Group #34188180 — subgroups

Subgroups — #34188180

Order 20224.

454 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 135 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	#23764378	C₂	1	2	yes	maximal
2	C₄×#14579071	C₂	1	1	yes	maximal, characteristic
3	#23762156	C₂	1	1	yes	maximal, characteristic
4	#23761855	C₂	1	2	yes	maximal
5	C₇₉×#3170	C₂	1	1	yes	maximal, characteristic
6	#19098587	C₂²	1	2	yes	—
7	C₂×#14579071	—	2	2	no	—
8	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
10	#19098322	—	2	4	no	—
11	#19098314	—	2	2	no	—
12	Q₈⋊(C₇₉⋊C₈)	—	2	4	no	—
13	#533×C₇₉	C₂²	1	2	yes	—
14	#500×C₇₉	C₄	1	1	yes	characteristic, complemented
15	#494×C₇₉	C₄	1	1	yes	characteristic, complemented
16	#487×C₇₉	C₄	1	2	yes	complemented
17	#467×C₇₉	—	2	2	no	—
18	C₄×Q₁₆×C₇₉	—	2	2	no	—
19	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#11929608	—	2	2	no	—
21	C₂²×C₇₉⋊C₈	—	2	1	no	—
22	C₂×C₄×Dic₇₉	—	2	1	no	—
23	C₂×C₄×Dic₇₉	—	2	1	no	—
24	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
25	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
27	#14579071	—	2	8	no	—
28	C₄×C₇₉⋊C₈	—	2	1	no	—
29	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
30	C₂×Q₁₆×C₇₉	—	2	2	no	—
31	C₂²×C₈×C₇₉	D₄	1	2	yes	—
32	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
33	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
34	#125×C₇₉	—	2	2	no	—
35	C₂²⋊Q₈×C₇₉	—	2	2	no	—
36	C₂²⋊Q₈×C₇₉	—	2	2	no	—
37	C₄×Q₈×C₇₉	—	2	2	no	—
38	C₄×Q₈×C₇₉	—	2	2	no	—
39	#117×C₇₉	—	2	2	no	—
40	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
41	#107×C₇₉	—	2	2	no	—
42	#103×C₇₉	—	2	4	no	—
43	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₇₉	D₄	1	2	yes	—
46	C₂²×Dic₇₉	—	2	2	no	—
47	#11929608	—	4	4	no	—
48	C₂×C₇₉⋊C₈	—	2	4	no	—
49	C₂×C₇₉⋊C₈	—	2	2	no	—
50	C₂×C₇₉⋊C₈	—	4	2	no	—
51	C₄×Dic₇₉	—	2	4	no	—
52	C₄×Dic₇₉	—	2	4	no	—
53	C₄×Dic₇₉	—	4	2	no	—
54	C₂×Q₈×C₇₉	—	2	2	no	—
55	C₂×Q₈×C₇₉	—	2	2	no	—
56	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
59	Q₁₆×C₇₉	—	4	4	no	—
60	C₂×C₈×C₇₉	—	2	4	no	—
61	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
63	C₄⋊C₄×C₇₉	—	2	2	no	—
64	C₄⋊C₄×C₇₉	—	2	2	no	—
65	C₄⋊C₄×C₇₉	—	2	2	no	—
66	C₄⋊C₄×C₇₉	—	2	2	no	—
67	C₄⋊C₄×C₇₉	—	4	2	no	—
68	C₄⋊C₄×C₇₉	—	4	2	no	—
69	C₂²⋊C₄×C₇₉	—	4	2	no	—
70	C₄²×C₇₉	—	4	2	no	—
71	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₉	#41	1	1	yes	characteristic
75	C₂³×C₇₉	#121	1	1	yes	characteristic
76	Q₈×C₇₉	—	4	4	no	—
77	Q₈×C₇₉	—	4	4	no	—
78	C₂×C₄×C₇₉	—	2	2	no	—
79	C₂×C₄×C₇₉	—	2	2	no	—
80	C₂×C₄×C₇₉	—	4	2	no	—
81	C₂×C₄×C₇₉	—	4	2	no	—
82	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
88	C₂×C₄×C₇₉	#137	1	4	yes	—
89	C₂×Dic₇₉	—	2	4	no	—
90	C₂×Dic₇₉	—	4	2	no	—
91	C₂×Dic₇₉	—	4	2	no	—
92	C₈×C₇₉	—	2	2	no	—
93	C₈×C₇₉	#104	1	4	yes	—
94	C₇₉⋊C₈	—	2	4	no	—
95	C₇₉⋊C₈	—	8	2	no	—
96	C₂²×C₇₉	—	2	1	no	—
97	C₂²×C₇₉	—	2	1	no	—
98	C₂²×C₇₉	#390	1	1	yes	characteristic
99	C₂²×C₇₉	#470	1	2	yes	—
100	C₄×C₇₉	—	2	1	no	—
101	C₄×C₇₉	—	2	1	no	—
102	C₄×C₇₉	—	8	2	no	—
103	C₄×C₇₉	—	8	2	no	—
104	C₄×C₇₉	C₂×#104	1	2	yes	—
105	C₄×C₇₉	#441	1	2	yes	—
106	C₄×C₇₉	#444	1	2	yes	—
107	C₄×C₇₉	#497	1	2	yes	—
108	Dic₇₉	—	4	4	no	—
109	#9850	—	79	1	no	maximal, Sylow
110	C₂×C₇₉	—	2	2	no	—
111	C₂×C₇₉	#1962	1	1	yes	characteristic
112	C₂×C₇₉	#1971	1	1	yes	characteristic
