Group #23776271 — subgroups

Subgroups — #23776271

Order 10112.

338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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	#19099273	C₂	1	1	yes	maximal, characteristic
2	#19098962	C₂	1	2	yes	maximal, complemented
3	#19098959	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098870	C₂	1	2	yes	maximal, complemented
5	#19098860	C₂	1	2	yes	maximal
6	#19098858	C₂	1	1	yes	maximal, characteristic, complemented
7	#19098840	C₂	1	1	yes	maximal, characteristic
8	Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11929611	C₂	1	1	yes	maximal, characteristic
10	C₄×#11929611	C₂	1	2	yes	maximal
11	#557×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11929611	C₂²	1	1	yes	characteristic
13	#14579161	C₂²	1	1	yes	characteristic
14	#14579153	C₂²	1	2	yes	—
15	#14579139	—	2	2	no	—
16	#14579137	—	2	1	no	—
17	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
18	C₄×D₃₁₆	C₂²	1	2	yes	—
19	C₄⋊C₄×D₇₉	—	2	1	no	—
20	#14579094	C₂²	1	2	yes	—
21	#14579094	C₂²	1	2	yes	—
22	#14579092	C₂²	1	2	yes	—
23	#14579092	C₂²	1	1	yes	characteristic
24	#14579092	C₂²	1	2	yes	—
25	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
27	#14579085	C₂²	1	2	yes	—
28	#14579085	C₂²	1	1	yes	characteristic
29	#14579081	C₂²	1	2	yes	—
30	#14579081	C₂²	1	1	yes	characteristic
31	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₇₉	—	2	1	no	—
34	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
35	#125×C₇₉	—	2	2	no	—
36	#125×C₇₉	C₂²	1	2	yes	—
37	C₄×Q₈×C₇₉	—	2	1	no	—
38	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×Q₈×C₇₉	C₂²	1	2	yes	—
40	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₅₈	—	2	1	no	—
42	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₇₉	—	2	1	no	—
44	C₂×C₄×D₇₉	—	2	2	no	—
45	#11929611	Q₈	1	4	yes	complemented
46	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
48	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
49	C₄⋊Dic₇₉	—	2	1	no	—
50	C₄⋊Dic₇₉	C₂³	1	2	yes	—
51	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
52	Dic₇₉⋊C₄	—	2	2	no	—
53	Dic₇₉⋊C₄	—	2	2	no	—
54	(C₂×D₇₉)⋊C₄	—	2	2	no	—
55	(C₂×D₇₉)⋊C₄	—	2	1	no	—
56	C₂×Q₈×C₇₉	—	2	1	no	—
57	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
58	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
59	C₄⋊C₄×C₇₉	—	2	2	no	—
60	C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₄⋊C₄×C₇₉	—	2	2	no	—
62	C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₄⋊C₄×C₇₉	—	2	2	no	—
64	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
65	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
66	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
68	C₄²×C₇₉	—	2	2	no	—
69	C₄²×C₇₉	—	2	1	no	—
70	C₄²×C₇₉	C₂³	1	2	yes	—
71	C₄²×C₇₉	C₂³	1	1	yes	characteristic
72	C₂²×D₇₉	—	2	1	no	—
73	Q₈×C₇₉	—	2	2	no	—
74	Q₈×C₇₉	—	2	1	no	—
75	Q₈×C₇₉	—	4	2	no	—
76	Q₈×C₇₉	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₇₉	—	2	1	no	—
78	C₂×C₄×C₇₉	—	2	1	no	—
79	C₂×C₄×C₇₉	—	2	2	no	—
80	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
81	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
85	C₂×Dic₇₉	—	2	1	no	—
86	C₂×Dic₇₉	—	2	2	no	—
87	D₃₁₆	—	2	1	no	—
88	D₃₁₆	C₂×Q₈	1	2	yes	—
89	C₄×D₇₉	—	4	2	no	—
90	C₄×D₇₉	—	8	2	no	—
91	Dic₁₅₈	—	8	1	no	—
92	C₇₉⋊C₈	—	2	1	no	—
93	C₇₉⋊C₈	—	2	2	no	—
94	C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
95	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
96	C₂×D₇₉	—	2	2	no	—
97	C₂×D₇₉	—	4	1	no	—
98	C₂×D₇₉	—	4	1	no	—
99	C₄×C₇₉	—	2	2	no	—
100	C₄×C₇₉	—	2	2	no	—
101	C₄×C₇₉	—	2	1	no	—
102	C₄×C₇₉	—	2	2	no	—
103	C₄×C₇₉	—	4	2	no	—
104	C₄×C₇₉	—	4	1	no	—
105	C₄×C₇₉	#135	1	2	yes	—
