Group #34199891 — subgroups

Subgroups — #34199891

Order 20224.

232 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 99 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	#23765202	C₂	1	1	yes	maximal, characteristic
2	#23765154	C₂	1	1	yes	maximal, characteristic
3	C₈×#11929607	C₂	1	1	yes	maximal, characteristic
4	#23761469	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761464	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761463	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1370	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14579100	—	2	1	no	—
9	#19098614	C₄	1	1	yes	characteristic
10	C₄×#11929607	C₄	1	1	yes	characteristic
11	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
12	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
14	Dic₇₉⋊C₁₆	—	2	1	no	—
15	(C₂×D₇₉)⋊C₁₆	—	2	1	no	—
16	#19098338	—	2	1	no	—
17	#19098285	C₄	1	1	yes	characteristic
18	#19098284	C₄	1	1	yes	characteristic
19	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic
21	C₄⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic
22	C₈²×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#11929607	C₈	1	1	yes	characteristic
24	C₂×#11929607	C₈	1	1	yes	characteristic
25	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×D₇₉	Q₈	1	1	yes	characteristic
27	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
28	#14579100	—	4	2	no	—
29	C₂×C₇₉⋊C₁₆	—	2	1	no	—
30	C₂×C₇₉⋊C₁₆	—	2	1	no	—
31	Dic₇₉⋊C₈	—	2	1	no	—
32	(C₂×D₇₉)⋊C₈	—	2	1	no	—
33	#14579071	C₈	1	1	yes	characteristic
34	#14579071	C₈	1	1	yes	characteristic
35	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₈×Dic₇₉	D₄	1	1	yes	characteristic
39	C₈×Dic₇₉	Q₈	1	1	yes	characteristic
40	C₂×C₁₆×C₇₉	—	2	1	no	—
41	C₂×C₁₆×C₇₉	—	2	1	no	—
42	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
45	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×D₇₉	C₂×C₈	1	1	yes	characteristic
47	C₂×C₄×D₇₉	M₁₆	1	1	yes	characteristic
48	#11929607	—	2	2	no	—
49	#11929607	—	2	2	no	—
50	C₂×C₇₉⋊C₈	—	2	1	no	—
51	C₂×C₇₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₇₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₇₉⋊C₈	C₂×C₈	1	1	yes	characteristic
54	C₂×C₇₉⋊C₈	C₂×C₈	1	1	yes	characteristic
55	C₈×D₇₉	—	2	1	no	—
56	C₈×D₇₉	—	2	1	no	—
57	C₈×D₇₉	—	4	1	no	—
58	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
59	C₄×Dic₇₉	C₂×C₈	1	1	yes	characteristic
60	C₄×Dic₇₉	M₁₆	1	1	yes	characteristic
61	C₇₉⋊C₁₆	—	4	1	no	—
62	C₇₉⋊C₁₆	—	4	1	no	—
63	C₂×C₈×C₇₉	—	2	1	no	—
64	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
65	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
66	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
68	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
69	C₁₆×C₇₉	—	4	1	no	—
70	C₁₆×C₇₉	—	4	1	no	—
71	C₂²×D₇₉	C₄⋊C₈	1	1	yes	characteristic
72	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
74	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
75	C₂×Dic₇₉	C₄⋊C₈	1	1	yes	characteristic
76	C₂×Dic₇₉	C₄⋊C₈	1	1	yes	characteristic
77	C₂×Dic₇₉	C₄⋊C₈	1	1	yes	characteristic
78	C₄×D₇₉	—	2	1	no	—
79	C₄×D₇₉	—	2	1	no	—
80	C₄×D₇₉	—	2	1	no	—
81	C₄×D₇₉	—	2	1	no	—
82	C₄×D₇₉	—	4	1	no	—
83	C₈×C₇₉	—	2	1	no	—
84	C₈×C₇₉	—	2	1	no	—
85	C₈×C₇₉	—	4	1	no	—
86	C₈×C₇₉	M₃₂	1	2	yes	complemented
87	C₈×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₈×C₇₉	#137	1	1	yes	characteristic
89	C₇₉⋊C₈	—	2	1	no	—
90	C₇₉⋊C₈	—	2	1	no	—
91	C₇₉⋊C₈	—	2	1	no	—
92	C₇₉⋊C₈	—	4	1	no	—
93	C₇₉⋊C₈	M₃₂	1	2	yes	complemented
94	C₂²×C₇₉	C₂×C₄⋊C₈	1	1	yes	characteristic
95	C₂×D₇₉	—	2	1	no	—
96	C₂×D₇₉	—	2	1	no	—
97	C₂×D₇₉	—	2	1	no	—
98	C₄×C₇₉	—	2	1	no	—
99	C₄×C₇₉	#428	1	1	yes	characteristic
