Group #34182148 — subgroups

Subgroups — #34182148

Order 20224.

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

normal subgroups only

This group has 386 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	#23772485	C₂	1	1	yes	maximal, characteristic
2	#23764337	C₂	1	1	yes	maximal, characteristic
3	#23762152	C₂	1	2	yes	maximal
4	#23761238	C₂	1	2	yes	maximal
5	C₄×#101×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#19098694	—	2	2	no	—
7	#19098694	—	2	2	no	—
8	#19098620	—	2	2	no	—
9	#19098616	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
12	#19098318	—	2	2	no	—
13	#19098316	—	2	2	no	—
14	#19098314	—	2	2	no	—
15	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#101×C₇₉	C₄	1	2	yes	—
17	C₄×M₁₆×C₇₉	C₂²	1	2	yes	—
18	#343×C₇₉	C₄	1	1	yes	characteristic
19	#343×C₇₉	C₄	1	1	yes	characteristic
20	C₂²×C₇₉⋊C₈	—	2	1	no	—
21	C₂²×C₇₉⋊C₈	—	2	1	no	—
22	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
23	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
24	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
26	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
27	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
28	#14579072	—	2	4	no	—
29	C₄×C₇₉⋊C₈	—	2	2	no	—
30	C₄×C₇₉⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
32	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
33	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
34	C₄×Q₈×C₇₉	—	2	2	no	—
35	C₄×Q₈×C₇₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₇₉	Q₈	1	2	yes	—
38	C₂×C₄²×C₇₉	D₄	1	2	yes	—
39	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
40	#101×C₇₉	—	2	4	no	—
41	#97×C₇₉	—	2	2	no	—
42	C₄×C₈×C₇₉	—	2	2	no	—
43	C₂×C₇₉⋊C₈	—	2	2	no	—
44	C₂×C₇₉⋊C₈	—	2	2	no	—
45	C₂×C₇₉⋊C₈	—	2	2	no	—
46	C₂×C₇₉⋊C₈	—	4	1	no	—
47	C₂×C₇₉⋊C₈	—	4	2	no	—
48	C₂×C₇₉⋊C₈	—	4	1	no	—
49	C₂×C₇₉⋊C₈	—	4	1	no	—
50	C₂×Q₈×C₇₉	—	2	2	no	—
51	C₂×Q₈×C₇₉	—	2	2	no	—
52	C₂×Q₈×C₇₉	—	2	1	no	—
53	C₂×Q₈×C₇₉	—	2	1	no	—
54	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
59	M₁₆×C₇₉	—	2	2	no	—
60	M₁₆×C₇₉	—	2	2	no	—
61	M₁₆×C₇₉	—	2	2	no	—
62	M₁₆×C₇₉	M₁₆	1	4	yes	—
63	C₂×C₈×C₇₉	—	2	2	no	—
64	C₂×C₈×C₇₉	—	2	2	no	—
65	C₄⋊C₄×C₇₉	—	2	2	no	—
66	C₄⋊C₄×C₇₉	—	2	4	no	—
67	C₄²×C₇₉	—	2	2	no	—