113	C₂×C₇₉	#1975	1	1	yes	characteristic
114	#3170	D₇₉	1	1	yes	characteristic
115	#1994	—	79	2	no	—
116	C₄×#97	—	79	1	no	—
117	#1566	—	79	1	no	—
118	#1493	—	79	2	no	—
119	C₇₉	#9850	1	1	yes	characteristic, complemented, Sylow
120	#533	C₂×D₇₉	1	2	yes	—
121	#500	Dic₇₉	1	1	yes	characteristic, complemented
122	#494	Dic₇₉	1	1	yes	characteristic, complemented
123	#487	Dic₇₉	1	2	yes	complemented
124	#467	—	2	2	no	—
125	C₄×Q₁₆	—	2	2	no	—
126	#423	—	79	2	no	—
127	C₂×#97	—	158	2	no	—
128	C₂×C₄×C₈	—	79	1	no	—
129	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
130	C₄³	—	79	1	no	—
131	#339	—	158	4	no	—
132	#334	—	158	2	no	—
133	Q₈⋊C₈	—	158	4	no	—
134	C₂×Q₁₆	—	2	2	no	—
135	C₂×M₁₆	—	158	2	no	—
136	C₂²×C₈	—	158	1	no	—
137	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
138	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
139	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
140	#125	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₂²⋊Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	#117	—	2	2	no	—
146	C₂×C₄²	—	79	2	no	—
147	C₂×C₄²	—	158	1	no	—
148	C₂×C₄²	—	158	1	no	—
149	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
150	#107	—	2	2	no	—
151	C₄⋊C₈	—	158	2	no	—
152	C₄⋊C₈	—	158	2	no	—
153	#103	—	2	4	no	—
154	#97	—	158	8	no	—
155	C₄×C₈	—	79	2	no	—
156	C₄×C₈	—	158	1	no	—
157	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
158	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂²×C₄	—	158	2	no	—
163	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
165	C₂²×C₄	#11929623	1	1	yes	characteristic
166	Q₁₆	—	4	4	no	—
167	M₁₆	—	316	4	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	316	2	no	—
170	C₂×C₈	—	158	4	no	—
171	C₂×C₈	—	158	2	no	—
172	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
173	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₂²⋊C₄	—	4	2	no	—
181	C₄²	—	4	2	no	—
182	C₄²	—	316	2	no	—
183	C₄²	—	158	4	no	—
184	C₄²	—	158	4	no	—
185	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
186	C₄²	D₄×D₇₉	1	1	yes	characteristic
187	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
188	C₄²	#11929623	1	1	yes	characteristic
189	C₂³	#14579132	1	1	yes	characteristic
190	Q₈	—	4	4	no	—
191	Q₈	—	4	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	316	2	no	—
197	C₂×C₄	—	316	2	no	—
198	C₂×C₄	—	158	4	no	—
199	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
200	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
201	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
202	C₂×C₄	#14579132	1	1	yes	characteristic
203	C₂×C₄	#14579148	1	1	yes	characteristic
204	C₂×C₄	#14579157	1	1	yes	characteristic
205	C₂×C₄	#14579193	1	4	yes	—
206	C₈	—	2	2	no	—
207	C₈	—	632	2	no	—
208	C₈	—	158	4	no	—
209	C₈	#14579088	1	4	yes	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	#19098466	1	1	yes	characteristic
213	C₂²	#19098818	1	2	yes	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	8	2	no	—
217	C₄	—	8	2	no	—
218	C₄	—	316	4	no	—
219	C₄	C₂×#14579088	1	2	yes	—
220	C₄	#19098670	1	2	yes	—
221	C₄	#19098685	1	2	yes	—
222	C₄	#19098956	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	#23764229	1	1	yes	characteristic
225	C₂	#23764272	1	1	yes	characteristic
226	C₂	#23764294	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764378