106	C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
107	C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
108	Dic₇₉	—	4	1	no	—
109	Dic₇₉	—	4	2	no	—
110	C₂×C₇₉	D₄×Q₈	1	1	yes	characteristic
111	C₂×C₇₉	C₂×#135	1	1	yes	characteristic
112	C₂×C₇₉	#577	1	1	yes	characteristic
113	D₇₉	—	4	2	no	—
114	#3381	—	79	1	no	maximal, Sylow
115	C₇₉	#3381	1	1	yes	characteristic, complemented, Sylow
116	#557	D₇₉	1	1	yes	characteristic, complemented
117	#554	—	79	1	no	—
118	#499	—	79	2	no	—
119	#498	—	79	1	no	—
120	#479	—	79	2	no	—
121	#478	—	79	2	no	—
122	#477	—	79	1	no	—
123	#474	—	79	1	no	—
124	C₈×Q₈	—	79	1	no	—
125	C₄×SD₁₆	—	79	1	no	—
126	C₄×SD₁₆	—	79	2	no	—
127	C₂×SD₁₆	—	79	1	no	—
128	C₄⋊Q₈	—	2	1	no	—
129	C₄⋊Q₈	—	79	1	no	—
130	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
131	#125	—	2	2	no	—
132	#125	—	79	2	no	—
133	#125	C₂×D₇₉	1	2	yes	—
134	C₂²⋊Q₈	—	158	1	no	—
135	C₂²⋊Q₈	—	158	2	no	—
136	C₄×Q₈	—	2	1	no	—
137	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
138	C₄×Q₈	C₂×D₇₉	1	2	yes	—
139	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
140	C₄×D₄	—	79	1	no	—
141	C₄×D₄	—	79	2	no	—
142	C₂×C₄⋊C₄	—	158	1	no	—
143	#107	—	79	2	no	—
144	#107	—	79	2	no	—
145	#106	—	79	2	no	—
146	#106	—	79	1	no	—
147	#106	—	79	2	no	—
148	C₄⋊C₈	—	79	1	no	—
149	C₄⋊C₈	—	79	2	no	—
150	#103	—	79	2	no	—
151	#103	—	79	1	no	—
152	#102	—	79	2	no	—
153	#102	—	79	1	no	—
154	C₄×C₈	—	79	1	no	—
155	C₄×C₈	—	79	2	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	158	1	no	—
158	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
159	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
160	C₂×D₄	—	79	1	no	—
161	C₂²×C₄	—	158	1	no	—
162	C₂²×C₄	—	158	2	no	—
163	SD₁₆	—	79	4	no	—
164	C₂×C₈	—	79	1	no	—
165	C₂×C₈	—	79	1	no	—
166	C₂×C₈	—	79	2	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	1	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	79	2	no	—
173	C₄⋊C₄	—	79	1	no	—
174	C₄⋊C₄	—	158	2	no	—
175	C₄⋊C₄	—	158	2	no	—
176	C₄⋊C₄	—	158	1	no	—
177	C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
178	C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
179	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
180	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
181	C₂²⋊C₄	—	158	1	no	—
182	C₂²⋊C₄	—	158	2	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	C₂²×D₇₉	1	2	yes	—
186	C₄²	C₂²×D₇₉	1	1	yes	characteristic
187	C₂³	—	158	1	no	—
188	Q₈	—	2	1	no	—
189	Q₈	—	2	2	no	—
190	Q₈	—	4	2	no	—
191	Q₈	—	632	1	no	—
192	Q₈	Q₈×D₇₉	1	2	yes	—
193	D₄	—	79	2	no	—
194	D₄	—	158	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	316	2	no	—
199	C₂×C₄	—	632	2	no	—
200	C₂×C₄	—	158	1	no	—
201	C₂×C₄	—	158	2	no	—
202	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
203	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
204	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
205	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
206	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
207	C₈	—	79	2	no	—
208	C₈	—	158	1	no	—
209	C₈	—	158	2	no	—
210	C₂²	—	316	1	no	—
211	C₂²	—	316	1	no	—
212	C₂²	—	158	2	no	—
213	C₂²	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
214	C₄	—	2	2	no	—
215	C₄	—	2	2	no	—
216	C₄	—	2	2	no	—
217	C₄	—	2	1	no	—
218	C₄	—	4	2	no	—
219	C₄	—	4	1	no	—
220	C₄	—	316	1	no	—
221	C₄	—	316	2	no	—
222	C₄	#14579181	1	2	yes	—
223	C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
224	C₄	#14579209	1	1	yes	characteristic
225	C₂	—	316	2	no	—
226	C₂	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
227	C₂	C₂×#14579181	1	1	yes	characteristic
228	C₂	#19099371	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099273

