Group #23776429 — subgroups

Subgroups — #23776429

Order 10112.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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	#19099291	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099283	C₂	1	1	yes	maximal, characteristic
3	#19098954	C₂	1	2	yes	maximal
4	#19098943	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098784	C₂	1	2	yes	maximal
6	#19098773	C₂	1	1	yes	maximal, characteristic, complemented
7	#19098772	C₂	1	2	yes	maximal, complemented
8	#19098768	C₂	1	1	yes	maximal, characteristic
9	#19098693	C₂	1	1	yes	maximal, characteristic, complemented
10	#19098669	C₂	1	2	yes	maximal, complemented
11	C₄×SD₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×Dic₃₁₆	C₂²	1	2	yes	—
13	C₂×Dic₃₁₆	C₂²	1	2	yes	—
14	C₂×#11929614	C₂²	1	2	yes	—
15	C₂×#11929612	C₂²	1	2	yes	—
16	#14579161	C₂²	1	1	yes	characteristic
17	#14579161	C₂²	1	1	yes	characteristic
18	#14579159	C₂²	1	2	yes	—
19	#14579154	—	2	2	no	—
20	#14579153	—	2	1	no	—
21	#14579151	—	2	2	no	—
22	#14579148	C₂²	1	2	yes	—
23	#14579140	—	2	1	no	—
24	C₄×Dic₁₅₈	—	2	1	no	—
25	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
26	#14579126	C₂²	1	2	yes	—
27	#14579126	C₂²	1	2	yes	—
28	#14579120	—	2	1	no	—
29	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	Dic₇₉⋊C₈	C₂²	1	2	yes	—
31	#14579084	C₂²	1	2	yes	—
32	#14579084	C₂²	1	2	yes	—
33	#14579071	C₂²	1	2	yes	—
34	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
37	#106×C₇₉	C₂²	1	1	yes	characteristic
38	#103×C₇₉	C₂²	1	1	yes	characteristic
39	#102×C₇₉	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₅₈	D₄	1	1	yes	characteristic
42	C₂×Dic₁₅₈	C₂³	1	2	yes	—
43	C₂×Dic₁₅₈	C₂³	1	2	yes	—
44	Dic₃₁₆	—	2	4	no	—
45	Dic₃₁₆	—	4	2	no	—
46	#11929614	—	4	2	no	—
47	#11929612	—	4	2	no	—
48	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
49	C₄⋊Dic₇₉	—	2	1	no	—
50	C₄⋊Dic₇₉	—	2	1	no	—
51	C₄⋊Dic₇₉	—	2	1	no	—
52	C₄⋊Dic₇₉	—	2	1	no	—
53	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
54	Dic₇₉⋊C₄	—	2	2	no	—
55	Dic₇₉⋊C₄	—	2	2	no	—
56	Dic₇₉⋊C₄	—	2	2	no	—
57	Dic₇₉⋊C₄	—	2	2	no	—
58	Dic₇₉⋊C₄	D₄	1	2	yes	—
59	C₂²⋊Dic₇₉	—	2	2	no	—
60	C₂²⋊Dic₇₉	—	2	2	no	—
61	C₄×Dic₇₉	—	2	2	no	—
62	C₄×Dic₇₉	—	2	2	no	—
63	C₄×Dic₇₉	C₂³	1	2	yes	—
64	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	—	2	1	no	—
67	SD₁₆×C₇₉	—	2	2	no	—
68	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
69	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
70	C₄⋊C₄×C₇₉	—	2	1	no	—
71	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
72	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
73	C₂²⋊C₄×C₇₉	—	2	1	no	—
74	C₄²×C₇₉	—	2	1	no	—
75	C₄²×C₇₉	C₂³	1	1	yes	characteristic
76	C₂³×C₇₉	—	2	1	no	—
77	Q₈×C₇₉	—	2	1	no	—
78	Q₈×C₇₉	—	2	1	no	—
79	D₄×C₇₉	—	2	1	no	—
80	D₄×C₇₉	—	2	1	no	—
81	C₂×C₄×C₇₉	—	2	1	no	—
82	C₂×C₄×C₇₉	—	2	1	no	—
83	C₂×C₄×C₇₉	—	2	1	no	—
84	C₂×C₄×C₇₉	—	4	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	C₂×Dic₇₉	—	2	2	no	—
89	C₂×Dic₇₉	—	2	2	no	—
90	C₂×Dic₇₉	C₂×D₄	1	2	yes	—
91	C₂×Dic₇₉	C₂×D₄	1	2	yes	—
92	Dic₁₅₈	—	2	2	no	—
93	Dic₁₅₈	—	2	2	no	—
94	Dic₁₅₈	—	2	2	no	—
95	Dic₁₅₈	—	2	2	no	—
96	Dic₁₅₈	—	2	2	no	—
97	C₈×C₇₉	—	2	1	no	—
98	C₈×C₇₉	#41	1	2	yes	—
99	C₇₉⋊C₈	—	2	2	no	—
100	C₂²×C₇₉	—	4	1	no	—
101	C₂²×C₇₉	—	4	1	no	—
102	C₂²×C₇₉	—	4	1	no	—
103	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
104	C₄×C₇₉	—	2	1	no	—
105	C₄×C₇₉	—	4	1	no	—
106	C₄×C₇₉	—	4	1	no	—
107	C₄×C₇₉	—	4	1	no	—
108	C₄×C₇₉	#137	1	2	yes	—
109	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
110	C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
