Group #34205743 — subgroups

Subgroups — #34205743

Order 20224.

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

normal subgroups only

This group has 486 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	#23773048	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098377	C₂	1	2	yes	maximal, complemented
3	#23763450	C₂	1	1	yes	maximal, characteristic, complemented
4	#23761515	C₂	1	2	yes	maximal, complemented
5	C₇₉×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₆₃₂	C₂²	1	1	yes	characteristic
7	#19099127	—	2	1	no	—
8	#19098816	C₄	1	4	yes	—
9	#19098799	—	2	2	no	—
10	C₂×#14579097	C₂²	1	2	yes	—
11	#19098601	C₂²	1	1	yes	characteristic
12	#19098569	—	2	1	no	—
13	#19098547	—	2	1	no	—
14	#19098377	—	2	4	no	—
15	C₇₉⋊#338	—	2	1	no	—
16	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
17	#504×C₇₉	—	2	4	no	—
18	C₂×M₃₂×C₇₉	—	2	2	no	—
19	C₂×M₃₂×C₇₉	C₂²	1	2	yes	—
20	C₂²×D₃₁₆	—	2	1	no	—
21	C₂×D₆₃₂	—	2	2	no	—
22	C₂×D₆₃₂	—	2	2	no	—
23	C₂×D₆₃₂	—	2	1	no	—
24	C₂×D₆₃₂	C₂×C₄	1	2	yes	—
25	C₂×#11929608	—	2	2	no	—
26	#14579157	—	4	1	no	—
27	#14579150	—	4	1	no	—
28	#14579135	—	2	4	no	—
29	#14579129	—	4	2	no	—
30	#14579120	—	2	1	no	—
31	#14579097	—	2	2	no	—
32	#14579097	—	2	2	no	—
33	#14579095	—	2	1	no	—
34	#14579093	C₂×C₄	1	2	yes	—
35	#14579083	—	2	4	no	—
36	#14579080	—	4	1	no	—
37	#14579078	—	4	1	no	—
38	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
39	#131×C₇₉	—	2	2	no	—
40	#131×C₇₉	—	2	2	no	—
41	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₇₉	D₄	1	2	yes	—
44	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
45	M₃₂×C₇₉	—	2	4	no	—
46	M₃₂×C₇₉	—	2	2	no	—
47	M₃₂×C₇₉	D₄	1	4	yes	complemented
48	C₂×C₁₆×C₇₉	—	2	4	no	—
49	C₂×C₁₆×C₇₉	—	2	2	no	—
50	C₂³×D₇₉	—	4	1	no	—
51	C₂×D₃₁₆	—	2	2	no	—
52	C₂×D₃₁₆	—	4	2	no	—
53	C₂×D₃₁₆	—	4	1	no	—
54	C₂×D₃₁₆	—	4	2	no	—
55	C₂×C₂²⋊D₇₉	—	4	4	no	—
56	D₆₃₂	—	2	4	no	—
57	D₆₃₂	—	4	1	no	—
58	D₆₃₂	—	4	1	no	—
59	#11929608	—	4	2	no	—
60	#11929608	—	4	2	no	—
61	C₂×C₇₉⋊C₈	—	4	2	no	—
62	C₄⋊Dic₇₉	—	2	2	no	—
63	C₂²⋊Dic₇₉	—	4	1	no	—
64	(C₂×D₇₉)⋊C₄	—	4	4	no	—
65	C₄×Dic₇₉	—	4	1	no	—
66	#41×C₇₉	—	2	2	no	—
67	#41×C₇₉	—	2	2	no	—
68	C₂×Q₈×C₇₉	D₈	1	1	yes	characteristic
69	C₂×D₄×C₇₉	D₈	1	1	yes	characteristic
70	C₂×D₄×C₇₉	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
73	M₁₆×C₇₉	—	2	4	no	—
74	M₁₆×C₇₉	—	2	2	no	—
75	C₂×C₈×C₇₉	—	2	2	no	—
76	C₂×C₈×C₇₉	—	2	2	no	—
77	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
