Group #34193259 — subgroups

Subgroups — #34193259

Order 20224.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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	#23764339	C₂	1	1	yes	maximal, characteristic
2	#23763574	C₂	1	1	yes	maximal, characteristic
3	#23762170	C₂	1	1	yes	maximal, characteristic
4	#23761830	C₂	1	1	yes	maximal, characteristic
5	#23761828	C₂	1	1	yes	maximal, characteristic
6	#23761230	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1570	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
9	#19098616	C₂²	1	1	yes	characteristic
10	C₂×#14579096	—	2	2	no	—
11	#19098587	C₂²	1	1	yes	characteristic
12	C₂×#14579072	C₂²	1	1	yes	characteristic
13	#19098317	—	2	2	no	—
14	#19098313	—	2	2	no	—
15	#19098295	—	2	2	no	—
16	#19098293	—	2	2	no	—
17	#431×C₇₉	C₂²	1	1	yes	characteristic
18	#423×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
20	#334×C₇₉	—	2	2	no	—
21	C₂²×Dic₁₅₈	Q₈	1	1	yes	characteristic
22	C₂×#11929608	—	2	1	no	—
23	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
24	C₄×Dic₁₅₈	—	2	1	no	—
25	C₄×Dic₁₅₈	—	2	1	no	—
26	C₄×Dic₁₅₈	—	2	1	no	—
27	C₄×Dic₁₅₈	—	2	1	no	—
28	C₂×C₄⋊Dic₇₉	Q₈	1	1	yes	characteristic
29	C₂×Dic₇₉⋊C₄	—	2	1	no	—
30	C₂×C₄×Dic₇₉	—	2	1	no	—
31	#14579096	—	4	4	no	—
32	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
33	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
34	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
35	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
36	#14579072	—	2	1	no	—
37	#14579072	—	2	1	no	—
38	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
39	C₂×M₁₆×C₇₉	—	2	1	no	—
40	C₂²×C₈×C₇₉	—	2	1	no	—
41	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₉	—	2	1	no	—
43	C₄⋊C₈×C₇₉	—	2	1	no	—
44	C₄⋊C₈×C₇₉	—	2	1	no	—
45	C₄⋊C₈×C₇₉	—	2	1	no	—
46	C₄⋊C₈×C₇₉	—	2	1	no	—
47	C₂²⋊C₈×C₇₉	—	2	1	no	—
48	C₄×C₈×C₇₉	D₄	1	2	yes	—
49	C₂×Dic₁₅₈	—	2	1	no	—
50	C₂×Dic₁₅₈	—	2	1	no	—
51	C₂×Dic₁₅₈	—	4	2	no	—
52	C₂²×Dic₇₉	—	2	1	no	—
53	C₂²×Dic₇₉	—	2	1	no	—
54	#11929608	—	4	2	no	—
55	C₂×C₇₉⋊C₈	—	2	2	no	—
56	C₂×C₇₉⋊C₈	—	2	2	no	—
57	C₂×C₇₉⋊C₈	—	2	2	no	—
58	C₂×C₇₉⋊C₈	—	4	1	no	—
59	C₂×C₇₉⋊C₈	SD₁₆	1	4	yes	—
60	C₄⋊Dic₇₉	—	2	1	no	—
61	C₄⋊Dic₇₉	—	2	1	no	—
62	Dic₇₉⋊C₄	—	4	1	no	—
63	Dic₇₉⋊C₄	—	4	1	no	—
64	C₄×Dic₇₉	—	4	1	no	—
65	C₄×Dic₇₉	—	4	1	no	—
66	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