111	Dic₇₉	—	2	2	no	—
112	Dic₇₉	—	2	2	no	—
113	Dic₇₉	—	4	2	no	—
114	Dic₇₉	—	4	2	no	—
115	C₂×C₇₉	—	8	1	no	—
116	C₂×C₇₉	#550	1	1	yes	characteristic
117	C₂×C₇₉	C₂×#137	1	1	yes	characteristic
118	C₂×C₇₉	#578	1	1	yes	characteristic
119	#3398	—	79	1	no	maximal, Sylow
120	C₇₉	#3398	1	1	yes	characteristic, complemented, Sylow
121	#557	—	79	1	no	—
122	#556	—	79	1	no	—
123	#497	—	79	2	no	—
124	#494	—	79	1	no	—
125	#464	—	79	2	no	—
126	#462	—	79	1	no	—
127	#462	—	79	2	no	—
128	#461	—	79	1	no	—
129	#446	—	79	1	no	—
130	#441	—	79	2	no	—
131	C₄×SD₁₆	D₇₉	1	1	yes	characteristic
132	C₂×Q₁₆	—	79	2	no	—
133	C₂×Q₁₆	—	79	2	no	—
134	C₂×Q₁₆	—	79	2	no	—
135	C₂×SD₁₆	—	79	2	no	—
136	C₂×SD₁₆	C₂×D₇₉	1	1	yes	characteristic
137	C₄⋊Q₈	—	79	2	no	—
138	C₄⋊Q₈	—	79	1	no	—
139	C₄⋊Q₈	—	79	1	no	—
140	#126	—	158	2	no	—
141	#125	—	158	1	no	—
142	#125	—	158	2	no	—
143	#124	—	79	2	no	—
144	C₂²⋊Q₈	—	158	1	no	—
145	C₄×Q₈	—	79	1	no	—
146	C₄×Q₈	—	79	2	no	—
147	C₄×Q₈	—	79	2	no	—
148	C₄×Q₈	—	158	1	no	—
149	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
150	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
151	#117	—	158	1	no	—
152	#106	C₂×D₇₉	1	1	yes	characteristic
153	C₄⋊C₈	—	79	2	no	—
154	C₄⋊C₈	—	79	1	no	—
155	#103	—	79	2	no	—
156	#103	—	79	2	no	—
157	#103	C₂×D₇₉	1	1	yes	characteristic
158	#102	C₂×D₇₉	1	1	yes	characteristic
159	#97	—	79	2	no	—
160	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
161	C₂×Q₈	—	79	1	no	—
162	C₂×Q₈	—	79	2	no	—
163	C₂×Q₈	—	79	2	no	—
164	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
165	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
166	C₂²×C₄	—	2	1	no	—
167	Q₁₆	—	316	2	no	—
168	Q₁₆	—	316	2	no	—
169	Q₁₆	—	158	4	no	—
170	SD₁₆	—	2	2	no	—
171	SD₁₆	—	316	2	no	—
172	C₂×C₈	—	79	2	no	—
173	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
174	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
175	C₄⋊C₄	—	2	1	no	—
176	C₄⋊C₄	—	79	2	no	—
177	C₄⋊C₄	—	79	1	no	—
178	C₄⋊C₄	—	158	2	no	—
179	C₄⋊C₄	—	158	2	no	—
180	C₄⋊C₄	—	158	2	no	—
181	C₄⋊C₄	—	158	2	no	—
182	C₄⋊C₄	—	158	1	no	—
183	C₄⋊C₄	—	158	1	no	—
184	C₄⋊C₄	—	158	1	no	—
185	C₄⋊C₄	—	158	1	no	—
186	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
187	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
188	C₂²⋊C₄	—	2	1	no	—
189	C₂²⋊C₄	—	158	2	no	—
190	C₂²⋊C₄	—	158	2	no	—
191	C₄²	—	2	1	no	—
192	C₄²	—	79	2	no	—
193	C₄²	—	158	2	no	—
194	C₄²	—	158	2	no	—
195	C₄²	C₂²×D₇₉	1	1	yes	characteristic
196	C₂³	—	2	1	no	—
197	Q₈	—	2	1	no	—
198	Q₈	—	2	1	no	—
199	Q₈	—	158	2	no	—
200	Q₈	—	158	2	no	—
201	Q₈	—	158	2	no	—
202	Q₈	—	158	2	no	—
203	Q₈	—	158	2	no	—
204	D₄	—	2	1	no	—
205	D₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	79	2	no	—
211	C₂×C₄	—	79	2	no	—
212	C₂×C₄	—	158	2	no	—
213	C₂×C₄	—	158	2	no	—
214	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
215	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
216	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	158	2	no	—
219	C₈	#11929624	1	2	yes	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	4	1	no	—
223	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	4	1	no	—
226	C₄	—	4	1	no	—
227	C₄	—	4	1	no	—
228	C₄	—	316	2	no	—
229	C₄	—	316	2	no	—
230	C₄	—	158	2	no	—
231	C₄	—	158	2	no	—
232	C₄	#14579190	1	2	yes	—
233	C₄	C₂×#11929624	1	1	yes	characteristic
234	C₄	#14579207	1	1	yes	characteristic
235	C₂	—	8	1	no	—
236	C₂	#19099234	1	1	yes	characteristic
237	C₂	C₂×#14579190	1	1	yes	characteristic
238	C₂	#19099377	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099291

