Group #34193298 — subgroups

Subgroups — #34193298

Order 20224.

296 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 91 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	#23763520	C₂	1	1	yes	maximal, characteristic
2	#23762176	C₂	1	1	yes	maximal, characteristic
3	#23762172	C₂	1	1	yes	maximal, characteristic
4	#23761803	C₂	1	1	yes	maximal, characteristic
5	#23761803	C₂	1	1	yes	maximal, characteristic
6	#23761229	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1995	C₂	1	1	yes	maximal, characteristic
8	#19098616	C₂²	1	1	yes	characteristic
9	#19098616	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
12	#19098318	—	2	2	no	—
13	#19098315	—	2	2	no	—
14	#19098313	—	2	2	no	—
15	Q₈⋊(C₇₉⋊C₈)	—	2	2	no	—
16	Q₈⋊(C₇₉⋊C₈)	—	2	2	no	—
17	#533×C₇₉	C₂²	1	1	yes	characteristic
18	#423×C₇₉	C₂²	1	1	yes	characteristic
19	#376×C₇₉	C₂²	1	1	yes	characteristic
20	#339×C₇₉	—	2	2	no	—
21	C₂²×C₇₉⋊C₈	—	2	1	no	—
22	C₂²×C₇₉⋊C₈	—	2	1	no	—
23	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
24	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
25	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
27	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
28	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
29	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
30	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
31	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
32	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
33	C₂×M₁₆×C₇₉	—	2	1	no	—
34	C₄⋊Q₈×C₇₉	Q₈	1	1	yes	characteristic
35	C₄⋊Q₈×C₇₉	Q₈	1	1	yes	characteristic
36	#125×C₇₉	—	2	1	no	—
37	C₂²⋊Q₈×C₇₉	—	2	1	no	—
38	C₂²⋊Q₈×C₇₉	—	2	1	no	—
39	C₄×Q₈×C₇₉	—	2	1	no	—
40	C₄×Q₈×C₇₉	—	2	1	no	—
41	#117×C₇₉	—	2	1	no	—
42	C₂×C₄²×C₇₉	D₄	1	2	yes	—
43	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₇₉	—	2	1	no	—
45	C₄⋊C₈×C₇₉	—	2	1	no	—
46	#95×C₇₉	—	2	1	no	—
47	#95×C₇₉	—	2	1	no	—
48	C₂×C₇₉⋊C₈	—	2	2	no	—
49	C₂×C₇₉⋊C₈	—	2	2	no	—
50	C₂×C₇₉⋊C₈	—	4	1	no	—
51	C₂×C₇₉⋊C₈	—	4	1	no	—
52	C₂×C₇₉⋊C₈	—	4	2	no	—
53	C₂×C₇₉⋊C₈	—	4	2	no	—
54	C₂×Q₈×C₇₉	—	2	1	no	—
55	C₂×Q₈×C₇₉	—	2	1	no	—
56	C₂²×C₄×C₇₉	—	2	2	no	—
57	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
59	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
60	M₁₆×C₇₉	—	4	2	no	—
61	C₂×C₈×C₇₉	—	4	1	no	—