69	M₁₆×C₇₉	—	4	2	no	—
70	C₂×C₈×C₇₉	—	2	2	no	—
71	C₂×C₈×C₇₉	—	4	1	no	—
72	C₂×C₈×C₇₉	—	4	1	no	—
73	C₂×C₈×C₇₉	—	4	2	no	—
74	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₇₉	#41	1	1	yes	characteristic
77	C₄²×C₇₉	#41	1	1	yes	characteristic
78	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₇₉	—	4	1	no	—
80	C₂×C₄×C₇₉	—	4	1	no	—
81	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₇₉	#137	1	2	yes	—
89	C₂×Dic₇₉	—	2	2	no	—
90	C₂×Dic₇₉	—	4	1	no	—
91	C₂×Dic₇₉	—	4	1	no	—
92	C₂×Dic₇₉	—	4	2	no	—
93	C₂×Dic₇₉	—	4	1	no	—
94	Dic₁₅₈	—	2	2	no	—
95	Dic₁₅₈	—	2	2	no	—
96	Dic₁₅₈	—	4	1	no	—
97	Dic₁₅₈	—	4	1	no	—
98	C₈×C₇₉	—	4	2	no	—
99	C₈×C₇₉	—	8	1	no	—
100	C₈×C₇₉	—	8	1	no	—
101	C₇₉⋊C₈	—	2	4	no	—
102	C₇₉⋊C₈	—	4	2	no	—
103	C₇₉⋊C₈	—	8	1	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	—	2	1	no	—
106	C₂²×C₇₉	#399	1	1	yes	characteristic
107	C₂²×C₇₉	#475	1	2	yes	—
108	C₄×C₇₉	—	2	1	no	—
109	C₄×C₇₉	—	2	1	no	—
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	2	1	no	—
112	C₄×C₇₉	#483	1	2	yes	—
113	C₄×C₇₉	#492	1	1	yes	characteristic
114	C₄×C₇₉	#497	1	1	yes	characteristic
115	Dic₇₉	—	4	2	no	—
116	Dic₇₉	—	8	1	no	—
117	#10663	—	79	1	no	maximal, Sylow
118	C₂×C₇₉	—	2	2	no	—
119	C₂×C₇₉	#2091	1	1	yes	characteristic
120	C₂×C₇₉	#2096	1	1	yes	characteristic
121	C₂×C₇₉	#2098	1	1	yes	characteristic
122	#1985	—	79	1	no	—
123	#1849	—	79	1	no	—
124	#1570	—	79	1	no	—
125	#1570	D₇₉	1	1	yes	characteristic
126	#1487	—	79	1	no	—
127	#1487	—	79	1	no	—
128	#1275	—	79	1	no	—
129	C₇₉	#10663	1	1	yes	characteristic, complemented, Sylow
130	C₂×C₄×Q₈	—	79	1	no	—
131	#431	—	79	1	no	—
132	#431	C₂×D₇₉	1	1	yes	characteristic
133	C₂×#108	—	158	2	no	—
134	#423	—	79	1	no	—
135	#423	C₂×D₇₉	1	1	yes	characteristic
136	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
137	C₂×#97	—	79	1	no	—
138	#336	—	158	2	no	—
139	#334	—	2	2	no	—
140	#334	—	158	2	no	—
141	Q₈⋊C₈	—	158	2	no	—
142	Q₈⋊C₈	—	158	2	no	—
143	C₂²×Q₈	—	79	1	no	—
144	C₂×M₁₆	—	2	1	no	—
145	C₂×M₁₆	—	158	1	no	—
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	—	79	2	no	—
148	C₄×Q₈	—	158	1	no	—
149	C₄×Q₈	—	158	1	no	—
150	C₄×Q₈	—	158	1	no	—
151	C₄×Q₈	—	158	1	no	—
152	C₂×C₄⋊C₄	—	79	1	no	—
153	C₂×C₄⋊C₄	—	158	1	no	—
154	C₂×C₄²	—	158	1	no	—
155	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
156	#108	—	316	4	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₄⋊C₈	—	2	1	no	—
