Group #34205724 — subgroups

Subgroups — #34205724

Order 20224.

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

normal subgroups only

This group has 458 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	#23776503	C₂	1	1	yes	maximal, characteristic
2	#23765120	C₂	1	2	yes	maximal, complemented
3	#23763446	C₂	1	1	yes	maximal, characteristic
4	#23761501	C₂	1	2	yes	maximal, complemented
5	C₇₉×#3059	C₂	1	1	yes	maximal, characteristic
6	#19098980	—	2	4	no	—
7	C₂×#14579101	—	2	2	no	—
8	C₂×#14579101	C₂²	1	2	yes	—
9	#19098601	C₂²	1	2	yes	—
10	#19098537	—	2	1	no	—
11	#19098367	—	2	4	no	—
12	#19098320	—	2	1	no	—
13	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
15	#536×C₇₉	—	2	1	no	—
16	#470×C₇₉	C₄	1	4	yes	complemented
17	#467×C₇₉	—	2	2	no	—
18	#427×C₇₉	C₂²	1	1	yes	characteristic
19	#419×C₇₉	—	2	1	no	—
20	#14579120	—	2	2	no	—
21	#14579101	—	2	4	no	—
22	#14579101	—	2	2	no	—
23	#14579101	—	2	2	no	—
24	C₂×C₇₉⋊C₁₆	—	2	4	no	—
25	C₂×C₇₉⋊C₁₆	D₄	1	4	yes	—
26	#14579095	—	2	2	no	—
27	#14579093	—	2	2	no	—
28	#14579076	—	4	2	no	—
29	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
30	C₂²×Q₈×C₇₉	—	2	1	no	—
31	C₂×Q₁₆×C₇₉	—	2	2	no	—
32	C₂×Q₁₆×C₇₉	—	2	1	no	—
33	C₂×Q₁₆×C₇₉	—	2	2	no	—
34	C₂×Q₁₆×C₇₉	C₂×C₄	1	2	yes	—
35	#131×C₇₉	—	2	2	no	—
36	#131×C₇₉	—	2	2	no	—
37	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₇₉	D₄	1	2	yes	—
40	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
41	C₄⋊Q₈×C₇₉	—	4	1	no	—
42	#124×C₇₉	—	4	1	no	—
43	#123×C₇₉	—	4	2	no	—
44	C₂²⋊Q₈×C₇₉	—	2	4	no	—
45	#117×C₇₉	—	2	1	no	—
46	#107×C₇₉	—	2	1	no	—
47	#106×C₇₉	C₂×C₄	1	2	yes	—
48	#103×C₇₉	—	2	4	no	—
49	C₄⋊Dic₇₉	—	4	2	no	—
50	C₂²⋊Dic₇₉	—	4	2	no	—
51	C₄×Dic₇₉	—	4	2	no	—
52	C₇₉⋊C₁₆	—	2	4	no	—
53	#41×C₇₉	—	2	2	no	—
54	#41×C₇₉	—	2	2	no	—
55	C₂×Q₈×C₇₉	—	2	2	no	—
56	C₂×Q₈×C₇₉	—	4	1	no	—
57	C₂×Q₈×C₇₉	—	4	2	no	—
58	C₂×Q₈×C₇₉	—	4	2	no	—
59	C₂×Q₈×C₇₉	SD₁₆	1	1	yes	characteristic
60	C₂×D₄×C₇₉	D₈	1	2	yes	—
61	C₂×D₄×C₇₉	SD₁₆	1	1	yes	characteristic
62	C₂²×C₄×C₇₉	—	4	1	no	—
63	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
65	Q₁₆×C₇₉	—	2	4	no	—
66	Q₁₆×C₇₉	—	4	1	no	—
67	Q₁₆×C₇₉	—	4	1	no	—
68	M₁₆×C₇₉	—	2	4	no	—
69	M₁₆×C₇₉	—	2	2	no	—
70	C₂×C₈×C₇₉	—	2	2	no	—
71	C₂×C₈×C₇₉	—	2	2	no	—
72	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₇₉	#41	1	2	yes	—
77	C₄⋊C₄×C₇₉	—	2	2	no	—
78	C₄⋊C₄×C₇₉	—	4	4	no	—
79	C₂²⋊C₄×C₇₉	—	4	4	no	—
80	C₂²⋊C₄×C₇₉	—	4	1	no	—
81	C₄²×C₇₉	—	4	1	no	—
82	C₂³×C₇₉	#102	1	2	yes	—
83	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
84	Q₈×C₇₉	—	2	2	no	—
85	Q₈×C₇₉	—	4	2	no	—
86	Q₈×C₇₉	—	4	2	no	—
87	Q₈×C₇₉	—	8	2	no	—
88	D₄×C₇₉	—	2	4	no	—
89	D₄×C₇₉	—	2	2	no	—
90	C₂×C₄×C₇₉	—	2	2	no	—
91	C₂×C₄×C₇₉	—	2	2	no	—
92	C₂×C₄×C₇₉	—	4	2	no	—
93	C₂×C₄×C₇₉	—	4	2	no	—
94	C₂×C₄×C₇₉	—	8	2	no	—
95	C₂×C₄×C₇₉	#102	1	2	yes	—
96	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₇₉	#121	1	2	yes	—
98	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
99	C₂×C₄×C₇₉	#135	1	2	yes	—
100	C₂×Dic₇₉	—	8	2	no	—
101	C₈×C₇₉	—	2	2	no	—
102	C₈×C₇₉	C₄×D₄	1	2	yes	—
103	C₈×C₇₉	#120	1	1	yes	characteristic
104	C₈×C₇₉	#123	1	1	yes	characteristic
105	C₂²×C₇₉	—	2	2	no	—
106	C₂²×C₇₉	—	4	1	no	—
107	C₂²×C₇₉	—	4	2	no	—
108	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
109	C₂²×C₇₉	#466	1	2	yes	—
110	C₄×C₇₉	—	2	2	no	—
111	C₄×C₇₉	—	8	2	no	—
112	C₄×C₇₉	—	8	2	no	—
113	C₄×C₇₉	#386	1	1	yes	characteristic
114	C₄×C₇₉	#416	1	1	yes	characteristic