100	C₄×C₇₉	#430	1	1	yes	characteristic
101	C₄×C₇₉	C₂×M₃₂	1	1	yes	characteristic
102	C₄×C₇₉	C₂×M₃₂	1	1	yes	characteristic
103	Dic₇₉	—	2	1	no	—
104	Dic₇₉	—	2	1	no	—
105	Dic₇₉	—	2	1	no	—
106	#12017	—	79	1	no	maximal, Sylow
107	C₂×C₇₉	#1565	1	1	yes	characteristic
108	C₂×C₇₉	#2150	1	1	yes	characteristic
109	C₂×C₇₉	#2153	1	1	yes	characteristic
110	D₇₉	—	4	1	no	—
111	#2163	—	79	1	no	—
112	#2150	—	79	1	no	—
113	C₈×M₁₆	—	79	1	no	—
114	#1370	—	79	1	no	—
115	#1370	D₇₉	1	1	yes	characteristic, complemented
116	#1367	—	79	1	no	—
117	#1367	—	79	1	no	—
118	C₇₉	#12017	1	1	yes	characteristic, complemented, Sylow
119	C₂×M₃₂	—	158	1	no	—
120	#431	—	79	1	no	—
121	C₄×M₁₆	—	79	1	no	—
122	C₂×C₄×C₈	—	79	1	no	—
123	C₄⋊C₁₆	—	79	1	no	—
124	C₄⋊C₁₆	—	79	1	no	—
125	C₄⋊C₁₆	—	158	1	no	—
126	C₄⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic
127	C₄⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic
128	C₂²⋊C₁₆	—	158	1	no	—
129	#346	—	158	1	no	—
130	#322	—	79	1	no	—
131	#322	—	79	1	no	—
132	C₈²	—	79	1	no	—
133	C₈²	C₂×D₇₉	1	1	yes	characteristic
134	C₂×M₁₆	—	79	1	no	—
135	C₂×M₁₆	—	79	1	no	—
136	C₂²×C₈	—	79	1	no	—
137	C₂²×C₈	—	79	1	no	—
138	C₂×C₄²	—	79	1	no	—
139	M₃₂	—	316	2	no	—
140	C₂×C₁₆	—	2	1	no	—
141	C₂×C₁₆	—	2	1	no	—
142	C₂×C₁₆	—	158	1	no	—
143	C₂×C₁₆	—	158	1	no	—
144	C₄⋊C₈	—	158	1	no	—
145	C₂²⋊C₈	—	158	1	no	—
146	#97	—	79	1	no	—
147	#97	—	79	1	no	—
148	C₄×C₈	—	79	1	no	—
149	C₄×C₈	—	79	1	no	—
150	C₄×C₈	—	79	1	no	—
151	C₄×C₈	—	79	1	no	—
152	C₄×C₈	—	79	1	no	—
153	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
154	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
155	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
156	C₂²×C₄	—	79	1	no	—
157	C₂²×C₄	—	79	1	no	—
158	C₂²×C₄	—	79	1	no	—
159	M₁₆	—	158	2	no	—
160	M₁₆	—	158	2	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	316	1	no	—
163	C₂×C₈	—	79	1	no	—
164	C₂×C₈	—	79	1	no	—
165	C₂×C₈	—	79	1	no	—
166	C₂×C₈	—	79	1	no	—
167	C₂×C₈	—	158	1	no	—
168	C₂×C₈	—	158	1	no	—
169	C₂×C₈	—	158	1	no	—
170	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
171	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
172	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
173	C₂×C₈	Q₈×D₇₉	1	1	yes	characteristic
174	C₄²	—	79	1	no	—
175	C₄²	—	79	1	no	—
176	C₄²	—	79	1	no	—
177	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
178	C₁₆	—	4	1	no	—
179	C₁₆	—	4	1	no	—
180	C₁₆	—	316	1	no	—
181	C₁₆	—	316	1	no	—
182	C₂³	—	79	1	no	—
183	C₂×C₄	—	316	1	no	—
184	C₂×C₄	—	79	1	no	—
185	C₂×C₄	—	79	1	no	—
186	C₂×C₄	—	79	1	no	—
187	C₂×C₄	—	158	1	no	—
188	C₂×C₄	—	158	1	no	—
189	C₂×C₄	—	158	1	no	—
190	C₂×C₄	—	158	1	no	—
191	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
192	C₂×C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
193	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
194	C₈	—	2	1	no	—
195	C₈	—	2	1	no	—
196	C₈	—	4	1	no	—
197	C₈	—	316	1	no	—
198	C₈	—	79	2	no	—
199	C₈	—	158	1	no	—
200	C₈	—	158	1	no	—
201	C₈	—	158	1	no	—
202	C₈	#14579100	1	2	yes	complemented
203	C₈	#14579185	1	1	yes	characteristic
204	C₈	#14579193	1	1	yes	characteristic
205	C₂²	—	158	1	no	—
206	C₂²	—	158	1	no	—
207	C₂²	—	158	1	no	—
208	C₂²	C₄⋊C₈×D₇₉	1	1	yes	characteristic
209	C₄	—	2	1	no	—
210	C₄	—	158	1	no	—
211	C₄	—	158	1	no	—
212	C₄	—	158	1	no	—
213	C₄	#19098604	1	1	yes	characteristic
214	C₄	#19098610	1	1	yes	characteristic
215	C₄	M₃₂×D₇₉	1	1	yes	characteristic
216	C₄	C₂×#14579100	1	1	yes	characteristic
217	C₂	—	316	1	no	—
218	C₂	#23762151	1	1	yes	characteristic
219	C₂	#23765154	1	1	yes	characteristic
220	C₂	#23765164	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23765202