78	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
81	C₂×C₈×C₇₉	#41	1	2	yes	—
82	C₁₆×C₇₉	—	2	4	no	—
83	C₂³×C₇₉	#102	1	2	yes	—
84	C₂³×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
85	C₂²×D₇₉	—	4	2	no	—
86	C₂²×D₇₉	—	8	2	no	—
87	C₂²×D₇₉	—	16	2	no	—
88	Q₈×C₇₉	—	2	2	no	—
89	D₄×C₇₉	—	2	4	no	—
90	D₄×C₇₉	—	2	2	no	—
91	C₂×C₄×C₇₉	—	2	2	no	—
92	C₂×C₄×C₇₉	—	2	2	no	—
93	C₂×C₄×C₇₉	#102	1	2	yes	—
94	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₇₉	#121	1	2	yes	—
96	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₇₉	#135	1	2	yes	—
98	C₂²⋊D₇₉	—	16	4	no	—
99	C₂×Dic₇₉	—	4	2	no	—
100	D₃₁₆	—	4	2	no	—
101	D₃₁₆	—	4	2	no	—
102	D₃₁₆	—	8	2	no	—
103	C₈×C₇₉	—	2	2	no	—
104	C₈×C₇₉	C₄×D₄	1	2	yes	—
105	C₈×C₇₉	#120	1	1	yes	characteristic
106	C₈×C₇₉	#123	1	1	yes	characteristic
107	C₇₉⋊C₈	—	8	2	no	—
108	C₂²×C₇₉	—	2	2	no	—
109	C₂²×C₇₉	—	4	1	no	—
110	C₂²×C₇₉	—	4	2	no	—
111	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
112	C₂²×C₇₉	#465	1	2	yes	—
113	C₂×D₇₉	—	8	4	no	—
114	C₂×D₇₉	—	8	2	no	—
115	C₂×D₇₉	—	16	4	no	—
116	C₄×C₇₉	—	2	2	no	—
117	C₄×C₇₉	#386	1	1	yes	characteristic
118	C₄×C₇₉	#416	1	1	yes	characteristic
119	C₄×C₇₉	#466	1	2	yes	—
120	Dic₇₉	—	8	2	no	—
121	#13079	—	79	1	no	maximal, Sylow
122	C₂×C₇₉	—	2	1	no	—
123	C₂×C₇₉	—	2	2	no	—
124	C₂×C₇₉	—	4	2	no	—
125	C₂×C₇₉	#1893	1	1	yes	characteristic
126	D₇₉	—	16	2	no	—
127	#3407	D₇₉	1	1	yes	characteristic, complemented
128	#3058	—	79	1	no	—
129	C₂×#361	—	79	2	no	—
130	#1813	—	79	1	no	—
131	#1389	—	79	2	no	—
132	C₇₉	#13079	1	1	yes	characteristic, complemented, Sylow
133	C₂²×D₈	—	79	1	no	—
134	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
135	#535	—	158	1	no	—
136	#504	—	2	4	no	—
137	C₂×M₃₂	—	2	2	no	—
138	C₂×M₃₂	C₂×D₇₉	1	2	yes	—
139	#469	—	79	4	no	—
140	#466	—	158	2	no	—
141	C₂×#108	—	79	2	no	—
142	#427	—	79	1	no	—
143	#418	—	158	1	no	—
144	#413	—	158	1	no	—
145	#361	—	158	4	no	—
146	#338	—	158	1	no	—
147	C₂×#41	D₃₁₆	1	1	yes	characteristic
148	C₂²×D₄	—	158	1	no	—
149	C₂×D₈	—	79	2	no	—
150	C₂×D₈	—	158	1	no	—
151	C₂×D₈	—	158	2	no	—
152	C₂×D₈	—	158	2	no	—
153	#131	—	2	2	no	—
154	#131	—	2	2	no	—
155	C₂×M₁₆	—	158	2	no	—
156	C₂×M₁₆	C₄×D₇₉	1	2	yes	—
157	C₂×M₁₆	D₃₁₆	1	1	yes	characteristic
158	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
159	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
160	#127	—	316	1	no	—
161	#124	—	316	1	no	—
162	#121	—	158	4	no	—
163	#120	—	316	2	no	—
164	#117	—	158	1	no	—