160	C₄⋊C₈	—	2	1	no	—
161	C₄⋊C₈	—	2	1	no	—
162	C₄⋊C₈	—	158	1	no	—
163	C₄⋊C₈	—	158	1	no	—
164	C₄⋊C₈	—	158	1	no	—
165	C₂²⋊C₈	—	2	1	no	—
166	C₂²⋊C₈	—	158	1	no	—
167	#97	—	158	1	no	—
168	#97	—	158	1	no	—
169	C₄×C₈	—	79	2	no	—
170	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
171	C₂×Q₈	—	316	2	no	—
172	C₂×Q₈	—	158	1	no	—
173	C₂×Q₈	—	158	1	no	—
174	C₂²×C₄	—	158	1	no	—
175	C₂²×C₄	—	158	1	no	—
176	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
177	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
178	C₂²×C₄	#11929624	1	1	yes	characteristic
179	M₁₆	—	4	2	no	—
180	M₁₆	—	316	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	4	1	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	316	1	no	—
186	C₂×C₈	—	79	4	no	—
187	C₂×C₈	—	158	2	no	—
188	C₂×C₈	—	158	2	no	—
189	C₂×C₈	—	158	2	no	—
190	C₄⋊C₄	—	316	1	no	—
191	C₄⋊C₄	—	316	1	no	—
192	C₄⋊C₄	—	158	1	no	—
193	C₄⋊C₄	—	158	1	no	—
194	C₄²	—	316	1	no	—
195	C₄²	—	316	1	no	—
196	C₄²	D₄×D₇₉	1	1	yes	characteristic
197	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
198	C₄²	#11929624	1	1	yes	characteristic
199	C₄²	#11929625	1	1	yes	characteristic
200	C₂³	#14579139	1	1	yes	characteristic
201	Q₈	—	316	1	no	—
202	Q₈	—	316	1	no	—
203	Q₈	—	158	2	no	—
204	Q₈	—	158	2	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	316	1	no	—
208	C₂×C₄	—	316	1	no	—
209	C₂×C₄	—	316	2	no	—
210	C₂×C₄	—	316	1	no	—
211	C₂×C₄	—	158	2	no	—
212	C₂×C₄	#14579137	1	1	yes	characteristic
213	C₂×C₄	#14579139	1	1	yes	characteristic
214	C₂×C₄	#14579144	1	1	yes	characteristic
215	C₂×C₄	#14579146	1	1	yes	characteristic
216	C₂×C₄	#14579146	1	1	yes	characteristic
217	C₂×C₄	#14579157	1	1	yes	characteristic
218	C₂×C₄	SD₁₆×D₇₉	1	2	yes	—
219	C₂×C₄	#14579190	1	2	yes	—
220	C₈	—	4	2	no	—
221	C₈	—	8	1	no	—
222	C₈	—	8	1	no	—
223	C₈	—	316	2	no	—
224	C₈	—	632	1	no	—
225	C₈	—	158	4	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#19098498	1	1	yes	characteristic
229	C₂²	#19098847	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	316	2	no	—
235	C₄	—	632	1	no	—
236	C₄	#19098895	1	2	yes	—
237	C₄	#19098934	1	1	yes	characteristic
238	C₄	#19098954	1	1	yes	characteristic
239	C₂	—	2	2	no	—
240	C₂	#23764915	1	1	yes	characteristic
241	C₂	#23764940	1	1	yes	characteristic
242	C₂	#23764956	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764339