115	C₄×C₇₉	#465	1	2	yes	—
116	Dic₇₉	—	16	2	no	—
117	#13075	—	79	1	no	maximal, Sylow
118	C₂×C₇₉	—	2	2	no	—
119	C₂×C₇₉	—	2	1	no	—
120	C₂×C₇₉	—	4	2	no	—
121	C₂×C₇₉	#1893	1	1	yes	characteristic
122	#3407	—	79	1	no	—
123	#3059	D₇₉	1	1	yes	characteristic
124	#2141	—	79	2	no	—
125	#1812	—	79	1	no	—
126	#1384	—	79	2	no	—
127	C₇₉	#13075	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
129	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
130	#536	—	2	1	no	—
131	#504	—	158	4	no	—
132	C₂×M₃₂	—	79	2	no	—
133	C₂×M₃₂	—	158	2	no	—
134	#470	Dic₇₉	1	4	yes	complemented
135	#467	—	2	2	no	—
136	#427	—	79	2	no	—
137	#427	C₂×D₇₉	1	1	yes	characteristic
138	#419	—	2	1	no	—
139	#410	—	158	1	no	—
140	#358	—	158	4	no	—
141	H(3,ℤ/4)	—	158	1	no	—
142	C₂×#41	C₂²⋊D₇₉	1	1	yes	characteristic
143	C₂²×Q₈	—	2	1	no	—
144	C₂×Q₁₆	—	2	2	no	—
145	C₂×Q₁₆	—	2	1	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	C₂×Dic₇₉	1	2	yes	—
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
151	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
152	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
153	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
154	C₄⋊Q₈	—	4	1	no	—
155	#124	—	4	1	no	—
156	#123	—	4	2	no	—
157	C₂²⋊Q₈	—	2	4	no	—
158	#117	—	2	1	no	—
159	#117	—	158	2	no	—
160	M₃₂	—	158	4	no	—
161	M₃₂	—	158	2	no	—
162	M₃₂	—	158	2	no	—
163	C₂×C₁₆	—	79	4	no	—
164	C₂×C₁₆	—	158	4	no	—
165	#107	—	2	1	no	—
166	#107	—	158	2	no	—
167	#106	—	158	2	no	—
168	#106	C₂×Dic₇₉	1	2	yes	—
169	#103	—	2	4	no	—
170	#99	—	316	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	#11929612	1	1	yes	characteristic
178	C₂×D₄	#11929609	1	2	yes	—
179	C₂×D₄	#11929612	1	1	yes	characteristic
180	C₂²×C₄	—	4	1	no	—
181	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
182	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
183	Q₁₆	—	2	4	no	—
184	Q₁₆	—	4	1	no	—
185	Q₁₆	—	4	1	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	4	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
191	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
192	C₂×C₈	D₄×D₇₉	1	2	yes	—
193	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
194	C₂×C₈	#11929623	1	2	yes	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	4	4	no	—
197	C₄⋊C₄	—	316	2	no	—
198	C₂²⋊C₄	—	4	4	no	—
199	C₂²⋊C₄	—	4	1	no	—
200	C₂²⋊C₄	—	316	2	no	—
201	C₄²	—	4	1	no	—
202	C₄²	—	316	2	no	—
203	C₁₆	—	158	4	no	—
204	C₂³	#14579082	1	2	yes	—
205	C₂³	C₂×#11929609	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	4	2	no	—
209	Q₈	—	8	2	no	—
210	D₄	—	2	4	no	—
211	D₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	632	2	no	—
218	C₂×C₄	#14579082	1	2	yes	—
219	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
220	C₂×C₄	#14579133	1	2	yes	—
221	C₂×C₄	C₂×#11929612	1	1	yes	characteristic
222	C₂×C₄	#14579181	1	2	yes	—
223	C₈	—	2	2	no	—
224	C₈	D₄×Dic₇₉	1	2	yes	—
225	C₈	#14579129	1	1	yes	characteristic
226	C₈	#14579142	1	1	yes	characteristic
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂×#14579082	1	1	yes	characteristic
231	C₂²	#19098797	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	8	2	no	—
234	C₄	—	8	2	no	—
235	C₄	—	1264	2	no	—
236	C₄	#19098443	1	1	yes	characteristic
237	C₄	#19098559	1	1	yes	characteristic
238	C₄	#19098790	1	2	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#23763829	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23776503