C₂

yes

maximal, characteristic

#19098962

C₂

yes

maximal, complemented

#19098959

C₂

yes

maximal, characteristic, complemented

#19098870

C₂

yes

maximal, complemented

#19098860

C₂

yes

maximal

#19098858

C₂

yes

maximal, characteristic, complemented

#19098840

C₂

yes

maximal, characteristic

Q₈×C₇₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#11929611

C₂

yes

maximal, characteristic

C₄×#11929611

C₂

yes

maximal

#557×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929611

C₂²

yes

characteristic

#14579161

C₂²

yes

characteristic

#14579153

C₂²

yes

—

#14579139

—

#14579137

—

C₄×D₃₁₆

C₂²

yes

characteristic

C₄×D₃₁₆

C₂²

yes

—

C₄⋊C₄×D₇₉

—

#14579094

C₂²

yes

—

#14579094

C₂²

yes

—

#14579092

C₂²

yes

—

#14579092

C₂²

yes

characteristic

#14579092

C₂²

yes

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579085

C₂²

yes

—

#14579085

C₂²

yes

characteristic

#14579081

C₂²

yes

—

#14579081

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#125×C₇₉

—

#125×C₇₉

C₂²

yes

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₄×Q₈×C₇₉

C₂²

yes

—

C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

C₂³

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

#11929611

Q₈

yes

complemented

C₂×C₇₉⋊C₈

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₂×C₇₉⋊C₈

C₂³

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×Q₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂³