165	M₃₂	—	2	4	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	C₂²⋊D₇₉	1	4	yes	complemented
168	C₂×C₁₆	—	2	4	no	—
169	C₂×C₁₆	—	2	2	no	—
170	#108	—	158	2	no	—
171	#108	—	158	2	no	—
172	#107	—	158	1	no	—
173	#106	—	79	2	no	—
174	#102	—	158	4	no	—
175	#101	—	316	1	no	—
176	#100	—	316	1	no	—
177	C₂⁴	—	316	1	no	—
178	#41	—	2	2	no	—
179	#41	—	2	2	no	—
180	C₂×Q₈	D₆₃₂	1	1	yes	characteristic
181	C₂×D₄	—	316	4	no	—
182	C₂×D₄	—	316	2	no	—
183	C₂×D₄	—	316	1	no	—
184	C₂×D₄	—	316	2	no	—
185	C₂×D₄	—	158	2	no	—
186	C₂×D₄	D₆₃₂	1	1	yes	characteristic
187	C₂×D₄	#11929613	1	2	yes	—
188	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
189	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
190	D₈	—	316	1	no	—
191	D₈	—	316	1	no	—
192	D₈	—	158	4	no	—
193	M₁₆	—	2	2	no	—
194	M₁₆	—	2	4	no	—
195	M₁₆	—	316	2	no	—
196	M₁₆	—	316	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	316	2	no	—
200	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
201	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
202	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
203	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
204	C₂×C₈	#11929624	1	2	yes	—
205	C₄⋊C₄	—	158	2	no	—
206	C₂²⋊C₄	—	316	1	no	—
207	C₂²⋊C₄	—	316	4	no	—
208	C₄²	—	316	1	no	—
209	C₁₆	—	2	4	no	—
210	C₂³	—	316	2	no	—
211	C₂³	—	632	2	no	—
212	C₂³	—	1264	2	no	—
213	C₂³	#14579083	1	2	yes	—
214	C₂³	C₂×#11929613	1	1	yes	characteristic
215	Q₈	—	2	2	no	—
216	D₄	—	2	4	no	—
217	D₄	—	2	2	no	—
218	D₄	—	316	2	no	—
219	D₄	—	316	2	no	—
220	D₄	—	632	2	no	—
221	D₄	—	1264	4	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	316	2	no	—
225	C₂×C₄	#14579083	1	2	yes	—
226	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
227	C₂×C₄	#14579135	1	2	yes	—
228	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
229	C₂×C₄	#14579183	1	2	yes	—
230	C₈	—	2	2	no	—
231	C₈	—	632	2	no	—
232	C₈	C₄×C₂²⋊D₇₉	1	2	yes	—
233	C₈	#14579130	1	1	yes	characteristic
234	C₈	#14579144	1	1	yes	characteristic
235	C₂²	—	2	2	no	—
236	C₂²	—	4	1	no	—
237	C₂²	—	4	2	no	—
238	C₂²	—	632	4	no	—
239	C₂²	—	632	2	no	—
240	C₂²	—	1264	4	no	—
241	C₂²	C₂×#14579083	1	1	yes	characteristic
242	C₂²	#19098792	1	2	yes	—
243	C₄	—	2	2	no	—
244	C₄	—	632	2	no	—
245	C₄	#19098442	1	1	yes	characteristic
246	C₄	#19098560	1	1	yes	characteristic
247	C₄	#19098799	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	2	no	—
250	C₂	—	4	2	no	—
251	C₂	—	1264	2	no	—
252	C₂	#23763828	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773048