C₂

yes

maximal, characteristic

#23765120

C₂

yes

maximal, complemented

#23763446

C₂

yes

maximal, characteristic

#23761501

C₂

yes

maximal, complemented

C₇₉×#3059

C₂

yes

maximal, characteristic

#19098980

—

C₂×#14579101

—

C₂×#14579101

C₂²

yes

—

#19098601

C₂²

yes

—

#19098537

—

#19098367

—

#19098320

—

C₂²×Q₁₆×C₇₉

C₂²

yes

characteristic

C₂×#131×C₇₉

C₂²

yes

characteristic

#536×C₇₉

—

#470×C₇₉

C₄

yes

complemented

#467×C₇₉

—

#427×C₇₉

C₂²

yes

characteristic

#419×C₇₉

—

—

—

—

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

D₄

yes

—

#14579095

—

#14579093

—

#14579076

—

C₂×#41×C₇₉

D₄

yes

characteristic

C₂²×Q₈×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

C₂×C₄

yes

—

#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

C₄⋊Q₈×C₇₉

—

#124×C₇₉

—

#123×C₇₉

—

C₂²⋊Q₈×C₇₉

—

#117×C₇₉

—

#107×C₇₉

—

#106×C₇₉

C₂×C₄

yes

—

#103×C₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

#41×C₇₉

—

#41×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

SD₁₆

yes

characteristic

C₂×D₄×C₇₉

D₈

yes

—

C₂×D₄×C₇₉

SD₁₆

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

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

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

#102

yes

—

C₂³×C₇₉

C₂×D₈

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×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×SD₁₆

yes

characteristic

C₂×C₄×C₇₉

#135

yes

—

100

C₂×Dic₇₉

—

101

C₈×C₇₉

—

102

C₈×C₇₉

C₄×D₄

yes

—

103

C₈×C₇₉

#120

yes

characteristic

104

C₈×C₇₉

#123

yes

characteristic

105

C₂²×C₇₉

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

—

108

C₂²×C₇₉

C₂×#102

yes

characteristic

109

C₂²×C₇₉

#466

yes

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

—

113

C₄×C₇₉

#386

yes

characteristic

114

C₄×C₇₉

#416

yes

characteristic

115

C₄×C₇₉

#465

yes

—

116

Dic₇₉

—

117

#13075

—

maximal, Sylow

118

C₂×C₇₉

—

119

C₂×C₇₉

—

120

C₂×C₇₉

—

121

C₂×C₇₉

#1893

yes

characteristic

122

#3407

—

123

#3059

D₇₉

yes

characteristic

124

#2141

—

125

#1812

—

126

#1384

—

127

C₇₉

#13075

yes

characteristic, complemented, Sylow

128

C₂²×Q₁₆

C₂×D₇₉

yes

characteristic

129

C₂×#131

C₂×D₇₉

yes

characteristic

130

#536

—

131

#504

—

158

—

132

C₂×M₃₂

—

133

C₂×M₃₂

—

158

—

134

#470

Dic₇₉

yes

complemented

135

#467

—

136

#427

—

137

#427

C₂×D₇₉

yes

characteristic

138

#419

—

139

#410

—

158

—

140

#358

—

158

—

141

H(3,ℤ/4)

