Group #23774635 — subgroups

Subgroups — #23774635

Order 10112.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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	#19099118	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099092	C₂	1	1	yes	maximal, characteristic
3	#19098972	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098969	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098922	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098902	C₂	1	2	yes	maximal, complemented
7	#19098885	C₂	1	2	yes	maximal
8	#19098872	C₂	1	2	yes	maximal, complemented
9	#19098865	C₂	1	2	yes	maximal, complemented
10	#19098618	C₂	1	1	yes	maximal, characteristic, complemented
11	#489×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#14579161	C₂²	1	1	yes	characteristic
13	#14579154	—	2	1	no	—
14	#14579153	C₂²	1	1	yes	characteristic
15	#14579152	C₂²	1	2	yes	—
16	#14579143	—	2	1	no	—
17	#14579141	—	2	1	no	—
18	#14579137	—	2	1	no	—
19	#14579137	C₂²	1	1	yes	characteristic
20	#14579132	C₂²	1	1	yes	characteristic
21	Q₈×Dic₇₉	—	2	1	no	—
22	Q₈×Dic₇₉	C₂²	1	1	yes	characteristic
23	#14579126	—	2	1	no	—
24	D₄×Dic₇₉	C₂²	1	1	yes	characteristic
25	(C₂²⋊D₇₉)⋊C₄	—	2	1	no	—
26	#14579119	C₂²	1	2	yes	—
27	#14579117	—	2	1	no	—
28	C₄²×D₇₉	C₂²	1	1	yes	characteristic
29	#14579095	C₂²	1	2	yes	—
30	#14579094	C₂²	1	2	yes	—
31	#14579093	C₂²	1	2	yes	—
32	#14579092	C₂²	1	2	yes	—
33	Dic₇₉⋊C₈	C₂²	1	2	yes	—
34	#14579085	C₂²	1	2	yes	—
35	#14579082	C₂²	1	2	yes	—
36	(C₂×D₇₉)⋊C₈	C₂²	1	2	yes	—
37	#14579072	C₂²	1	1	yes	characteristic
38	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
39	#124×C₇₉	C₂²	1	1	yes	characteristic
40	#103×C₇₉	C₂²	1	2	yes	—
41	#102×C₇₉	C₂²	1	2	yes	—
42	#97×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×Dic₁₅₈	—	2	1	no	—
44	C₂×C₂²⋊D₇₉	—	2	1	no	—
45	C₂²×Dic₇₉	—	2	1	no	—
46	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
47	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
48	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
49	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
50	C₄⋊Dic₇₉	—	2	2	no	—
51	C₄⋊Dic₇₉	—	2	1	no	—
52	C₄⋊Dic₇₉	—	2	1	no	—
53	C₄⋊Dic₇₉	C₂³	1	2	yes	—
54	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
55	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
56	Dic₇₉⋊C₄	—	2	1	no	—
57	Dic₇₉⋊C₄	—	2	2	no	—
58	Dic₇₉⋊C₄	—	2	1	no	—
59	Dic₇₉⋊C₄	—	2	1	no	—
60	C₂²⋊Dic₇₉	—	2	1	no	—
61	C₂²⋊Dic₇₉	—	2	1	no	—
62	(C₂×D₇₉)⋊C₄	—	2	2	no	—
63	(C₂×D₇₉)⋊C₄	—	2	1	no	—
64	C₄×Dic₇₉	—	2	1	no	—
65	C₄×Dic₇₉	—	2	2	no	—
66	C₄×Dic₇₉	D₄	1	1	yes	characteristic
67	C₄×Dic₇₉	D₄	1	1	yes	characteristic
68	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
69	C₂×Q₈×C₇₉	—	2	1	no	—
70	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₇₉	C₂³	1	2	yes	—
73	C₄⋊C₄×C₇₉	—	2	1	no	—
74	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
75	C₂²⋊C₄×C₇₉	—	2	1	no	—
76	C₂²⋊C₄×C₇₉	—	2	1	no	—
77	C₄²×C₇₉	C₂³	1	1	yes	characteristic
78	C₂³×C₇₉	—	2	1	no	—
79	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
80	Q₈×C₇₉	—	2	2	no	—
81	Q₈×C₇₉	—	4	2	no	—
82	D₄×C₇₉	—	2	2	no	—
83	C₂×C₄×C₇₉	—	2	1	no	—
84	C₂×C₄×C₇₉	—	2	2	no	—
85	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
88	C₂²⋊D₇₉	—	4	2	no	—
89	C₂×Dic₇₉	—	2	2	no	—
90	C₂×Dic₇₉	—	2	1	no	—
91	C₂×Dic₇₉	—	2	1	no	—
92	C₂×Dic₇₉	—	4	2	no	—
93	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
94	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
96	C₄×D₇₉	—	2	2	no	—
97	C₄×D₇₉	—	4	1	no	—
98	C₄×D₇₉	—	4	1	no	—
99	Dic₁₅₈	—	4	2	no	—
100	C₈×C₇₉	—	2	2	no	—
101	C₇₉⋊C₈	—	2	2	no	—
102	C₂²×C₇₉	—	4	1	no	—
103	C₂²×C₇₉	—	4	1	no	—
104	C₂²×C₇₉	—	4	1	no	—
105	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
106	C₂×D₇₉	—	2	1	no	—
107	C₂×D₇₉	—	2	1	no	—
108	C₂×D₇₉	—	2	1	no	—
109	C₄×C₇₉	—	2	1	no	—