C₂

yes

maximal

C₄×#14579071

C₂

yes

maximal, characteristic

#23762156

C₂

yes

maximal, characteristic

#23761855

C₂

yes

maximal

C₇₉×#3170

C₂

yes

maximal, characteristic

#19098587

C₂²

yes

—

C₂×#14579071

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₇₉

C₂²

yes

characteristic

#19098322

—

#19098314

—

Q₈⋊(C₇₉⋊C₈)

—

#533×C₇₉

C₂²

yes

—

#500×C₇₉

C₄

yes

characteristic, complemented

#494×C₇₉

C₄

yes

characteristic, complemented

#487×C₇₉

C₄

yes

complemented

#467×C₇₉

—

C₄×Q₁₆×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

D₄

yes

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579071

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂×Q₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

#125×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

#117×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#107×C₇₉

—

#103×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

—

C₂²×Dic₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

#104

yes

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#390

yes

characteristic

C₂²×C₇₉

#470

yes

—

100

C₄×C₇₉

—

101

C₄×C₇₉

—

102

C₄×C₇₉

—

103

C₄×C₇₉

—

104

C₄×C₇₉

C₂×#104

yes

—

105

C₄×C₇₉

#441

yes

—

106

C₄×C₇₉

#444

yes

—

107

C₄×C₇₉

#497

yes

—

108

Dic₇₉

—

109

#9850

—

maximal, Sylow

110

C₂×C₇₉

—

111

C₂×C₇₉

#1962

yes

characteristic

112

C₂×C₇₉

#1971

yes

characteristic

113

C₂×C₇₉

#1975

yes

characteristic

114

#3170

D₇₉

yes

characteristic

115

#1994

—

116

C₄×#97

—

117

#1566

—

118

#1493

—

119

C₇₉

#9850

yes

characteristic, complemented, Sylow

120

#533

C₂×D₇₉

yes

—

121

#500

Dic₇₉

yes

characteristic, complemented

122

#494

Dic₇₉

yes

characteristic, complemented

123

#487

Dic₇₉

yes

complemented

124

#467

—

125

C₄×Q₁₆

—

126

#423

—

127

C₂×#97

—

158

—

128

C₂×C₄×C₈

—

129

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

130

C₄³

—

131

#339

—

158

—

132

#334

—

158

—

133

Q₈⋊C₈

—

158

—

134

C₂×Q₁₆

—

135

C₂×M₁₆

—

158

—

136

C₂²×C₈

—

158

—

137

C₂²×C₈

C₂²⋊D₇₉

yes

—

138

C₄⋊Q₈

C₂×Dic₇₉

yes

—

139

C₄⋊Q₈

C₂×Dic₇₉

yes

—

140

#125

—

141

C₂²⋊Q₈

—

142

C₂²⋊Q₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

#117

—

146

C₂×C₄²

—

147

C₂×C₄²

—

158

—

148

C₂×C₄²

—

158

—

149

C₂×C₄²

C₂²×D₇₉

yes

characteristic

150

#107

—

151

C₄⋊C₈

—

158

—

152

C₄⋊C₈

—

158

—

153

#103

—

154

#97

—

158

—

155

C₄×C₈

—

156

C₄×C₈

—

158

—

157

C₄×C₈

C₂×Dic₇₉

yes

characteristic

158

C₄×C₈

C₂×Dic₇₉

yes

characteristic

159

C₄×C₈

C₂²⋊D₇₉

yes