C₂

yes

maximal, characteristic

C₂×#19098377

C₂

yes

maximal, complemented

#23763450

C₂

yes

maximal, characteristic, complemented

#23761515

C₂

yes

maximal, complemented

C₇₉×#3407

C₂

yes

maximal, characteristic, complemented

C₂²×D₆₃₂

C₂²

yes

characteristic

#19099127

—

#19098816

C₄

yes

—

#19098799

—

C₂×#14579097

C₂²

yes

—

#19098601

C₂²

yes

—

—

—

C₇₉⋊#338

—

C₂×#131×C₇₉

C₂²

yes

characteristic

#504×C₇₉

—

C₂×M₃₂×C₇₉

—

C₂×M₃₂×C₇₉

C₂²

yes

—

C₂²×D₃₁₆

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×D₆₃₂

C₂×C₄

yes

—

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#14579083

—

#14579080

—

#14579078

—

C₂×#41×C₇₉

D₄

yes

characteristic

#131×C₇₉

—

#131×C₇₉

—

C₂×M₁₆×C₇₉

C₂×C₄

yes

—

C₂×M₁₆×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

D₄

yes

—

C₂²×C₈×C₇₉

C₂³

yes

characteristic

M₃₂×C₇₉

—

M₃₂×C₇₉

—

M₃₂×C₇₉

D₄

yes

complemented

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂³×D₇₉

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

D₆₃₂

—

D₆₃₂

—

D₆₃₂

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

#41×C₇₉

—

#41×C₇₉

—

C₂×Q₈×C₇₉

D₈

yes

characteristic

C₂×D₄×C₇₉

D₈

yes

characteristic

C₂×D₄×C₇₉

SD₁₆

yes

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

#41

yes

—

C₁₆×C₇₉

—

C₂³×C₇₉

#102

yes

—

C₂³×C₇₉

C₂×SD₁₆

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#102

yes

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×C₄×C₇₉

#135

yes

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

100

D₃₁₆

—

101

D₃₁₆

—

102

D₃₁₆

—

103

C₈×C₇₉

—

104

C₈×C₇₉

C₄×D₄

yes

—

105

C₈×C₇₉

#120

yes

characteristic

106

C₈×C₇₉

#123

yes

characteristic

107

C₇₉⋊C₈

—

108

C₂²×C₇₉

—

109

C₂²×C₇₉

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

C₂×#102

yes

characteristic

112

C₂²×C₇₉

#465

yes

—

113

C₂×D₇₉

—

114

C₂×D₇₉

—

115

C₂×D₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

#386

yes

characteristic

118

C₄×C₇₉

#416

yes

characteristic

119

C₄×C₇₉

#466

yes

—

120

Dic₇₉

—

121

#13079

—

maximal, Sylow

122

C₂×C₇₉

—

123

C₂×C₇₉

—

124

C₂×C₇₉

—

125

C₂×C₇₉

#1893

yes

characteristic

126

D₇₉

—

127

#3407

D₇₉

yes

characteristic, complemented

128

#3058

—

129

C₂×#361

—

130

#1813

—

131

#1389

—

132

C₇₉

#13079

yes

characteristic, complemented, Sylow

133

C₂²×D₈

—

134

C₂×#131

C₂×D₇₉

yes

characteristic

135

#535

—

158

—

136

#504

—

137

C₂×M₃₂

—

138

C₂×M₃₂

C₂×D₇₉

yes

—

139

#469

—

140

#466

—

158

—

141

C₂×#108

—

142

#427

—

143

#418

—

158

—

144

#413

—

158

—

145

#361

—

158

—

146

#338

—

158

—

147

C₂×#41

D₃₁₆

yes

characteristic

148

C₂²×D₄

—

158

—

149

C₂×D₈

—

150

C₂×D₈

—

158

—

151

C₂×D₈

—

158

—

152

C₂×D₈

—

158

—

153

#131

—

154

#131

—

155

C₂×M₁₆

—

158

—

156

C₂×M₁₆

C₄×D₇₉

yes

—

157

C₂×M₁₆

D₃₁₆

yes

characteristic

158

C₂²×C₈

C₂²⋊D₇₉

yes

—

159

C₂²×C₈

C₂²×D₇₉

yes

characteristic

160

#127

—

316

—

161

#124

—

316

—

162

#121

—

158

—

163

#120

—

316

—

164

#117

—

158

—

165

M₃₂

—

166

M₃₂

—

167

M₃₂

C₂²⋊D₇₉

yes

complemented

168

C₂×C₁₆

—

169

C₂×C₁₆

—

170

#108

—

158

—

171

#108

—

158