62	C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₄⋊C₄×C₇₉	—	2	1	no	—
66	C₄⋊C₄×C₇₉	—	4	1	no	—
67	C₄⋊C₄×C₇₉	—	4	1	no	—
68	C₂²⋊C₄×C₇₉	—	4	1	no	—
69	C₄²×C₇₉	—	2	2	no	—
70	C₄²×C₇₉	—	2	2	no	—
71	C₄²×C₇₉	—	4	1	no	—
72	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
75	C₄²×C₇₉	#41	1	1	yes	characteristic
76	C₂³×C₇₉	#123	1	1	yes	characteristic
77	Q₈×C₇₉	—	4	2	no	—
78	Q₈×C₇₉	—	4	2	no	—
79	C₂×C₄×C₇₉	—	4	1	no	—
80	C₂×C₄×C₇₉	—	4	1	no	—
81	C₂×C₄×C₇₉	—	4	2	no	—
82	C₂×C₄×C₇₉	—	4	2	no	—
83	C₂×C₄×C₇₉	—	4	1	no	—
84	C₂×C₄×C₇₉	—	4	1	no	—
85	C₂×C₄×C₇₉	—	4	2	no	—
86	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
90	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
91	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
92	C₂×C₄×C₇₉	#135	1	2	yes	—
93	C₂×C₄×C₇₉	#137	1	2	yes	—
94	C₈×C₇₉	—	8	1	no	—
95	C₇₉⋊C₈	—	4	2	no	—
96	C₇₉⋊C₈	—	4	2	no	—
97	C₇₉⋊C₈	—	8	1	no	—
98	C₇₉⋊C₈	—	8	1	no	—
99	C₂²×C₇₉	—	2	1	no	—
100	C₂²×C₇₉	—	2	1	no	—
101	C₂²×C₇₉	#399	1	1	yes	characteristic
102	C₂²×C₇₉	#485	1	2	yes	—
103	C₄×C₇₉	—	2	1	no	—
104	C₄×C₇₉	—	2	1	no	—
105	C₄×C₇₉	—	2	1	no	—
106	C₄×C₇₉	—	2	1	no	—
107	C₄×C₇₉	—	8	2	no	—
108	C₄×C₇₉	—	8	1	no	—
109	C₄×C₇₉	—	8	1	no	—
110	C₄×C₇₉	#479	1	2	yes	—
111	C₄×C₇₉	#495	1	1	yes	characteristic
112	C₄×C₇₉	#497	1	1	yes	characteristic
113	#10669	—	79	1	no	maximal, Sylow
114	C₂×C₇₉	—	2	2	no	—
115	C₂×C₇₉	#2097	1	1	yes	characteristic
116	C₂×C₇₉	#2098	1	1	yes	characteristic
117	C₂×C₇₉	#2098	1	1	yes	characteristic
118	#1995	D₇₉	1	1	yes	characteristic
119	#1832	—	79	1	no	—
120	#1571	—	79	1	no	—
121	#1570	—	79	1	no	—
122	#1481	—	79	1	no	—
123	#1481	—	79	1	no	—
124	#1274	—	79	1	no	—
125	C₇₉	#10669	1	1	yes	characteristic, complemented, Sylow
126	#533	C₂×D₇₉	1	1	yes	characteristic
127	#431	—	79	1	no	—
128	#431	—	79	1	no	—
129	#423	C₂×D₇₉	1	1	yes	characteristic
130	C₂×C₄⋊C₈	—	79	1	no	—
131	C₂×C₄⋊C₈	—	79	1	no	—
132	#376	C₂×D₇₉	1	1	yes	characteristic
133	#339	—	2	2	no	—
134	#336	—	158	2	no	—
135	#335	—	158	2	no	—
136	#334	—	158	2	no	—
137	Q₈⋊C₈	—	158	2	no	—
138	Q₈⋊C₈	—	158	2	no	—
139	C₂×M₁₆	—	2	1	no	—
140	C₂²×C₈	—	158	1	no	—
141	C₂²×C₈	—	158	1	no	—
142	C₄⋊Q₈	Dic₁₅₈	1	1	yes	characteristic
143	C₄⋊Q₈	Dic₁₅₈	1	1	yes	characteristic
144	#125	—	2	1	no	—
145	C₂²⋊Q₈	—	2	1	no	—
146	C₂²⋊Q₈	—	2	1	no	—