C₂

yes

maximal, characteristic

#23765154

C₂

yes

maximal, characteristic

C₈×#11929607

C₂

yes

maximal, characteristic

#23761469

C₂

yes

maximal, characteristic, complemented

#23761464

C₂

yes

maximal, characteristic, complemented

#23761463

C₂

yes

maximal, characteristic, complemented

C₇₉×#1370

C₂

yes

maximal, characteristic, complemented

C₂×#14579100

—

#19098614

C₄

yes

characteristic

C₄×#11929607

C₄

yes

characteristic

C₄×C₈×D₇₉

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₁₆)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₁₆)

C₂²

yes

characteristic

Dic₇₉⋊C₁₆

—

(C₂×D₇₉)⋊C₁₆

—

#19098338

—

#19098285

C₄

yes

characteristic

#19098284

C₄

yes

characteristic

C₈×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₉

C₂²

yes

characteristic

C₈²×C₇₉

C₂²

yes

characteristic

C₂×#11929607

C₈

yes

characteristic

C₂×#11929607

C₈

yes

characteristic

C₂×C₈×D₇₉

D₄

yes

characteristic

C₂×C₈×D₇₉

Q₈

yes

characteristic

C₄²×D₇₉

C₂×C₄

yes

characteristic

#14579100

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

—

Dic₇₉⋊C₈

—

(C₂×D₇₉)⋊C₈

—

#14579071

C₈

yes

characteristic

#14579071

C₈

yes

characteristic

C₄×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₈×Dic₇₉

D₄

yes

characteristic

C₈×Dic₇₉

Q₈

yes

characteristic

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄×D₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×D₇₉