68	C₄²×C₇₉	—	2	2	no	—
69	C₄²×C₇₉	C₂×D₄	1	2	yes	—
70	C₄²×C₇₉	#41	1	2	yes	—
71	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
72	Q₈×C₇₉	—	4	2	no	—
73	Q₈×C₇₉	—	4	2	no	—
74	C₂×C₄×C₇₉	—	2	1	no	—
75	C₂×C₄×C₇₉	—	2	1	no	—
76	C₂×C₄×C₇₉	—	2	2	no	—
77	C₂×C₄×C₇₉	—	2	2	no	—
78	C₂×C₄×C₇₉	—	2	2	no	—
79	C₂×C₄×C₇₉	—	2	2	no	—
80	C₂×C₄×C₇₉	—	4	1	no	—
81	C₂×C₄×C₇₉	—	4	2	no	—
82	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
86	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
87	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
88	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
89	C₈×C₇₉	—	2	4	no	—
90	C₈×C₇₉	—	4	2	no	—
91	C₇₉⋊C₈	—	4	2	no	—
92	C₇₉⋊C₈	—	4	2	no	—
93	C₇₉⋊C₈	—	4	2	no	—
94	C₇₉⋊C₈	—	8	1	no	—
95	C₂²×C₇₉	—	2	1	no	—
96	C₂²×C₇₉	—	2	1	no	—
97	C₂²×C₇₉	#385	1	1	yes	characteristic
98	C₂²×C₇₉	#423	1	1	yes	characteristic
99	C₂²×C₇₉	#424	1	1	yes	characteristic
100	C₄×C₇₉	—	2	1	no	—
101	C₄×C₇₉	—	2	2	no	—
102	C₄×C₇₉	—	4	2	no	—
103	C₄×C₇₉	—	4	2	no	—
104	C₄×C₇₉	#435	1	2	yes	—
105	C₄×C₇₉	#436	1	2	yes	—
106	C₄×C₇₉	#454	1	1	yes	characteristic
107	C₄×C₇₉	#456	1	1	yes	characteristic
108	#8838	—	79	1	no	maximal, Sylow
109	C₂×C₇₉	—	2	1	no	—
110	C₂×C₇₉	—	2	1	no	—
111	C₂×C₇₉	#1851	1	1	yes	characteristic
112	C₂×C₇₉	#1857	1	1	yes	characteristic
113	C₂×C₇₉	#1858	1	1	yes	characteristic
114	#2983	—	79	1	no	—
115	#1984	—	79	1	no	—
116	C₄×#101	D₇₉	1	1	yes	characteristic
117	#1565	—	79	2	no	—
118	#1278	—	79	2	no	—
119	C₇₉	#8838	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
121	#446	—	158	2	no	—
122	#446	—	158	2	no	—
123	#432	—	158	2	no	—
124	#431	—	79	2	no	—
125	C₂×C₄⋊C₈	—	79	1	no	—
126	C₂×#101	Dic₇₉	1	2	yes	—
127	C₄×M₁₆	C₂×D₇₉	1	2	yes	—
128	C₂×C₄×C₈	—	79	1	no	—
129	#343	Dic₇₉	1	1	yes	characteristic
130	#343	Dic₇₉	1	1	yes	characteristic
131	#336	—	158	2	no	—
132	#335	—	158	2	no	—
133	#334	—	158	2	no	—
134	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
135	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
136	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
137	C₂²×C₈	—	158	1	no	—
138	C₂²×C₈	—	158	1	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₂×C₄⋊C₄	Dic₁₅₈	1	2	yes	—
142	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