147	C₄×Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	#117	—	2	1	no	—
150	C₂×C₄²	C₂²⋊D₇₉	1	2	yes	—
151	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
152	C₄⋊C₈	—	2	1	no	—
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	158	1	no	—
155	C₄⋊C₈	—	158	1	no	—
156	C₄⋊C₈	—	158	1	no	—
157	C₄⋊C₈	—	158	1	no	—
158	C₄⋊C₈	—	158	1	no	—
159	C₄⋊C₈	—	158	1	no	—
160	C₂²⋊C₈	—	158	1	no	—
161	C₂²⋊C₈	—	158	1	no	—
162	C₄×C₈	—	79	2	no	—
163	C₄×C₈	—	79	2	no	—
164	#95	—	2	1	no	—
165	#95	—	2	1	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	—	2	1	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
170	C₂²×C₄	#11929623	1	1	yes	characteristic
171	C₂²×C₄	#11929623	1	1	yes	characteristic
172	M₁₆	—	4	2	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	—	316	1	no	—
175	C₂×C₈	—	316	1	no	—
176	C₂×C₈	—	316	2	no	—
177	C₂×C₈	—	316	2	no	—
178	C₂×C₈	—	158	2	no	—
179	C₂×C₈	—	158	2	no	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	4	1	no	—
185	C₄⋊C₄	—	4	1	no	—
186	C₂²⋊C₄	—	4	1	no	—
187	C₄²	—	2	2	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	4	1	no	—
190	C₄²	D₄×D₇₉	1	1	yes	characteristic
191	C₄²	D₄×D₇₉	1	1	yes	characteristic
192	C₄²	C₂×Dic₁₅₈	1	1	yes	characteristic
193	C₄²	#11929624	1	1	yes	characteristic
194	C₂³	#14579142	1	1	yes	characteristic
195	Q₈	—	4	2	no	—
196	Q₈	—	4	2	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	#14579138	1	1	yes	characteristic
205	C₂×C₄	#14579138	1	1	yes	characteristic
206	C₂×C₄	#14579140	1	1	yes	characteristic
207	C₂×C₄	#14579143	1	1	yes	characteristic
208	C₂×C₄	#14579143	1	1	yes	characteristic
209	C₂×C₄	#14579157	1	1	yes	characteristic
210	C₂×C₄	#14579181	1	2	yes	—
211	C₂×C₄	#14579192	1	2	yes	—
212	C₈	—	8	1	no	—
213	C₈	—	316	2	no	—
214	C₈	—	316	2	no	—
215	C₈	—	632	1	no	—
216	C₈	—	632	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#19098499	1	1	yes	characteristic
220	C₂²	#19098901	1	2	yes	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	8	2	no	—
226	C₄	—	8	1	no	—
227	C₄	—	8	1	no	—
228	C₄	#19098870	1	2	yes	—
229	C₄	#19098945	1	1	yes	characteristic
230	C₄	#19098955	1	1	yes	characteristic
231	C₂	—	2	2	no	—
232	C₂	#23764948	1	1	yes	characteristic
233	C₂	#23764955	1	1	yes	characteristic
234	C₂	#23764955	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23763520