—

158

—

142

C₂×#41

C₂²⋊D₇₉

yes

characteristic

143

C₂²×Q₈

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

C₂×Dic₇₉

yes

—

148

#131

—

149

#131

—

150

C₂×M₁₆

C₂×Dic₇₉

yes

—

151

C₂×M₁₆

C₂²⋊D₇₉

yes

characteristic

152

C₂²×C₈

C₂²⋊D₇₉

yes

—

153

C₂²×C₈

C₂²×D₇₉

yes

characteristic

154

C₄⋊Q₈

—

155

#124

—

156

#123

—

157

C₂²⋊Q₈

—

158

#117

—

159

#117

—

158

—

160

M₃₂

—

158

—

161

M₃₂

—

158

—

162

M₃₂

—

158

—

163

C₂×C₁₆

—

164

C₂×C₁₆

—

158

—

165

#107

—

166

#107

—

158

—

167

#106

—

158

—

168

#106

C₂×Dic₇₉

yes

—

169

#103

—

170

#99

—

316

—

171

#41

—

172

#41

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

#11929612

yes

characteristic

178

C₂×D₄

#11929609

yes

—

179

C₂×D₄

#11929612

yes

characteristic

180

C₂²×C₄

—

181

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

182

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

183

Q₁₆

—

184

Q₁₆

—

185

Q₁₆

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

C₂²⋊Dic₇₉

yes

—

191

C₂×C₈

C₂²×Dic₇₉

yes

characteristic

192

C₂×C₈

D₄×D₇₉

yes

—

193

C₂×C₈

C₂×C₂²⋊D₇₉

yes

characteristic

194

C₂×C₈

#11929623

yes

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

316

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

316

—

201

C₄²

—

202

C₄²

—

316

—

203

C₁₆

—

158

—

204

C₂³

#14579082

yes

—

205

C₂³

C₂×#11929609

yes

characteristic

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

Q₈

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

632

—

218

C₂×C₄

#14579082

yes

—

219

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

220

C₂×C₄

#14579133

yes

—

221

C₂×C₄

C₂×#11929612

yes

characteristic

222

C₂×C₄

#14579181

yes

—

223

C₈

—

224

C₈

D₄×Dic₇₉

yes

—

225

C₈

#14579129

yes

characteristic

226

C₈

#14579142

yes

characteristic

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂×#14579082

yes

characteristic

231

C₂²

#19098797

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

1264

—

236

C₄

#19098443

yes

characteristic

237

C₄

#19098559

yes

characteristic

238

C₄

#19098790

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#23763829

yes

characteristic

	subgroup	G/H
center	C₂	#23763829
commutator	C₂×C₈×C₇₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#3059	C₂
socle	C₂×C₇₉	#1893
prime radical	C₂×#41×C₇₉	D₄
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#3059	D₇₉
hypocenter	C₇₉	#13075
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

subgroup

G/H

center

C₂

#23763829

commutator

C₂×C₈×C₇₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#3059

C₂

socle

C₂×C₇₉

#1893

prime radical

C₂×#41×C₇₉

D₄

cosocle

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

N	H ≅ G/N	type
2. #23765120	C₂	semidirect
4. #23761501	C₂	semidirect
16. #470×C₇₉	C₄	semidirect
127. C₇₉	#13075	semidirect
134. #470	Dic₇₉	semidirect

H ≅ G/N

type

2. #23765120

C₂

semidirect

4. #23761501

C₂

semidirect

16. #470×C₇₉

C₄

semidirect

127. C₇₉

#13075

semidirect

134. #470

Dic₇₉

semidirect

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

subgroup	index
#23776503	2
#23765120	2
#23763446	2
#23761501	2
C₇₉×#3059	2
#13075	79

subgroup

index

C₇₉×#3059

Subgroups — #34205724

Conjugacy classes of subgroups

Complements

Maximal subgroups