143	C₂×C₄²	D₃₁₆	1	2	yes	—
144	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
145	C₄⋊C₈	—	79	2	no	—
146	C₄⋊C₈	—	79	2	no	—
147	C₄⋊C₈	—	158	2	no	—
148	C₄⋊C₈	—	158	2	no	—
149	C₄⋊C₈	—	158	2	no	—
150	#101	—	2	4	no	—
151	C₂²⋊C₈	—	158	2	no	—
152	#97	—	2	2	no	—
153	#97	—	158	4	no	—
154	C₄×C₈	—	2	2	no	—
155	C₄×C₈	—	158	2	no	—
156	C₄×C₈	—	158	2	no	—
157	C₂×Q₈	—	2	2	no	—
158	C₂×Q₈	—	2	2	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	2	1	no	—
161	C₂²×C₄	C₄⋊Dic₇₉	1	2	yes	—
162	C₂²×C₄	C₄⋊Dic₇₉	1	2	yes	—
163	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
164	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
165	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
166	M₁₆	—	2	2	no	—
167	M₁₆	—	2	2	no	—
168	M₁₆	—	2	2	no	—
169	M₁₆	#11929608	1	4	yes	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	316	1	no	—
173	C₂×C₈	—	316	1	no	—
174	C₂×C₈	—	316	2	no	—
175	C₂×C₈	—	316	1	no	—
176	C₂×C₈	—	158	2	no	—
177	C₂×C₈	—	158	2	no	—
178	C₂×C₈	—	158	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄²	—	2	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	D₄×D₇₉	1	2	yes	—
184	C₄²	#11929623	1	2	yes	—
185	C₂³	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
186	Q₈	—	4	2	no	—
187	Q₈	—	4	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
197	C₂×C₄	#14579131	1	1	yes	characteristic
198	C₂×C₄	#14579138	1	2	yes	—
199	C₂×C₄	#14579145	1	1	yes	characteristic
200	C₂×C₄	C₂×#11929608	1	2	yes	—
201	C₂×C₄	#14579168	1	1	yes	characteristic
202	C₂×C₄	#14579168	1	1	yes	characteristic
203	C₈	—	2	4	no	—
204	C₈	—	4	2	no	—
205	C₈	—	316	2	no	—
206	C₈	—	316	2	no	—
207	C₈	—	316	2	no	—
208	C₈	—	632	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	#19098438	1	1	yes	characteristic
212	C₂²	#19098587	1	1	yes	characteristic
213	C₂²	#19098590	1	1	yes	characteristic
214	C₄	—	2	1	no	—
215	C₄	—	2	2	no	—
216	C₄	—	4	2	no	—
217	C₄	—	4	2	no	—
218	C₄	#19098635	1	2	yes	—
219	C₄	#19098641	1	2	yes	—
220	C₄	#19098738	1	1	yes	characteristic
221	C₄	#19098748	1	1	yes	characteristic
222	C₂	—	2	1	no	—
223	C₂	—	2	1	no	—
224	C₂	#23763585	1	1	yes	characteristic
225	C₂	#23763617	1	1	yes	characteristic
226	C₂	#23763622	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772485

