Group #34188233 — subgroups

Subgroups — #34188233

Order 20224.

498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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	#23773828	C₂	1	1	yes	maximal, characteristic
2	#23763538	C₂	1	1	yes	maximal, characteristic, complemented
3	#23761852	C₂	1	2	yes	maximal, complemented
4	#23761852	C₂	1	2	yes	maximal, complemented
5	C₂×#322×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14579183	—	2	2	no	—
7	#19099113	C₂²	1	2	yes	—
8	#19098947	—	2	2	no	—
9	#19098943	C₄	1	1	yes	characteristic
10	#19098940	C₄	1	1	yes	characteristic
11	#19098936	C₄	1	2	yes	—
12	#19098587	C₂²	1	2	yes	—
13	#19098328	—	2	2	no	—
14	#19098292	—	2	4	no	—
15	#19098292	—	2	4	no	—
16	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	#322×C₇₉	—	2	2	no	—
20	C₂×#11929624	—	2	2	no	—
21	#14579183	—	4	8	no	—
22	C₂×Dic₃₁₆	—	2	2	no	—
23	C₂×#11929613	—	2	4	no	—
24	C₂×D₆₃₂	—	2	2	no	—
25	C₂×#11929608	—	2	2	no	—
26	#14579161	C₂×C₄	1	2	yes	—
27	#14579158	C₂×C₄	1	2	yes	—
28	#14579149	—	2	2	no	—
29	#14579135	—	2	2	no	—
30	#14579135	—	2	2	no	—
31	C₄×D₃₁₆	—	2	2	no	—
32	C₄×D₃₁₆	—	2	2	no	—
33	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
34	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
35	C₂²×C₈×C₇₉	—	2	1	no	—
36	C₂²×C₈×C₇₉	—	2	1	no	—
37	C₂²×C₈×C₇₉	D₄	1	2	yes	—
38	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
39	C₄×C₈×C₇₉	—	2	1	no	—
40	C₄×C₈×C₇₉	—	2	1	no	—
41	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₉	D₄	1	2	yes	—
44	C₄×C₈×C₇₉	D₄	1	2	yes	—
45	C₄×C₈×C₇₉	D₄	1	2	yes	—
46	#11929624	—	4	8	no	—
47	C₂×Dic₁₅₈	—	2	2	no	—
48	C₂×D₃₁₆	—	2	2	no	—
49	C₂×D₃₁₆	—	2	2	no	—
50	C₂×D₃₁₆	—	2	2	no	—
51	C₂×C₂²⋊D₇₉	—	4	2	no	—
52	C₂×C₄×D₇₉	—	4	2	no	—
53	Dic₃₁₆	—	4	4	no	—
54	#11929613	—	4	8	no	—
55	D₆₃₂	—	4	4	no	—
56	#11929608	—	4	4	no	—
57	C₂×C₇₉⋊C₈	—	4	2	no	—
58	C₄⋊Dic₇₉	—	2	2	no	—
59	C₄⋊Dic₇₉	—	2	2	no	—
60	(C₂×D₇₉)⋊C₄	—	4	2	no	—
61	(C₂×D₇₉)⋊C₄	—	4	2	no	—
62	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
65	C₂×C₈×C₇₉	—	2	4	no	—
66	C₂×C₈×C₇₉	—	2	2	no	—
67	C₂×C₈×C₇₉	—	2	2	no	—
68	C₂×C₈×C₇₉	—	2	4	no	—
69	C₂×C₈×C₇₉	—	4	2	no	—
70	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
71	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
72	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₂³×C₇₉	#124	1	1	yes	characteristic
77	C₂²×D₇₉	—	4	2	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	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#121	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	C₂²⋊D₇₉	—	8	4	no	—
88	C₂×Dic₇₉	—	4	2	no	—
89	D₃₁₆	—	4	4	no	—
90	D₃₁₆	—	4	4	no	—
91	D₃₁₆	—	4	4	no	—
92	C₄×D₇₉	—	8	4	no	—
93	Dic₁₅₈	—	4	4	no	—
94	C₈×C₇₉	—	2	4	no	—
95	C₈×C₇₉	—	2	2	no	—
96	C₈×C₇₉	—	2	2	no	—
97	C₈×C₇₉	—	4	2	no	—
98	C₇₉⋊C₈	—	8	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	#490	1	2	yes	—
103	C₂×D₇₉	—	8	2	no	—
104	C₂×D₇₉	—	8	2	no	—
105	C₂×D₇₉	—	8	2	no	—
106	C₄×C₇₉	—	2	1	no	—
107	C₄×C₇₉	—	2	1	no	—
108	C₄×C₇₉	#418	1	2	yes	—
109	C₄×C₇₉	#443	1	2	yes	—
110	C₄×C₇₉	#444	1	2	yes	—
111	C₄×C₇₉	#496	1	2	yes	—
112	Dic₇₉	—	8	2	no	—
113	#9860	—	79	1	no	maximal, Sylow
114	C₂×C₇₉	—	2	2	no	—
115	C₂×C₇₉	#1961	1	1	yes	characteristic
116	C₂×C₇₉	#1974	1	1	yes	characteristic
117	C₂×C₇₉	#1975	1	1	yes	characteristic
118	D₇₉	—	16	2	no	—
119	#3147	—	79	1	no	—
120	#1837	—	79	1	no	—
121	#1492	—	79	2	no	—
122	#1492	—	79	2	no	—