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

C₂×Q₈

yes

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

C₂×Q₈

yes

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

100

C₄×C₇₉

—

101

C₄×C₇₉

—

102

C₄×C₇₉

—

103

C₄×C₇₉

—

104

C₄×C₇₉

—

105

C₄×C₇₉

#135

yes

—

106

C₄×C₇₉

C₂²×Q₈

yes

characteristic

107

C₄×C₇₉

2₋¹⁺⁴

yes

characteristic

108

Dic₇₉

—

109

Dic₇₉

—

110

C₂×C₇₉

D₄×Q₈

yes

characteristic

111

C₂×C₇₉

C₂×#135

yes

characteristic

112

C₂×C₇₉

#577

yes

characteristic

113

D₇₉

—

114

#3381

—

maximal, Sylow

115

C₇₉

#3381

yes

characteristic, complemented, Sylow

116

#557

D₇₉

yes

characteristic, complemented

117

#554

—

118

#499

—

119

#498

—

120

#479

—

121

#478

—

122

#477

—

123

#474

—

124

C₈×Q₈

—

125

C₄×SD₁₆

—

126

C₄×SD₁₆

—

127

C₂×SD₁₆

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

131

#125

—

132

#125

—

133

#125

C₂×D₇₉

yes

—

134

C₂²⋊Q₈

—

158

—

135

C₂²⋊Q₈

—

158

—

136

C₄×Q₈

—

137

C₄×Q₈

C₂×D₇₉

yes

characteristic

138

C₄×Q₈

C₂×D₇₉

yes

—

139

C₄×Q₈

C₂×D₇₉

yes

characteristic

140

C₄×D₄

—

141

C₄×D₄

—

142

C₂×C₄⋊C₄

—

158

—

143

#107

—

144

#107

—

145

#106

—

146

#106

—

147

#106

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#103

—

151

#103

—

152

#102

—

153

#102

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

—

158

C₂×Q₈

C₂²⋊D₇₉

yes

characteristic

159

C₂×Q₈

C₂²×D₇₉

yes

characteristic

160

C₂×D₄

—

161

C₂²×C₄

—

158

—

162

C₂²×C₄

—

158

—

163

SD₁₆

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

158

—

175

C₄⋊C₄

—

158

—

176

C₄⋊C₄

—

158

—

177

C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

178

C₄⋊C₄

C₂²⋊D₇₉

yes

—

179

C₄⋊C₄

C₂²×D₇₉

yes

—

180

C₄⋊C₄

C₂²×D₇₉

yes

characteristic

181

C₂²⋊C₄

—

158

—

182

C₂²⋊C₄

—

158

—

183

C₄²

—

184

C₄²

—

185

C₄²

C₂²×D₇₉

yes

—

186

C₄²

C₂²×D₇₉

yes

characteristic

187

C₂³

—

158

—

188

Q₈

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

632

—

192

Q₈

Q₈×D₇₉

yes

—

193

D₄

—

194

D₄

—

158

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

316

—

199

C₂×C₄

—

632

—

200

C₂×C₄

—

158

—

201

C₂×C₄

—

158

—

202

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

203

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

204

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

205

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

206

C₂×C₄

C₂³×D₇₉

yes

characteristic

207

C₈

—

208

C₈

—

158

—

209

C₈

—

158

—

210

C₂²

—

316

—

211

C₂²

—

316

—

212

C₂²

—

158

—

213

C₂²

C₂²×C₂²⋊D₇₉

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

316

—

221

C₄

—

316

—

222

C₄

#14579181

yes

—

223

C₄

C₂×Q₈×D₇₉

yes

characteristic

224

C₄

#14579209

yes

characteristic

225

C₂

—

316

—

226

C₂

Q₈×C₂²⋊D₇₉

yes

characteristic

227

C₂

C₂×#14579181

yes

characteristic

228

C₂

#19099371

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#557×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂×D₃₁₆	C₂³
hypercenter	#557	D₇₉
hypocenter	C₇₉	#3381
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #557

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#557×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

prime radical

C₂×D₃₁₆

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #557

N	H ≅ G/N	type
2. #19098962	C₂	semidirect
3. #19098959	C₂	semidirect
4. #19098870	C₂	semidirect
6. #19098858	C₂	semidirect
8. Q₈×C₇₉⋊C₈	C₂	semidirect
11. #557×C₇₉	C₂	semidirect
45. #11929611	Q₈	semidirect
115. C₇₉	#3381	semidirect
116. #557	D₇₉	semidirect

H ≅ G/N

type

2. #19098962

C₂

semidirect

3. #19098959

C₂

semidirect

4. #19098870

C₂

semidirect

6. #19098858

C₂

semidirect

8. Q₈×C₇₉⋊C₈

C₂

semidirect

11. #557×C₇₉

C₂

semidirect

45. #11929611

Q₈

semidirect

115. C₇₉

#3381

semidirect

116. #557

D₇₉

semidirect

Subgroups — #23776271

Conjugacy classes of subgroups

Complements