C₂

yes

maximal, characteristic

#23763574

C₂

yes

maximal, characteristic

#23762170

C₂

yes

maximal, characteristic

#23761830

C₂

yes

maximal, characteristic

#23761828

C₂

yes

maximal, characteristic

#23761230

C₂

yes

maximal, characteristic

C₇₉×#1570

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₅₈

C₂²

yes

characteristic

#19098616

C₂²

yes

characteristic

C₂×#14579096

—

#19098587

C₂²

yes

characteristic

C₂×#14579072

C₂²

yes

—

—

—

—

#431×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#334×C₇₉

—

C₂²×Dic₁₅₈

Q₈

yes

characteristic

C₂×#11929608

—

C₂²×C₇₉⋊C₈

D₄

yes

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

Q₈

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579096

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

#14579072

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

SD₁₆

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₄²×C₇₉

yes

C₂³×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂×SD₁₆

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

100

C₈×C₇₉

—

101

C₇₉⋊C₈

—

102

C₇₉⋊C₈

—

103

C₇₉⋊C₈

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

#399

yes

characteristic

107

C₂²×C₇₉

#475

yes

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

#483

yes

—

113

C₄×C₇₉

#492

yes

characteristic

114

C₄×C₇₉

#497

yes

characteristic

115

Dic₇₉

—

116

Dic₇₉

—

117

#10663

—

maximal, Sylow

118

C₂×C₇₉

—

119

C₂×C₇₉

#2091

yes

characteristic

120

C₂×C₇₉

#2096

yes

characteristic

121

C₂×C₇₉

#2098

yes

characteristic

122

#1985

—

123

#1849

—

124

#1570

—

125

#1570

D₇₉

yes

characteristic

126

#1487

—

127

#1487

—

128

#1275

—

129

C₇₉

#10663

yes

characteristic, complemented, Sylow

130

C₂×C₄×Q₈

—

131

#431

—

132

#431

C₂×D₇₉

yes

characteristic

133

C₂×#108

—

158

—

134

#423

—

135

#423

C₂×D₇₉

yes

characteristic

136

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

137

C₂×#97

—

138

#336

—

158

—

139

#334

—

140

#334

—

158

—

141

Q₈⋊C₈

—

158

—

142

Q₈⋊C₈

—

158

—

143

C₂²×Q₈

—

144

C₂×M₁₆

—

145

C₂×M₁₆

—

158

—

146

C₂²×C₈

—

147

C₂²×C₈

—

148

C₄×Q₈

—

158

—

149

C₄×Q₈

—

158

—

150

C₄×Q₈

—

158

—

151

C₄×Q₈

—

158

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

158

—

154

C₂×C₄²

—

158

—

155

C₂×C₄²

C₂²×D₇₉

yes

characteristic

156

#108

—

316

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

158

—

163

C₄⋊C₈

—

158

—

164

C₄⋊C₈

—

158

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

158

—

167

#97

—

158

—

168

#97

—

158

—

169

C₄×C₈

—

170

C₄×C₈

C₂²⋊D₇₉

yes

—

171

C₂×Q₈

—

316

—

172

C₂×Q₈

—

158

—

173

C₂×Q₈

—

158

—

174

C₂²×C₄

—

158

—

175

C₂²×C₄

—

158

—

176

C₂²×C₄

D₄×D₇₉

yes

characteristic

177

C₂²×C₄

Q₈×D₇₉

yes

characteristic

178

C₂²×C₄

#11929624

yes

characteristic

179

M₁₆

—

180

M₁₆

—

316

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

316

—

186

C₂×C₈

—

187

C₂×C₈

—

158

—

188

C₂×C₈

—

158

—

189

C₂×C₈

—

158

—

190

C₄⋊C₄

—

316

—

191

C₄⋊C₄

—

316

—

192

C₄⋊C₄

—

158

—

193

C₄⋊C₄

—

158

—

194

C₄²

—

316

—

195

C₄²

—

316

—

196

C₄²

D₄×D₇₉

yes

characteristic

197

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

198

C₄²

#11929624

yes

characteristic

199

C₄²

#11929625

yes

characteristic

200

C₂³

#14579139

yes

characteristic

201

Q₈

—

316

—

202

Q₈

—

316

—

203

Q₈

—

158

—

204

Q₈

—

158

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

316

—

208

C₂×C₄

—

316

—

209

C₂×C₄

—

316

—

210

C₂×C₄

—

316

—

211

C₂×C₄

—

158

—

212

C₂×C₄

#14579137

yes

characteristic

213

C₂×C₄

#14579139

yes

characteristic

214

C₂×C₄

#14579144

yes

characteristic

215

C₂×C₄

#14579146

yes

characteristic

216

C₂×C₄

#14579146

yes

characteristic

217

C₂×C₄

#14579157

yes

characteristic

218

C₂×C₄

SD₁₆×D₇₉

yes

—

219

C₂×C₄

#14579190

yes

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

316

—

224

C₈

—

632

—

225

C₈

—

158

—

226

C₂²

—

227

C₂²

—

228

C₂²

#19098498

yes

characteristic

229

C₂²

#19098847

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

316

—

235

C₄

—

632

—

236

C₄

#19098895

yes

—

237

C₄

#19098934

yes

characteristic

238

C₄

#19098954

yes

characteristic

239

C₂

—

240

C₂

#23764915

yes

characteristic

241

C₂

#23764940

yes

characteristic

242

C₂

#23764956

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1570	C₂
socle	C₂²×C₇₉	#399
prime radical	C₂³×C₇₉	C₂²⋊Q₈
hypercenter	#1570	D₇₉
hypocenter	C₇₉	#10663
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

subgroup

G/H

center

C₂×C₄

#14579157

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1570

C₂

socle

C₂²×C₇₉

#399

prime radical

C₂³×C₇₉

C₂²⋊Q₈

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

N	H ≅ G/N	type
129. C₇₉	#10663	semidirect

H ≅ G/N

type

129. C₇₉

#10663

semidirect

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

subgroup	index
#23764339	2
#23763574	2
#23762170	2
#23761830	2
#23761828	2
#23761230	2
C₇₉×#1570	2
#10663	79

subgroup

index

C₇₉×#1570

Subgroups — #34193259

Conjugacy classes of subgroups

Complements

Maximal subgroups