123	C₂×#322	D₇₉	1	1	yes	characteristic, complemented
124	C₇₉	#9860	1	1	yes	characteristic, complemented, Sylow
125	C₂×#135	—	158	2	no	—
126	#532	—	79	2	no	—
127	#495	—	158	2	no	—
128	#494	—	79	1	no	—
129	#493	—	79	1	no	—
130	#492	—	79	2	no	—
131	#423	—	79	2	no	—
132	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
133	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
134	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
135	#341	—	158	2	no	—
136	D₄⋊C₈	—	158	4	no	—
137	D₄⋊C₈	—	158	4	no	—
138	#322	—	2	2	no	—
139	C₂×#41	—	158	2	no	—
140	#135	—	316	8	no	—
141	C₂×Q₁₆	—	158	2	no	—
142	C₂×SD₁₆	—	158	4	no	—
143	C₂×D₈	—	158	2	no	—
144	C₂×M₁₆	—	158	2	no	—
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	D₃₁₆	1	2	yes	—
148	C₄⋊Q₈	—	79	2	no	—
149	#127	—	79	2	no	—
150	#124	—	158	2	no	—
151	#121	—	158	2	no	—
152	#121	—	158	2	no	—
153	C₄×D₄	—	158	2	no	—
154	C₄×D₄	—	158	2	no	—
155	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
156	C₄⋊C₈	—	158	2	no	—
157	C₄⋊C₈	—	158	2	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	—	2	1	no	—
160	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
161	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
162	C₄×C₈	D₃₁₆	1	2	yes	—
163	C₄×C₈	D₃₁₆	1	2	yes	—
164	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
165	#41	—	316	8	no	—
166	C₂×Q₈	—	158	2	no	—
167	C₂×D₄	—	316	2	no	—
168	C₂×D₄	—	158	2	no	—
169	C₂×D₄	—	158	2	no	—
170	C₂×D₄	—	158	2	no	—
171	C₂²×C₄	—	316	2	no	—
172	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
173	C₂²×C₄	#11929624	1	1	yes	characteristic
174	C₂²×C₄	#11929624	1	1	yes	characteristic
175	Q₁₆	—	316	4	no	—
176	SD₁₆	—	316	8	no	—
177	D₈	—	316	4	no	—
178	M₁₆	—	316	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	316	2	no	—
185	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
186	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
187	C₄⋊C₄	—	158	2	no	—
188	C₄⋊C₄	—	158	2	no	—
189	C₂²⋊C₄	—	316	2	no	—
190	C₂²⋊C₄	—	316	2	no	—
191	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
192	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
193	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
194	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
195	C₂³	—	316	2	no	—
196	C₂³	#14579149	1	1	yes	characteristic
197	Q₈	—	316	4	no	—
198	D₄	—	316	4	no	—
199	D₄	—	316	4	no	—
200	D₄	—	316	4	no	—
201	D₄	—	632	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	316	2	no	—
205	C₂×C₄	—	632	4	no	—
206	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
208	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
209	C₂×C₄	#14579135	1	1	yes	characteristic
210	C₂×C₄	#14579135	1	1	yes	characteristic
211	C₂×C₄	#14579158	1	1	yes	characteristic
212	C₂×C₄	#14579189	1	4	yes	—
213	C₈	—	2	4	no	—
214	C₈	—	2	2	no	—
215	C₈	—	2	2	no	—
216	C₈	—	4	2	no	—
217	C₈	—	632	2	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	632	2	no	—
221	C₂²	—	632	2	no	—
222	C₂²	—	632	2	no	—
223	C₂²	#19098465	1	1	yes	characteristic
224	C₂²	#19098928	1	2	yes	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	632	2	no	—
228	C₄	#19098569	1	2	yes	—
229	C₄	#19098681	1	2	yes	—
230	C₄	#19098686	1	2	yes	—
231	C₄	#19098952	1	2	yes	—
232	C₂	—	2	2	no	—
233	C₂	—	1264	2	no	—
234	C₂	#23764224	1	1	yes	characteristic
235	C₂	#23764288	1	1	yes	characteristic
236	C₂	#23764293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773828