C₂

yes

maximal, characteristic, complemented

#19099283

C₂

yes

maximal, characteristic

#19098954

C₂

yes

maximal

#19098943

C₂

yes

maximal, characteristic, complemented

#19098784

C₂

yes

maximal

#19098773

C₂

yes

maximal, characteristic, complemented

#19098772

C₂

yes

maximal, complemented

#19098768

C₂

yes

maximal, characteristic

#19098693

C₂

yes

maximal, characteristic, complemented

#19098669

C₂

yes

maximal, complemented

C₄×SD₁₆×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

—

C₂×Dic₃₁₆

C₂²

yes

—

C₂×#11929614

C₂²

yes

—

C₂×#11929612

C₂²

yes

—

#14579161

C₂²

yes

characteristic

#14579161

C₂²

yes

characteristic

#14579159

C₂²

yes

—

—

—

—

C₂²

yes

—

#14579140

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

C₂²

yes

characteristic

#14579126

C₂²

yes

—

#14579126

C₂²

yes

—

#14579120

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

Dic₇₉⋊C₈

C₂²

yes

—

#14579084

C₂²

yes

—

#14579084

C₂²

yes

—

#14579071

C₂²

yes

—

C₂×SD₁₆×C₇₉

C₂²

yes

characteristic

C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

C₂²

yes

characteristic

#106×C₇₉

C₂²

yes

characteristic

#103×C₇₉

C₂²

yes

characteristic

#102×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

D₄

yes

characteristic

C₂×Dic₁₅₈

C₂³

yes

—

C₂×Dic₁₅₈

C₂³

yes

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929614

—

#11929612

—

C₂×C₇₉⋊C₈

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

D₄

yes

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂³

yes

—

C₂×Q₈×C₇₉

C₂³

yes

characteristic

C₂×D₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

—

SD₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

C₂³

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×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×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₂×D₄

yes

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

#41

yes

—

C₇₉⋊C₈

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

—

102

C₂²×C₇₉

—

103

C₂²×C₇₉

C₂²×D₄

yes

characteristic

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

#137

yes

—

109

C₄×C₇₉

C₂×#41

yes

characteristic

110

C₄×C₇₉

H(5,𝔽₂)