C₂×C₈

yes

characteristic

C₂×C₄×D₇₉

M₁₆

yes

characteristic

#11929607

—

#11929607

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₂×C₈

yes

characteristic

C₂×C₇₉⋊C₈

C₂×C₈

yes

characteristic

C₈×D₇₉

—

C₈×D₇₉

—

C₈×D₇₉

—

C₄×Dic₇₉

C₄⋊C₄

yes

characteristic

C₄×Dic₇₉

C₂×C₈

yes

characteristic

C₄×Dic₇₉

M₁₆

yes

characteristic

C₇₉⋊C₁₆

—

C₇₉⋊C₁₆

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₈

yes

characteristic

C₂×C₈×C₇₉

C₂×C₈

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×Q₈

yes

characteristic

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

—

C₂²×D₇₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₂×Dic₇₉

C₄⋊C₈

yes

characteristic

C₂×Dic₇₉

C₄⋊C₈

yes

characteristic

C₂×Dic₇₉

C₄⋊C₈

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

M₃₂

yes

C₈×C₇₉

yes

C₈×C₇₉

yes

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

M₃₂

yes

complemented

C₂²×C₇₉

C₂×C₄⋊C₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#428

yes

characteristic

100

C₄×C₇₉

#430

yes

characteristic

101

C₄×C₇₉

C₂×M₃₂

yes

characteristic

102

C₄×C₇₉

C₂×M₃₂

yes

characteristic

103

Dic₇₉

—

104

Dic₇₉

—

105

Dic₇₉

—

106

#12017

—

maximal, Sylow

107

C₂×C₇₉

#1565

yes

characteristic

108

C₂×C₇₉

#2150

yes

characteristic

109

C₂×C₇₉

#2153

yes

characteristic

110

D₇₉

—

111

#2163

—

112

#2150

—

113

C₈×M₁₆

—

114

#1370

—

115

#1370

D₇₉

yes

characteristic, complemented

116

#1367

—

117

#1367

—

118

C₇₉

#12017

yes

characteristic, complemented, Sylow

119

C₂×M₃₂

—

158

—

120

#431

—

121

C₄×M₁₆

—

122

C₂×C₄×C₈

—

123

C₄⋊C₁₆

—

124

C₄⋊C₁₆

—

125

C₄⋊C₁₆

—

158

—

126

C₄⋊C₁₆

C₂×D₇₉

yes

characteristic

127

C₄⋊C₁₆

C₂×D₇₉

yes

characteristic

128

C₂²⋊C₁₆

—

158

—

129

#346

—

158

—

130

#322

—

131

#322

—

132

C₈²

—

133

C₈²

C₂×D₇₉

yes

characteristic

134

C₂×M₁₆

—

135

C₂×M₁₆

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂×C₄²

—

139

M₃₂

—

316

—

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

C₂×C₁₆

—

158

—

143

C₂×C₁₆

—

158

—

144

C₄⋊C₈

—

158

—

145

C₂²⋊C₈

—

158

—

146

#97

—

147

#97

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₄×C₈

—

153

C₄×C₈

C₄×D₇₉

yes

characteristic

154

C₄×C₈

C₄×D₇₉

yes

characteristic

155

C₄×C₈

C₂²×D₇₉

yes

characteristic

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

M₁₆

—

158

—

160

M₁₆

—

158

—

161

C₂×C₈

—

162

C₂×C₈

—

316

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

158

—

168

C₂×C₈

—

158

—

169

C₂×C₈

—

158

—

170

C₂×C₈