C₂

yes

maximal, characteristic

#23763538

C₂

yes

maximal, characteristic, complemented

#23761852

C₂

yes

maximal, complemented

#23761852

C₂

yes

maximal, complemented

C₂×#322×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#14579183

—

#19099113

C₂²

yes

—

#19098947

—

#19098943

C₄

yes

characteristic

#19098940

C₄

yes

characteristic

#19098936

C₄

yes

—

#19098587

C₂²

yes

—

#19098328

—

#19098292

—

#19098292

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#322×C₇₉

—

C₂×#11929624

—

#14579183

—

C₂×Dic₃₁₆

—

C₂×#11929613

—

C₂×D₆₃₂

—

C₂×#11929608

—

#14579161

C₂×C₄

yes

—

#14579158

C₂×C₄

yes

—

#14579149

—

#14579135

—

#14579135

—

C₄×D₃₁₆

—

C₄×D₃₁₆

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄×C₈×C₇₉

—

C₄×C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

D₄

yes

—

#11929624

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

—

Dic₃₁₆

—

#11929613

—

D₆₃₂

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₂²×C₄×C₇₉

C₂×D₄

yes

C₂²×C₄×C₇₉

yes

C₂²×C₄×C₇₉

yes

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₂³×C₇₉

#124

yes

characteristic

C₂²×D₇₉

—

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

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

#390

yes

characteristic

102

C₂²×C₇₉

#490

yes

—

103

C₂×D₇₉

—

104

C₂×D₇₉

—

105

C₂×D₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

#418

yes

—

109

C₄×C₇₉

#443

yes

—

110

C₄×C₇₉

#444

yes

—

111

C₄×C₇₉

#496

yes

—

112

Dic₇₉

—

113

#9860

—

maximal, Sylow

114

C₂×C₇₉

—

115

C₂×C₇₉

#1961

yes

characteristic

116

C₂×C₇₉

#1974

yes

characteristic

117

C₂×C₇₉

#1975

yes

characteristic

118

D₇₉

—

119

#3147

—

120

#1837

—

121

#1492

—

122

#1492

—

123

C₂×#322

D₇₉

yes

characteristic, complemented

124

C₇₉

#9860

yes

characteristic, complemented, Sylow

125

C₂×#135

—

158

—

126

#532

—

127

#495

—

158

—

128

#494

—

129

#493

—

130

#492

—

131

#423

—

132

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

133

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

134

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

135

#341

—

158

—

136

D₄⋊C₈

—

158

—

137

D₄⋊C₈

—

158

—

138

#322

—

139

C₂×#41

—

158

—

140

#135

—

316

—

141

C₂×Q₁₆

—

158

—

142

C₂×SD₁₆

—

158

—

143

C₂×D₈

—

158

—

144

C₂×M₁₆

—

158

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

D₃₁₆

yes

—

148

C₄⋊Q₈

—

149

#127

—

150

#124

—

158

—

151

#121

—

158

—

152

#121

—

158

—

153

C₄×D₄

—

158

—

154

C₄×D₄

—

158

—

155

C₂×C₄²

C₂²×D₇₉

yes

characteristic

156

C₄⋊C₈

—

158

—

157

C₄⋊C₈

—

158

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

C₄×D₇₉

yes

characteristic

161

C₄×C₈

C₄×D₇₉

yes

characteristic

162

C₄×C₈

D₃₁₆

yes

—

163

C₄×C₈

D₃₁₆

yes

—

164

C₄×C₈

C₂²⋊D₇₉

yes

—

165

#41

—

316

—

166

C₂×Q₈

—

158

—