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	4	1	no	—
112	C₄×C₇₉	—	4	2	no	—
113	C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
114	Dic₇₉	—	2	1	no	—
115	Dic₇₉	—	2	1	no	—
116	Dic₇₉	—	2	1	no	—
117	Dic₇₉	—	4	1	no	—
118	Dic₇₉	—	4	2	no	—
119	Dic₇₉	—	4	1	no	—
120	C₂×C₇₉	—	8	1	no	—
121	C₂×C₇₉	#536	1	1	yes	characteristic
122	C₂×C₇₉	#575	1	1	yes	characteristic
123	C₂×C₇₉	#575	1	1	yes	characteristic
124	D₇₉	—	4	1	no	—
125	#3240	—	79	1	no	maximal, Sylow
126	C₇₉	#3240	1	1	yes	characteristic, complemented, Sylow
127	#533	—	79	1	no	—
128	#529	—	79	1	no	—
129	#501	—	79	1	no	—
130	#501	—	79	1	no	—
131	#489	—	79	1	no	—
132	#489	D₇₉	1	1	yes	characteristic, complemented
133	#485	—	79	2	no	—
134	#482	—	79	2	no	—
135	#479	—	79	2	no	—
136	#478	—	79	2	no	—
137	#432	—	79	1	no	—
138	C₄⋊Q₈	—	79	1	no	—
139	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
140	#126	—	158	1	no	—
141	#125	—	79	2	no	—
142	#125	—	79	1	no	—
143	#124	C₂×D₇₉	1	1	yes	characteristic
144	#123	—	158	1	no	—
145	C₂²⋊Q₈	—	79	1	no	—
146	C₂²⋊Q₈	—	158	1	no	—
147	C₂²⋊Q₈	—	158	1	no	—
148	#121	—	79	1	no	—
149	C₄×Q₈	—	79	1	no	—
150	C₄×Q₈	—	158	1	no	—
151	C₄×Q₈	—	158	1	no	—
152	C₄×D₄	—	79	1	no	—
153	C₄×D₄	—	158	1	no	—
154	#117	—	79	2	no	—
155	#117	—	158	1	no	—
156	C₂×C₄²	—	79	1	no	—
157	#107	—	79	2	no	—
158	#107	—	79	2	no	—
159	#106	—	79	2	no	—
160	#106	—	79	2	no	—
161	C₄⋊C₈	—	79	2	no	—
162	#103	—	79	2	no	—
163	#103	C₂×D₇₉	1	2	yes	—
164	#102	—	79	2	no	—
165	#102	C₂×D₇₉	1	2	yes	—
166	C₂²⋊C₈	—	79	2	no	—
167	#97	—	79	1	no	—
168	#97	C₂×D₇₉	1	1	yes	characteristic
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	158	1	no	—
171	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
172	C₂×D₄	—	158	1	no	—
173	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
174	C₂²×C₄	—	79	1	no	—
175	C₂²×C₄	—	79	1	no	—
176	C₂²×C₄	—	79	1	no	—
177	C₂²×C₄	—	158	1	no	—
178	C₂×C₈	—	79	2	no	—
179	C₂×C₈	C₂²×D₇₉	1	2	yes	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	—	79	2	no	—
182	C₄⋊C₄	—	79	1	no	—
183	C₄⋊C₄	—	79	1	no	—
184	C₄⋊C₄	—	158	1	no	—
185	C₄⋊C₄	—	158	2	no	—
186	C₄⋊C₄	—	158	1	no	—
187	C₄⋊C₄	—	158	2	no	—
188	C₄⋊C₄	—	158	1	no	—
189	C₄⋊C₄	—	158	1	no	—
190	C₄⋊C₄	—	158	1	no	—
191	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
192	C₂²⋊C₄	—	2	1	no	—
193	C₂²⋊C₄	—	2	1	no	—
194	C₂²⋊C₄	—	158	2	no	—
195	C₂²⋊C₄	—	158	1	no	—
196	C₂²⋊C₄	—	158	1	no	—
197	C₂²⋊C₄	—	158	1	no	—
198	C₄²	—	79	1	no	—
199	C₄²	—	79	1	no	—
200	C₄²	—	79	1	no	—
201	C₄²	—	158	2	no	—
202	C₄²	—	158	1	no	—
203	C₄²	C₂²×D₇₉	1	1	yes	characteristic
204	C₂³	—	2	1	no	—
205	C₂³	—	79	1	no	—
206	Q₈	—	2	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	316	2	no	—
209	D₄	—	2	2	no	—
210	D₄	—	316	2	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	316	1	no	—
214	C₂×C₄	—	316	1	no	—
215	C₂×C₄	—	316	2	no	—
216	C₂×C₄	—	79	1	no	—
217	C₂×C₄	—	79	1	no	—
218	C₂×C₄	—	79	1	no	—
219	C₂×C₄	—	158	1	no	—
220	C₂×C₄	—	158	2	no	—
221	C₂×C₄	—	158	1	no	—
222	C₂×C₄	—	158	2	no	—
223	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
224	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
225	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
226	C₈	—	2	2	no	—
227	C₈	—	158	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	—	4	1	no	—
231	C₂²	—	158	1	no	—
232	C₂²	—	158	1	no	—
233	C₂²	—	158	1	no	—
234	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	4	2	no	—
238	C₄	—	4	1	no	—
239	C₄	—	316	1	no	—
240	C₄	—	316	1	no	—
241	C₄	—	316	2	no	—
242	C₄	—	158	1	no	—
243	C₄	—	158	1	no	—
244	C₄	—	158	1	no	—
245	C₄	#14579208	1	2	yes	—
246	C₂	—	8	1	no	—
247	C₂	—	316	1	no	—
248	C₂	#19099133	1	1	yes	characteristic
249	C₂	#19099359	1	1	yes	characteristic
250	C₂	#19099362	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099118