C₈×D₇₉

yes

characteristic

171

C₂×C₈

C₈×D₇₉

yes

characteristic

172

C₂×C₈

D₄×D₇₉

yes

characteristic

173

C₂×C₈

Q₈×D₇₉

yes

characteristic

174

C₄²

—

175

C₄²

—

176

C₄²

—

177

C₄²

C₂×C₄×D₇₉

yes

characteristic

178

C₁₆

—

179

C₁₆

—

180

C₁₆

—

316

—

181

C₁₆

—

316

—

182

C₂³

—

183

C₂×C₄

—

316

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

158

—

188

C₂×C₄

—

158

—

189

C₂×C₄

—

158

—

190

C₂×C₄

—

158

—

191

C₂×C₄

C₄⋊C₄×D₇₉

yes

characteristic

192

C₂×C₄

C₂×C₈×D₇₉

yes

characteristic

193

C₂×C₄

M₁₆×D₇₉

yes

characteristic

194

C₈

—

195

C₈

—

196

C₈

—

197

C₈

—

316

—

198

C₈

—

199

C₈

—

158

—

200

C₈

—

158

—

201

C₈

—

158

—

202

C₈

#14579100

yes

complemented

203

C₈

#14579185

yes

characteristic

204

C₈

#14579193

yes

characteristic

205

C₂²

—

158

—

206

C₂²

—

158

—

207

C₂²

—

158

—

208

C₂²

C₄⋊C₈×D₇₉

yes

characteristic

209

C₄

—

210

C₄

—

158

—

211

C₄

—

158

—

212

C₄

—

158

—

213

C₄

#19098604

yes

characteristic

214

C₄

#19098610

yes

characteristic

215

C₄

M₃₂×D₇₉

yes

characteristic

216

C₄

C₂×#14579100

yes

characteristic

217

C₂

—

316

—

218

C₂

#23762151

yes

characteristic

219

C₂

#23765154

yes

characteristic

220

C₂

#23765164

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₉
Fitting	C₇₉×#1370	C₂
socle	C₂²×C₇₉	C₂×C₄⋊C₈
prime radical	C₂²×D₇₉	C₄⋊C₈
cosocle	C₄×C₈×C₇₉	C₂³
hypercenter	#1370	D₇₉
hypocenter	C₇₉	#12017
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

subgroup

G/H

center

C₂×C₈

D₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₇₉

Fitting

C₇₉×#1370

C₂

socle

C₂²×C₇₉

C₂×C₄⋊C₈

prime radical

C₂²×D₇₉

C₄⋊C₈

cosocle

C₄×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

N	H ≅ G/N	type
4. #23761469	C₂	semidirect
5. #23761464	C₂	semidirect
6. #23761463	C₂	semidirect
7. C₇₉×#1370	C₂	semidirect
86. C₈×C₇₉	M₃₂	semidirect
93. C₇₉⋊C₈	M₃₂	semidirect
115. #1370	D₇₉	semidirect
118. C₇₉	#12017	semidirect
202. C₈	#14579100	semidirect

H ≅ G/N

type

4. #23761469

C₂

semidirect

5. #23761464

C₂

semidirect

6. #23761463

C₂

semidirect

7. C₇₉×#1370

C₂

semidirect

86. C₈×C₇₉

M₃₂

semidirect

93. C₇₉⋊C₈

M₃₂

semidirect

115. #1370

D₇₉

semidirect

118. C₇₉

#12017

semidirect

202. C₈

#14579100

semidirect

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

subgroup	index
#23765202	2
#23765154	2
C₈×#11929607	2
#23761469	2
#23761464	2
#23761463	2
C₇₉×#1370	2
#12017	79

subgroup

index

C₇₉×#1370

Subgroups — #34199891

Conjugacy classes of subgroups

Complements

Maximal subgroups