yes

characteristic

111

Dic₇₉

—

112

Dic₇₉

—

113

Dic₇₉

—

114

Dic₇₉

—

115

C₂×C₇₉

—

116

C₂×C₇₉

#550

yes

characteristic

117

C₂×C₇₉

C₂×#137

yes

characteristic

118

C₂×C₇₉

yes

119

—

120

C₇₉

#3398

yes

characteristic, complemented, Sylow

121

#557

—

122

#556

—

123

#497

—

124

#494

—

125

#464

—

126

#462

—

127

#462

—

128

#461

—

129

#446

—

130

#441

—

131

C₄×SD₁₆

D₇₉

yes

characteristic

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

—

135

C₂×SD₁₆

—

136

C₂×SD₁₆

C₂×D₇₉

yes

characteristic

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

#126

—

158

—

141

#125

—

158

—

142

#125

—

158

—

143

#124

—

144

C₂²⋊Q₈

—

158

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

158

—

149

C₄×Q₈

C₂×D₇₉

yes

characteristic

150

C₄×D₄

C₂×D₇₉

yes

characteristic

151

#117

—

158

—

152

#106

C₂×D₇₉

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

156

#103

—

157

#103

C₂×D₇₉

yes

characteristic

158

#102

C₂×D₇₉

yes

characteristic

159

#97

—

160

C₄×C₈

C₂×D₇₉

yes

characteristic

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

C₂²×D₇₉

yes

characteristic

165

C₂×D₄

C₂²×D₇₉

yes

characteristic

166

C₂²×C₄

—

167

Q₁₆

—

316

—

168

Q₁₆

—

316

—

169

Q₁₆

—

158

—

170

SD₁₆

—

171

SD₁₆

—

316

—

172

C₂×C₈

—

173

C₂×C₈

C₂²×D₇₉

yes

characteristic

174

C₂×C₈

C₂²×D₇₉

yes

characteristic

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

158

—

179

C₄⋊C₄

—

158

—

180

C₄⋊C₄

—

158

—

181

C₄⋊C₄

—

158

—

182

C₄⋊C₄

—

158

—

183

C₄⋊C₄

—

158

—

184

C₄⋊C₄

—

158

—

185

C₄⋊C₄

—

158

—

186

C₄⋊C₄

C₂²×D₇₉

yes

characteristic

187

C₄⋊C₄

C₂²×D₇₉

yes

characteristic

188

C₂²⋊C₄

—

189

C₂²⋊C₄

—

158

—

190

C₂²⋊C₄

—

158

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

158

—

194

C₄²

—

158

—

195

C₄²

C₂²×D₇₉

yes

characteristic

196

C₂³

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

158

—

200

Q₈

—

158

—

201

Q₈

—

158

—

202

Q₈

—

158

—

203

Q₈

—

158

—

204

D₄

—

205

D₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

158

—

213

C₂×C₄

—

158

—

214

C₂×C₄

D₄×D₇₉

yes

characteristic

215

C₂×C₄

D₄×D₇₉

yes

characteristic

216

C₂×C₄

C₂³×D₇₉

yes

characteristic

217

C₈

—

218

C₈

—

158

—

219

C₈

#11929624

yes

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

C₂×D₄×D₇₉

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

316

—

229

C₄

—

316

—

230

C₄

—

158

—

231

C₄

—

158

—

232

C₄

#14579190

yes

—

233

C₄

C₂×#11929624

yes

characteristic

234

C₄

#14579207

yes

characteristic

235

C₂

—

236

C₂

#19099234

yes

characteristic

237

C₂

C₂×#14579190

yes

characteristic

238

C₂

#19099377

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	C₄×SD₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂×D₄×C₇₉	C₂³
hypercenter	C₄×SD₁₆	D₇₉
hypocenter	C₇₉	#3398
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

C₄×SD₁₆×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

prime radical

C₂×D₄×C₇₉

C₂³

hypercenter

C₄×SD₁₆

D₇₉

hypocenter

C₇₉

#3398

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

N	H ≅ G/N	type
1. #19099291	C₂	semidirect
4. #19098943	C₂	semidirect
6. #19098773	C₂	semidirect
7. #19098772	C₂	semidirect
9. #19098693	C₂	semidirect
10. #19098669	C₂	semidirect
120. C₇₉	#3398	semidirect

H ≅ G/N

type

1. #19099291

C₂

semidirect

4. #19098943

C₂

semidirect

6. #19098773

C₂

semidirect

7. #19098772

C₂

semidirect

9. #19098693

C₂

semidirect

10. #19098669

C₂

semidirect

120. C₇₉

#3398

semidirect

Subgroups — #23776429

Conjugacy classes of subgroups

Complements