C₂

yes

maximal, characteristic, complemented

#19099092

C₂

yes

maximal, characteristic

#19098972

C₂

yes

maximal, characteristic, complemented

#19098969

C₂

yes

maximal, characteristic, complemented

#19098922

C₂

yes

maximal, characteristic, complemented

#19098902

C₂

yes

maximal, complemented

#19098885

C₂

yes

maximal

#19098872

C₂

yes

maximal, complemented

#19098865

C₂

yes

maximal, complemented

#19098618

C₂

yes

maximal, characteristic, complemented

#489×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579161

C₂²

yes

characteristic

#14579154

—

#14579153

C₂²

yes

characteristic

#14579152

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

#14579132

C₂²

yes

characteristic

Q₈×Dic₇₉

—

Q₈×Dic₇₉

C₂²

yes

characteristic

#14579126

—

D₄×Dic₇₉

C₂²

yes

characteristic

(C₂²⋊D₇₉)⋊C₄

—

#14579119

C₂²

yes

—

#14579117

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579095

C₂²

yes

—

#14579094

C₂²

yes

—

#14579093

C₂²

yes

—

#14579092

C₂²

yes

—

Dic₇₉⋊C₈

C₂²

yes

—

#14579085

C₂²

yes

—

#14579082

C₂²

yes

—

(C₂×D₇₉)⋊C₈

C₂²

yes

—

#14579072

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#124×C₇₉

C₂²

yes

characteristic

#103×C₇₉

C₂²

yes

—

#102×C₇₉

C₂²

yes

—

#97×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

C₄⋊Dic₇₉

C₂³

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂³

yes

characteristic

C₂×D₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

100

C₈×C₇₉

—

101

C₇₉⋊C₈

—

102

C₂²×C₇₉

—

103

C₂²×C₇₉

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

C₂²×D₄

yes

characteristic

106

C₂×D₇₉

—

107

C₂×D₇₉

—

108

C₂×D₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

—

113

C₄×C₇₉

2₋¹⁺⁴

yes

—

114

Dic₇₉

—

115

Dic₇₉

—

116

Dic₇₉

—

117

Dic₇₉

—

118

Dic₇₉

—

119

Dic₇₉

—

120

C₂×C₇₉

—

121

C₂×C₇₉

#536

yes

characteristic

122

C₂×C₇₉

#575

yes

characteristic

123

C₂×C₇₉

#575

yes

characteristic

124

D₇₉

—

125

#3240

—

maximal, Sylow

126

C₇₉

#3240

yes

characteristic, complemented, Sylow

127

#533

—

128

#529

—

129

#501

—

130

#501

—

131

#489

—

132

#489

D₇₉

yes

characteristic, complemented

133

#485

—

134

#482

—

135

#479

—

136

#478

—

137

#432

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

140

#126

—

158

—

141

#125

—

142

#125

—

143

#124

C₂×D₇₉

yes

characteristic

144

#123

—

158

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

158

—

147

C₂²⋊Q₈

—

158

—

148

#121

—

149

C₄×Q₈

—

150

C₄×Q₈

—

158

—

151

C₄×Q₈

—

158

—

152

C₄×D₄

—

153

C₄×D₄

—

158

—

154

#117

—

155

#117

—

158

—

156

C₂×C₄²

—

157

#107

—

158

#107

—

159

#106

—

160

#106

—

161

C₄⋊C₈

—

162

#103

—

163

#103

C₂×D₇₉

yes

—

164

#102

—

165

#102

C₂×D₇₉

yes

—

166

C₂²⋊C₈

—