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂²×C₄

—

158

—

163

C₂²×C₄

D₄×D₇₉

yes

characteristic

164

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

165

C₂²×C₄

#11929623

yes

characteristic

166

Q₁₆

—

167

M₁₆

—

316

—

168

C₂×C₈

—

169

C₂×C₈

—

316

—

170

C₂×C₈

—

158

—

171

C₂×C₈

—

158

—

172

C₂×C₈

C₂²⋊Dic₇₉

yes

—

173

C₂×C₈

C₂²⋊Dic₇₉

yes

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₂²⋊C₄

—

181

C₄²

—

182

C₄²

—

316

—

183

C₄²

—

158

—

184

C₄²

—

158

—

185

C₄²

C₂²×Dic₇₉

yes

characteristic

186

C₄²

D₄×D₇₉

yes

characteristic

187

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

188

C₄²

#11929623

yes

characteristic

189

C₂³

#14579132

yes

characteristic

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

316

—

197

C₂×C₄

—

316

—

198

C₂×C₄

—

158

—

199

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

200

C₂×C₄

D₄×Dic₇₉

yes

characteristic

201

C₂×C₄

D₄×Dic₇₉

yes

characteristic

202

C₂×C₄

#14579132

yes

characteristic

203

C₂×C₄

#14579148

yes

characteristic

204

C₂×C₄

#14579157

yes

characteristic

205

C₂×C₄

#14579193

yes

—

206

C₈

—

207

C₈

—

632

—

208

C₈

—

158

—

209

C₈

#14579088

yes

—

210

C₂²

—

211

C₂²

—

212

C₂²

#19098466

yes

characteristic

213

C₂²

#19098818

yes

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

316

—

219

C₄

C₂×#14579088

yes

—

220

C₄

#19098670

yes

—

221

C₄

#19098685

yes

—

222

C₄

#19098956

yes

—

223

C₂

—

224

C₂

#23764229

yes

characteristic

225

C₂

#23764272

yes

characteristic

226

C₂

#23764294

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3170	C₂
socle	C₂²×C₇₉	#390
prime radical	C₂³×C₇₉	#121
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3170	D₇₉
hypocenter	C₇₉	#9850
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#14579157

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3170

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. #500×C₇₉	C₄	semidirect
15. #494×C₇₉	C₄	semidirect
16. #487×C₇₉	C₄	semidirect
119. C₇₉	#9850	semidirect
121. #500	Dic₇₉	semidirect
122. #494	Dic₇₉	semidirect
123. #487	Dic₇₉	semidirect

H ≅ G/N

type

14. #500×C₇₉

C₄

semidirect

15. #494×C₇₉

C₄

semidirect

16. #487×C₇₉

C₄

semidirect

119. C₇₉

#9850

semidirect

121. #500

Dic₇₉

semidirect

122. #494

Dic₇₉

semidirect

123. #487

Dic₇₉

semidirect

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

subgroup	index
#23764378	2
C₄×#14579071	2
#23762156	2
#23761855	2
C₇₉×#3170	2
#9850	79

subgroup

index

C₇₉×#3170

Subgroups — #34188180

Conjugacy classes of subgroups

Complements

Maximal subgroups