—

172

#107

—

158

—

173

#106

—

174

#102

—

158

—

175

#101

—

316

—

176

#100

—

316

—

177

C₂⁴

—

316

—

178

#41

—

179

#41

—

180

C₂×Q₈

D₆₃₂

yes

characteristic

181

C₂×D₄

—

316

—

182

C₂×D₄

—

316

—

183

C₂×D₄

—

316

—

184

C₂×D₄

—

316

—

185

C₂×D₄

—

158

—

186

C₂×D₄

D₆₃₂

yes

characteristic

187

C₂×D₄

#11929613

yes

—

188

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

—

189

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

190

D₈

—

316

—

191

D₈

—

316

—

192

D₈

—

158

—

193

M₁₆

—

194

M₁₆

—

195

M₁₆

—

316

—

196

M₁₆

—

316

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

316

—

200

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

201

C₂×C₈

C₂×C₄×D₇₉

yes

characteristic

202

C₂×C₈

C₂×C₂²⋊D₇₉

yes

—

203

C₂×C₈

C₂×C₂²⋊D₇₉

yes

characteristic

204

C₂×C₈

#11929624

yes

—

205

C₄⋊C₄

—

158

—

206

C₂²⋊C₄

—

316

—

207

C₂²⋊C₄

—

316

—

208

C₄²

—

316

—

209

C₁₆

—

210

C₂³

—

316

—

211

C₂³

—

632

—

212

C₂³

—

1264

—

213

C₂³

#14579083

yes

—

214

C₂³

C₂×#11929613

yes

characteristic

215

Q₈

—

216

D₄

—

217

D₄

—

218

D₄

—

316

—

219

D₄

—

316

—

220

D₄

—

632

—

221

D₄

—

1264

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

316

—

225

C₂×C₄

#14579083

yes

—

226

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

227

C₂×C₄

#14579135

yes

—

228

C₂×C₄

C₂×D₆₃₂

yes

characteristic

229

C₂×C₄

#14579183

yes

—

230

C₈

—

231

C₈

—

632

—

232

C₈

C₄×C₂²⋊D₇₉

yes

—

233

C₈

#14579130

yes

characteristic

234

C₈

#14579144

yes

characteristic

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

632

—

239

C₂²

—

632

—

240

C₂²

—

1264

—

241

C₂²

C₂×#14579083

yes

characteristic

242

C₂²

#19098792

yes

—

243

C₄

—

244

C₄

—

632

—

245

C₄

#19098442

yes

characteristic

246

C₄

#19098560

yes

characteristic

247

C₄

#19098799

yes

—

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

—

1264

—

252

C₂

#23763828

yes

characteristic

	subgroup	G/H
center	C₂	#23763828
commutator	C₂×C₈×C₇₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#3407	C₂
socle	C₂×C₇₉	#1893
prime radical	#23773048	C₂
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#3407	D₇₉
hypocenter	C₇₉	#13079
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#23763828

commutator

C₂×C₈×C₇₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#3407

C₂

C₂×C₇₉

C₂

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. C₂×#19098377	C₂	semidirect
3. #23763450	C₂	semidirect
4. #23761515	C₂	semidirect
5. C₇₉×#3407	C₂	semidirect
47. M₃₂×C₇₉	D₄	semidirect
127. #3407	D₇₉	semidirect
132. C₇₉	#13079	semidirect
167. M₃₂	C₂²⋊D₇₉	semidirect

H ≅ G/N

type

2. C₂×#19098377

C₂

semidirect

3. #23763450

C₂

semidirect

4. #23761515

C₂

semidirect

5. C₇₉×#3407

C₂

semidirect

47. M₃₂×C₇₉

D₄

semidirect

127. #3407

D₇₉

semidirect

132. C₇₉

#13079

semidirect

167. M₃₂

C₂²⋊D₇₉

semidirect

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

subgroup	index
#23773048	2
C₂×#19098377	2
#23763450	2
#23761515	2
C₇₉×#3407	2
#13079	79

subgroup

index

C₇₉×#3407

Subgroups — #34205743

Conjugacy classes of subgroups

Complements

Maximal subgroups