167

C₂×D₄

—

316

—

168

C₂×D₄

—

158

—

169

C₂×D₄

—

158

—

170

C₂×D₄

—

158

—

171

C₂²×C₄

—

316

—

172

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

173

C₂²×C₄

#11929624

yes

characteristic

174

C₂²×C₄

#11929624

yes

characteristic

175

Q₁₆

—

316

—

176

SD₁₆

—

316

—

177

D₈

—

316

—

178

M₁₆

—

316

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

316

—

185

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

186

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

187

C₄⋊C₄

—

158

—

188

C₄⋊C₄

—

158

—

189

C₂²⋊C₄

—

316

—

190

C₂²⋊C₄

—

316

—

191

C₄²

C₂×C₄×D₇₉

yes

characteristic

192

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

193

C₄²

C₂×D₃₁₆

yes

characteristic

194

C₄²

C₂×D₃₁₆

yes

characteristic

195

C₂³

—

316

—

196

C₂³

#14579149

yes

characteristic

197

Q₈

—

316

—

198

D₄

—

316

—

199

D₄

—

316

—

200

D₄

—

316

—

201

D₄

—

632

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

316

—

205

C₂×C₄

—

632

—

206

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

207

C₂×C₄

C₄×D₃₁₆

yes

characteristic

208

C₂×C₄

C₄×D₃₁₆

yes

characteristic

209

C₂×C₄

#14579135

yes

characteristic

210

C₂×C₄

#14579135

yes

characteristic

211

C₂×C₄

#14579158

yes

characteristic

212

C₂×C₄

#14579189

yes

—

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

217

C₈

—

632

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

632

—

221

C₂²

—

632

—

222

C₂²

—

632

—

223

C₂²

#19098465

yes

characteristic

224

C₂²

#19098928

yes

—

225

C₄

—

226

C₄

—

227

C₄

—

632

—

228

C₄

#19098569

yes

—

229

C₄

#19098681

yes

—

230

C₄

#19098686

yes

—

231

C₄

#19098952

yes

—

232

C₂

—

233

C₂

—

1264

—

234

C₂

#23764224

yes

characteristic

235

C₂

#23764288

yes

characteristic

236

C₂

#23764293

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579158
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#322×C₇₉	C₂
socle	C₂²×C₇₉	#390
prime radical	#23773828	C₂
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₂×#322	D₇₉
hypocenter	C₇₉	#9860
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

#14579158

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×#322×C₇₉

C₂

C₂²×C₇₉

C₂

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
2. #23763538	C₂	semidirect
3. #23761852	C₂	semidirect
4. #23761852	C₂	semidirect
5. C₂×#322×C₇₉	C₂	semidirect
123. C₂×#322	D₇₉	semidirect
124. C₇₉	#9860	semidirect

H ≅ G/N

type

2. #23763538

C₂

semidirect

3. #23761852

C₂

semidirect

4. #23761852

C₂

semidirect

5. C₂×#322×C₇₉

C₂

semidirect

123. C₂×#322

D₇₉

semidirect

124. C₇₉

#9860

semidirect

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

subgroup	index
#23773828	2
#23763538	2
#23761852	2
C₂×#322×C₇₉	2
#9860	79

subgroup

index

C₂×#322×C₇₉

Subgroups — #34188233

Conjugacy classes of subgroups

Complements

Maximal subgroups