C₂

yes

maximal, characteristic

#23762176

C₂

yes

maximal, characteristic

#23762172

C₂

yes

maximal, characteristic

#23761803

C₂

yes

maximal, characteristic

#23761803

C₂

yes

maximal, characteristic

#23761229

C₂

yes

maximal, characteristic

C₇₉×#1995

C₂

yes

maximal, characteristic

#19098616

C₂²

yes

characteristic

#19098616

C₂²

yes

characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

—

—

Q₈⋊(C₇₉⋊C₈)

—

Q₈⋊(C₇₉⋊C₈)

—

#533×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

#376×C₇₉

C₂²

yes

characteristic

#339×C₇₉

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂×M₁₆×C₇₉

—

C₄⋊Q₈×C₇₉

Q₈

yes

characteristic

C₄⋊Q₈×C₇₉

Q₈

yes

characteristic

#125×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

#117×C₇₉

—

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

#95×C₇₉

—

#95×C₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

C₂²×C₄×C₇₉

yes

C₂²×C₄×C₇₉

yes

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

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

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×Q₈

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×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

#399

yes

characteristic

102

C₂²×C₇₉

#485

yes

—

103

C₄×C₇₉

—

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

#479

yes

—

111

C₄×C₇₉

#495

yes

characteristic

112

C₄×C₇₉

yes

113

—

114

C₂×C₇₉

—

115

C₂×C₇₉

#2097

yes

characteristic

116

C₂×C₇₉

#2098

yes

characteristic

117

C₂×C₇₉

#2098

yes

characteristic

118

#1995

D₇₉

yes

characteristic

119

#1832

—

120

#1571

—

121

#1570

—

122

#1481

—

123

#1481

—

124

#1274

—

125

C₇₉

#10669

yes

characteristic, complemented, Sylow

126

#533

C₂×D₇₉

yes

characteristic

127

#431

—

128

#431

—

129

#423

C₂×D₇₉

yes

characteristic

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

—

132

#376

C₂×D₇₉

yes

characteristic

133

#339

—

134

#336

—

158

—

135

#335

—

158

—

136

#334

—

158

—

137

Q₈⋊C₈

—

158

—

138

Q₈⋊C₈

—

158

—

139

C₂×M₁₆

—

140

C₂²×C₈

—

158

—

141

C₂²×C₈

—

158

—

142

C₄⋊Q₈

Dic₁₅₈

yes

characteristic

143

C₄⋊Q₈

Dic₁₅₈

yes

characteristic

144

#125

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

#117

—

150

C₂×C₄²

C₂²⋊D₇₉

yes

—

151

C₂×C₄²

C₂²×D₇₉

yes

characteristic

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

158

—

155

C₄⋊C₈

—

158

—

156

C₄⋊C₈

—

158

—

157

C₄⋊C₈

—

158

—

158

C₄⋊C₈

—

158

—

159

C₄⋊C₈

—

158

—

160

C₂²⋊C₈

—

158

—

161

C₂²⋊C₈

—

158

—

162

C₄×C₈

—

163

C₄×C₈

—

164

#95

—

165

#95

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

170

C₂²×C₄

#11929623

yes

characteristic

171

C₂²×C₄

#11929623

yes

characteristic

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

316

—

175

C₂×C₈

—

316

—

176

C₂×C₈

—

316

—

177

C₂×C₈

—

316

—

178

C₂×C₈

—

158

—

179

C₂×C₈

—

158

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₂²⋊C₄

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

D₄×D₇₉

yes

characteristic

191

C₄²

D₄×D₇₉

yes

characteristic

192

C₄²

C₂×Dic₁₅₈

yes

characteristic

193

C₄²

#11929624

yes

characteristic

194

C₂³

#14579142

yes

characteristic

195

Q₈

—

196

Q₈

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

#14579138

yes

characteristic

205

C₂×C₄

#14579138

yes

characteristic

206

C₂×C₄

#14579140

yes

characteristic

207

C₂×C₄

#14579143

yes

characteristic

208

C₂×C₄

#14579143

yes

characteristic

209

C₂×C₄

#14579157

yes

characteristic

210

C₂×C₄

#14579181

yes

—

211

C₂×C₄

#14579192

yes

—

212

C₈

—

213

C₈

—

316

—

214

C₈

—

316

—

215

C₈

—

632

—

216

C₈

—

632

—

217

C₂²

—

218

C₂²

—

219

C₂²

#19098499

yes

characteristic

220

C₂²

#19098901

yes

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

#19098870

yes

—

229

C₄

#19098945

yes

characteristic

230

C₄

#19098955

yes

characteristic

231

C₂

—

232

C₂

#23764948

yes

characteristic

233

C₂

#23764955

yes

characteristic

234

C₂

#23764955

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1995	C₂
socle	C₂²×C₇₉	#399
prime radical	C₂³×C₇₉	#123
hypercenter	#1995	D₇₉
hypocenter	C₇₉	#10669
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

subgroup

G/H

center

C₂×C₄

#14579157

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1995

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

N	H ≅ G/N	type
125. C₇₉	#10669	semidirect

H ≅ G/N

type

125. C₇₉

#10669

semidirect

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

subgroup	index
#23763520	2
#23762176	2
#23762172	2
#23761803	2
#23761229	2
C₇₉×#1995	2
#10669	79

subgroup

index

C₇₉×#1995

Subgroups — #34193298

Conjugacy classes of subgroups

Complements

Maximal subgroups