₉	—	4	1	no	—
118	C₂×C₇₉	#1793	1	1	yes	characteristic
119	C₂×C₇₉	#1796	1	2	yes	—
120	#3556	D₇₉	1	1	yes	characteristic
121	#1995	—	79	1	no	—
122	#1559	—	79	2	no	—
123	#1537	—	79	1	no	—
124	#1506	—	79	2	no	—
125	C₇₉	#8495	1	1	yes	characteristic, complemented, Sylow
126	#564	—	2	2	no	—
127	#557	—	2	2	no	—
128	#557	—	2	2	no	—
129	#557	Dic₇₉	1	4	yes	complemented
130	#541	—	2	4	no	—
131	#541	—	2	2	no	—
132	#533	C₂×D₇₉	1	2	yes	—
133	#533	C₂×D₇₉	1	1	yes	characteristic
134	#432	—	79	2	no	—
135	#423	—	79	1	no	—
136	#376	—	79	1	no	—
137	#339	—	158	2	no	—
138	#333	—	158	2	no	—
139	#332	—	158	2	no	—
140	#330	—	158	2	no	—
141	#328	—	158	4	no	—
142	C₂×M₁₆	—	158	1	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	4	no	—
145	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
146	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
147	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
148	#126	—	2	8	no	—
149	#125	—	2	2	no	—
150	#125	—	2	8	no	—
151	#125	—	2	8	no	—
152	#125	—	2	4	no	—
153	#125	—	2	8	no	—
154	#125	—	2	2	no	—
155	#125	C₂²⋊D₇₉	1	2	yes	—
156	C₂²⋊Q₈	—	2	2	no	—
157	C₂²⋊Q₈	—	2	2	no	—
158	C₂²⋊Q₈	C₂²⋊D₇₉	1	4	yes	—
159	C₄×Q₈	—	2	4	no	—
160	C₄×Q₈	—	2	4	no	—
161	C₄×Q₈	—	2	4	no	—
162	C₄×Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	C₄×Q₈	C₂×Dic₇₉	1	4	yes	—
165	#117	—	2	2	no	—
166	#117	C₂²⋊D₇₉	1	2	yes	—
167	C₂×C₄²	—	158	1	no	—
168	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
169	C₄⋊C₈	—	158	2	no	—
170	C₄⋊C₈	—	158	2	no	—
171	C₂²⋊C₈	—	158	2	no	—
172	#97	—	158	2	no	—
173	#95	—	158	2	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	C₂²⋊Dic₇₉	1	4	yes	—
177	C₂²×C₄	—	316	1	no	—
178	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
180	M₁₆	—	316	2	no	—
181	C₂×C₈	—	316	2	no	—
182	C₂×C₈	—	316	1	no	—
183	C₄⋊C₄	—	2	8	no	—
184	C₄⋊C₄	—	2	8	no	—
185	C₄⋊C₄	—	2	8	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	2	4	no	—
192	C₄⋊C₄	—	2	4	no	—
193	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
194	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
195	C₂²⋊C₄	—	2	4	no	—
196	C₂²⋊C₄	—	2	2	no	—
197	C₄²	—	2	8	no	—
198	C₄²	—	2	4	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	316	1	no	—
201	C₄²	—	158	2	no	—
202	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
203	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
204	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
205	C₂³	#14579130	1	1	yes	characteristic
206	Q₈	—	4	4	no	—
207	Q₈	—	4	4	no	—
208	Q₈	—	4	2	no	—
209	Q₈	—	4	2	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	4	no	—
213	C₂×C₄	—	2	4	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	316	2	no	—
217	C₂×C₄	—	632	2	no	—
218	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
219	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
220	C₂×C₄	#14579130	1	2	yes	—
221	C₂×C₄	#14579130	1	1	yes	characteristic
222	C₈	—	632	2	no	—
223	C₈	—	632	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	2	no	—
226	C₂²	#19098419	1	1	yes	characteristic
227	C₄	—	2	1	no	—
228	C₄	—	2	2	no	—
229	C₄	—	2	2	no	—
230	C₄	—	4	4	no	—
231	C₄	—	4	4	no	—
232	C₄	—	4	4	no	—
233	C₄	—	632	2	no	—
234	C₄	#19098736	1	1	yes	characteristic
235	C₄	#19098746	1	1	yes	characteristic
236	C₂	—	4	1	no	—
237	C₂	#23763359	1	1	yes	characteristic
238	C₂	#23763375	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23764382