167

#97

—

168

#97

C₂×D₇₉

yes

characteristic

169

C₂×Q₈

—

170

C₂×Q₈

—

158

—

171

C₂×Q₈

C₂²×D₇₉

yes

characteristic

172

C₂×D₄

—

158

—

173

C₂×D₄

C₂²×D₇₉

yes

characteristic

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

158

—

178

C₂×C₈

—

179

C₂×C₈

C₂²×D₇₉

yes

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

158

—

185

C₄⋊C₄

—

158

—

186

C₄⋊C₄

—

158

—

187

C₄⋊C₄

—

158

—

188

C₄⋊C₄

—

158

—

189

C₄⋊C₄

—

158

—

190

C₄⋊C₄

—

158

—

191

C₄⋊C₄

C₂²×D₇₉

yes

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

194

C₂²⋊C₄

—

158

—

195

C₂²⋊C₄

—

158

—

196

C₂²⋊C₄

—

158

—

197

C₂²⋊C₄

—

158

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

158

—

202

C₄²

—

158

—

203

C₄²

C₂²×D₇₉

yes

characteristic

204

C₂³

—

205

C₂³

—

206

Q₈

—

207

Q₈

—

208

Q₈

—

316

—

209

D₄

—

210

D₄

—

316

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

316

—

214

C₂×C₄

—

316

—

215

C₂×C₄

—

316

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

158

—

220

C₂×C₄

—

158

—

221

C₂×C₄

—

158

—

222

C₂×C₄

—

158

—

223

C₂×C₄

D₄×D₇₉

yes

characteristic

224

C₂×C₄

D₄×D₇₉

yes

characteristic

225

C₂×C₄

C₂³×D₇₉

yes

characteristic

226

C₈

—

227

C₈

—

158

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

158

—

232

C₂²

—

158

—

233

C₂²

—

158

—

234

C₂²

C₂×D₄×D₇₉

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

316

—

240

C₄

—

316

—

241

C₄

—

316

—

242

C₄

—

158

—

243

C₄

—

158

—

244

C₄

—

158

—

245

C₄

#14579208

yes

—

246

C₂

—

247

C₂

—

316

—

248

C₂

#19099133

yes

characteristic

249

C₂

#19099359

yes

characteristic

250

C₂

#19099362

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#489×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	#14579132	C₂²
hypercenter	#489	D₇₉
hypocenter	C₇₉	#3240
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #489

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#489×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

C₂²

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #489

N	H ≅ G/N	type
1. #19099118	C₂	semidirect
3. #19098972	C₂	semidirect
4. #19098969	C₂	semidirect
5. #19098922	C₂	semidirect
6. #19098902	C₂	semidirect
8. #19098872	C₂	semidirect
9. #19098865	C₂	semidirect
10. #19098618	C₂	semidirect
11. #489×C₇₉	C₂	semidirect
126. C₇₉	#3240	semidirect
132. #489	D₇₉	semidirect

H ≅ G/N

type

1. #19099118

C₂

semidirect

3. #19098972

C₂

semidirect

4. #19098969

C₂

semidirect

5. #19098922

C₂

semidirect

6. #19098902

C₂

semidirect

8. #19098872

C₂

semidirect

9. #19098865

C₂

semidirect

10. #19098618

C₂

semidirect

11. #489×C₇₉

C₂

semidirect

126. C₇₉

#3240

semidirect

132. #489

D₇₉

semidirect

Subgroups — #23774635

Conjugacy classes of subgroups

Complements