C₂

yes

maximal, characteristic

#23764337

C₂

yes

maximal, characteristic

#23762152

C₂

yes

maximal

#23761238

C₂

yes

maximal

C₄×#101×C₇₉

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₇₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₂×#101×C₇₉

C₄

yes

—

C₄×M₁₆×C₇₉

C₂²

yes

—

#343×C₇₉

C₄

yes

characteristic

#343×C₇₉

C₄

yes

characteristic

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₂²×Q₈×C₇₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₇₉

C₂×C₄

yes

—

C₂×M₁₆×C₇₉

C₂×C₄

yes

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₇₉

Q₈

yes

—

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#101×C₇₉

—

#97×C₇₉

—

C₄×C₈×C₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₄⋊C₄

yes

—

C₂²×C₄×C₇₉

C₄⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

M₁₆

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

C₂×C₄⋊C₄

yes

characteristic

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×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄×D₄

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₉

#123

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

100

C₄×C₇₉

—

101

C₄×C₇₉

—

102

C₄×C₇₉

—

103

C₄×C₇₉

—

104

C₄×C₇₉

#435

yes

—

105

C₄×C₇₉

#436

yes

—

106

C₄×C₇₉

#454

yes

characteristic

107

C₄×C₇₉

yes

108

—

109

C₂×C₇₉

—

110

C₂×C₇₉

—

111

C₂×C₇₉

#1851

yes

characteristic

112

C₂×C₇₉

#1857

yes

characteristic

113

C₂×C₇₉

#1858

yes

characteristic

114

#2983

—

115

#1984

—

116

C₄×#101

D₇₉

yes

characteristic

117

#1565

—

118

#1278

—

119

C₇₉

#8838

yes

characteristic, complemented, Sylow

120

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

121

#446

—

158

—

122

#446

—

158

—

123

#432

—

158

—

124

#431

—

125

C₂×C₄⋊C₈

—

126

C₂×#101

Dic₇₉

yes

—

127

C₄×M₁₆

C₂×D₇₉

yes

—

128

C₂×C₄×C₈

—

129

#343

Dic₇₉

yes

characteristic

130

#343

Dic₇₉

yes

characteristic

131

#336

—

158

—

132

#335

—

158

—

133

#334

—

158

—

134

C₂²×Q₈

C₂×Dic₇₉

yes

characteristic

135

C₂×M₁₆

C₂×Dic₇₉

yes

—

136

C₂×M₁₆

C₂×Dic₇₉

yes

—

137

C₂²×C₈

—

158

—

138

C₂²×C₈

—

158

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₂×C₄⋊C₄

Dic₁₅₈

yes

—

142

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

characteristic

143

C₂×C₄²

D₃₁₆

yes

—

144

C₂×C₄²

C₂²×D₇₉

yes

characteristic

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

158

—

148

C₄⋊C₈

—

158

—

149

C₄⋊C₈

—

158

—

150

#101

—

151

C₂²⋊C₈

—

158

—

152

#97

—

153

#97

—

158

—

154

C₄×C₈

—

155

C₄×C₈

—

158

—

156

C₄×C₈

—

158

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂²×C₄

C₄⋊Dic₇₉

yes

—

162

C₂²×C₄

C₄⋊Dic₇₉

yes

—

163

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

164

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

165

C₂²×C₄

C₂×Dic₁₅₈

yes

characteristic

166

M₁₆

—

167

M₁₆

—

168

M₁₆

—

169

M₁₆

#11929608

yes

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

316

—

173

C₂×C₈

—

316

—

174

C₂×C₈

—

316

—

175

C₂×C₈

—

316

—

176

C₂×C₈

—

158

—

177

C₂×C₈

—

158

—

178

C₂×C₈

—

158

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄²

—

182

C₄²

—

183

C₄²

D₄×D₇₉

yes

—

184

C₄²

#11929623

yes

—

185

C₂³

C₂×C₄⋊Dic₇₉

yes

characteristic

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

D₄×Dic₇₉

yes

—

197

C₂×C₄

#14579131

yes

characteristic

198

C₂×C₄

#14579138

yes

—

199

C₂×C₄

#14579145

yes

characteristic

200

C₂×C₄

C₂×#11929608

yes

—

201

C₂×C₄

#14579168

yes

characteristic

202

C₂×C₄

#14579168

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

316

—

206

C₈

—

316

—

207

C₈

—

316

—

208

C₈

—

632

—

209

C₂²

—

210

C₂²

—

211

C₂²

#19098438

yes

characteristic

212

C₂²

#19098587

yes

characteristic

213

C₂²

#19098590

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

#19098635

yes

—

219

C₄

#19098641

yes

—

220

C₄

#19098738

yes

characteristic

221

C₄

#19098748

yes

characteristic

222

C₂

—

223

C₂

—

224

C₂

#23763585

yes

characteristic

225

C₂

#23763617

yes

characteristic

226

C₂

#23763622

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579131
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₄×#101×C₇₉	C₂
socle	C₂²×C₇₉	#385
prime radical	C₂³×C₇₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₄×#101	D₇₉
hypocenter	C₇₉	#8838
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

subgroup

G/H

center

C₂×C₄

#14579131

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₄×#101×C₇₉

C₂

socle

C₂²×C₇₉

#385

prime radical

C₂³×C₇₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

N	H ≅ G/N	type
119. C₇₉	#8838	semidirect

H ≅ G/N

type

119. C₇₉

#8838

semidirect

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

subgroup	index
#23772485	2
#23764337	2
#23762152	2
#23761238	2
C₄×#101×C₇₉	2
#8838	79

subgroup

index

C₄×#101×C₇₉

Subgroups — #34182148

Conjugacy classes of subgroups

Complements

Maximal subgroups