C₂

yes

maximal, characteristic

#23762130

C₂

yes

maximal

#23762038

C₂

yes

maximal, characteristic

#23761912

C₂

yes

maximal

C₇₉×#3556

C₂

yes

maximal, characteristic

#19098620

C₂²

yes

—

#19098587

C₂²

yes

characteristic

#19098409

C₂²

yes

—

—

—

—

—

#564×C₇₉

—

#557×C₇₉

—

#557×C₇₉

—

#557×C₇₉

C₄

yes

complemented

#541×C₇₉

—

#541×C₇₉

—

#533×C₇₉

C₂²

yes

—

#533×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₂×C₄×Dic₇₉

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₇₉⋊#95

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

—

#126×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

D₄

yes

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

D₄

yes

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

C₂×C₄

yes

—

#117×C₇₉

—

#117×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₂³×C₇₉

#120

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

100

C₂×Dic₇₉

—

101

C₂×Dic₇₉

—

102

C₇₉⋊C₈

—

103

C₇₉⋊C₈

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

#379

yes

characteristic

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

—

113

C₄×C₇₉

#454

yes

characteristic

114

C₄×C₇₉

#456

yes

characteristic

115

Dic₇₉

—

116

#8495

—

maximal, Sylow

117

C₂×C₇₉

—

118

C₂×C₇₉

#1793

yes

characteristic

119

C₂×C₇₉

#1796

yes

—

120

#3556

D₇₉

yes

characteristic

121

#1995

—

122

#1559

—

123

#1537

—

124

#1506

—

125

C₇₉

#8495

yes

characteristic, complemented, Sylow

126

#564

—

127

#557

—

128

#557

—

129

#557

Dic₇₉

yes

complemented

130

#541

—

131

#541

—

132

#533

C₂×D₇₉

yes

—

133

#533

C₂×D₇₉

yes

characteristic

134

#432

—

135

#423

—

136

#376

—

137

#339

—

158

—

138

#333

—

158

—

139

#332

—

158

—

140

#330

—

158

—

141

#328

—

158

—

142

C₂×M₁₆

—

158

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

C₂×Dic₇₉

yes

—

146

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

147

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

148

#126

—

149

#125

—

150

#125

—

151

#125

—

152

#125

—

153

#125

—

154

#125

—

155

#125

C₂²⋊D₇₉

yes

—

156

C₂²⋊Q₈

—

157

C₂²⋊Q₈

—

158

C₂²⋊Q₈

C₂²⋊D₇₉

yes

—

159

C₄×Q₈

—

160

C₄×Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

C₂×Dic₇₉

yes

—

165

#117

—

166

#117

C₂²⋊D₇₉

yes

—

167

C₂×C₄²

—

158

—

168

C₂×C₄²

C₂²×D₇₉

yes

characteristic

169

C₄⋊C₈

—

158

—

170

C₄⋊C₈

—

158

—

171

C₂²⋊C₈

—

158

—

172

#97

—

158

—

173

#95

—

158

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

C₂²⋊Dic₇₉

yes

—

177

C₂²×C₄

—

316

—

178

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

—

180

M₁₆

—

316

—

181

C₂×C₈

—

316

—

182

C₂×C₈

—

316

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

C₂²⋊Dic₇₉

yes

—

194

C₄⋊C₄

C₂²⋊Dic₇₉

yes

—

195

C₂²⋊C₄

—

196

C₂²⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

316

—

201

C₄²

—

158

—

202

C₄²

C₂²×Dic₇₉

yes

characteristic

203

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

204

C₄²

C₂×C₂²⋊D₇₉

yes

—

205

C₂³

#14579130

yes

characteristic

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

Q₈

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

316

—

217

C₂×C₄

—

632

—

218

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

—

219

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

220

C₂×C₄

#14579130

yes

—

221

C₂×C₄

#14579130

yes

characteristic

222

C₈

—

632

—

223

C₈

—

632

—

224

C₂²

—

225

C₂²

—

226

C₂²

#19098419

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

632

—

234

C₄

#19098736

yes

characteristic

235

C₄

#19098746

yes

characteristic

236

C₂

—

237

C₂

#23763359

yes

characteristic

238

C₂

#23763375

yes

—

	subgroup	G/H
center	C₂²	#19098419
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3556	C₂
socle	C₂²×C₇₉	#379
prime radical	C₂³×C₇₉	#120
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3556	D₇₉
hypocenter	C₇₉	#8495
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3556

subgroup

G/H

center

C₂²

#19098419

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3556

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3556

N	H ≅ G/N	type
17. #557×C₇₉	C₄	semidirect
125. C₇₉	#8495	semidirect
129. #557	Dic₇₉	semidirect

H ≅ G/N

type

17. #557×C₇₉

C₄

semidirect

125. C₇₉

#8495

semidirect

129. #557

Dic₇₉

semidirect

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

subgroup	index
#23764382	2
#23762130	2
#23762038	2
#23761912	2
C₇₉×#3556	2
#8495	79

subgroup

index

C₇₉×#3556

Subgroups — #34180645

Conjugacy classes of subgroups

Complements

Maximal subgroups