Group #34193004 — subgroups

Subgroups — #34193004

Order 20224.

402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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	#23764194	C₂	1	1	yes	maximal, characteristic
2	#23763397	C₂	1	2	yes	maximal
3	#23761283	C₂	1	2	yes	maximal, complemented
4	#23761235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×#14579081	—	2	2	no	—
10	C₂×(C₂×D₇₉)⋊C₈	—	2	2	no	—
11	#19098325	—	2	2	no	—
12	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	#384×C₇₉	C₂²	1	2	yes	—
14	#340×C₇₉	—	2	2	no	—
15	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
16	C₂²×C₄×D₇₉	—	2	1	no	—
17	C₂²×C₇₉⋊C₈	—	2	1	no	—
18	C₂²×C₇₉⋊C₈	—	2	2	no	—
19	C₄×D₃₁₆	—	2	2	no	—
20	C₄×D₃₁₆	—	2	2	no	—
21	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
22	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
23	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
24	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	#14579081	—	4	4	no	—
27	(C₂×D₇₉)⋊C₈	—	4	4	no	—
28	C₂²×C₈×C₇₉	D₄	1	2	yes	—
29	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
32	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
33	C₄×C₈×C₇₉	—	2	2	no	—
34	C₂³×D₇₉	—	2	1	no	—
35	C₂×D₃₁₆	—	2	2	no	—
36	C₂×D₃₁₆	—	2	1	no	—
37	C₂×D₃₁₆	—	2	2	no	—
38	C₂×D₃₁₆	D₈	1	2	yes	—
39	C₂²×Dic₇₉	—	2	1	no	—
40	C₂×C₄×D₇₉	—	4	1	no	—
41	C₂×C₄×D₇₉	—	4	1	no	—
42	C₂×C₄×D₇₉	—	4	2	no	—
43	C₂×C₄×D₇₉	—	4	2	no	—
44	C₂×C₇₉⋊C₈	—	4	2	no	—
45	C₂×C₇₉⋊C₈	—	4	1	no	—
46	C₂×C₇₉⋊C₈	—	4	2	no	—
47	C₂×C₇₉⋊C₈	—	4	2	no	—
48	C₂×C₇₉⋊C₈	—	4	2	no	—
49	C₄⋊Dic₇₉	—	2	2	no	—
50	(C₂×D₇₉)⋊C₄	—	4	2	no	—
51	C₂²×C₄×C₇₉	—	4	2	no	—
52	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
55	C₂×C₈×C₇₉	—	2	2	no	—
56	C₂×C₈×C₇₉	—	2	2	no	—
57	C₂×C₈×C₇₉	—	2	2	no	—
58	C₄⋊C₄×C₇₉	—	4	2	no	—
59	C₄⋊C₄×C₇₉	—	4	2	no	—
60	C₄⋊C₄×C₇₉	—	4	2	no	—
61	C₄⋊C₄×C₇₉	—	4	2	no	—
62	C₄⋊C₄×C₇₉	—	8	2	no	—
63	C₄²×C₇₉	#41	1	2	yes	—
64	C₄²×C₇₉	#41	1	2	yes	—
65	C₂³×C₇₉	#121	1	1	yes	characteristic
66	C₂²×D₇₉	—	2	2	no	—
67	C₂²×D₇₉	—	4	1	no	—
68	C₂²×D₇₉	—	4	2	no	—
69	C₂²×D₇₉	—	4	1	no	—
70	C₂²×D₇₉	—	4	2	no	—
71	C₂×C₄×C₇₉	—	2	2	no	—
72	C₂×C₄×C₇₉	—	8	2	no	—
73	C₂×C₄×C₇₉	—	8	2	no	—
74	C₂×C₄×C₇₉	—	8	2	no	—
75	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
76	C₂×C₄×C₇₉	#123	1	2	yes	—
77	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
78	C₂×C₄×C₇₉	#126	1	2	yes	—
79	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
81	C₂×C₄×C₇₉	#135	1	2	yes	—
82	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
83	C₂×C₄×C₇₉	#137	1	2	yes	—
84	C₂×Dic₇₉	—	4	1	no	—
85	C₂×Dic₇₉	—	4	2	no	—
86	D₃₁₆	—	2	4	no	—
87	D₃₁₆	—	4	2	no	—
88	C₄×D₇₉	—	8	2	no	—
89	C₄×D₇₉	—	8	1	no	—
90	C₄×D₇₉	—	8	1	no	—
91	C₈×C₇₉	—	4	2	no	—
92	C₇₉⋊C₈	—	8	2	no	—
93	C₇₉⋊C₈	—	8	1	no	—
94	C₂²×C₇₉	#397	1	1	yes	characteristic
95	C₂²×C₇₉	#463	1	2	yes	—
96	C₂²×C₇₉	#466	1	1	yes	characteristic
97	C₂²×C₇₉	#470	1	1	yes	characteristic
98	C₂²×C₇₉	#471	1	2	yes	—
99	C₂×D₇₉	—	4	2	no	—
100	C₂×D₇₉	—	4	4	no	—
101	C₂×D₇₉	—	8	1	no	—
102	C₂×D₇₉	—	8	1	no	—
103	C₂×D₇₉	—	8	2	no	—
104	C₄×C₇₉	—	2	2	no	—
105	C₄×C₇₉	—	16	2	no	—
106	C₄×C₇₉	#480	1	2	yes	—
107	C₄×C₇₉	#482	1	2	yes	—
108	C₄×C₇₉	#485	1	2	yes	—
109	C₄×C₇₉	#488	1	1	yes	characteristic
110	C₄×C₇₉	#490	1	1	yes	characteristic
111	Dic₇₉	—	8	1	no	—
112	#10621	—	79	1	no	maximal, Sylow
113	C₂×C₇₉	#1681	1	2	yes	—
114	C₂×C₇₉	#1703	1	2	yes	—
115	C₂×C₇₉	#2073	1	1	yes	characteristic
116	C₂×C₇₉	#2075	1	1	yes	characteristic
117	C₂×C₇₉	#2079	1	1	yes	characteristic
118	D₇₉	—	8	2	no	—
119	#1954	—	79	1	no	—
120	#1834	D₇₉	1	1	yes	characteristic, complemented
121	#1802	—	79	2	no	—
122	#1296	—	79	2	no	—
123	#1277	—	79	1	no	—
124	C₇₉	#10621	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄×D₄	—	79	1	no	—
126	C₂×C₄⋊C₈	—	79	2	no	—
127	C₂×C₄⋊C₈	—	79	1	no	—
128	C₂×#102	—	158	2	no	—
129	C₂×C₂²⋊C₈	—	158	2	no	—
130	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
131	#384	C₂×D₇₉	1	2	yes	—
132	#340	—	2	2	no	—
133	#340	—	158	2	no	—
134	C₂²×D₄	—	79	1	no	—
135	C₂³×C₄	—	158	1	no	—
136	C₂²×C₈	—	158	2	no	—
137	C₂²×C₈	—	158	1	no	—
138	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
139	C₄×D₄	—	158	2	no	—
140	C₄×D₄	—	158	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	79	1	no	—
145	C₂×C₂²⋊C₄	—	158	1	no	—
146	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
147	C₄⋊C₈	—	158	2	no	—
148	C₄⋊C₈	—	158	2	no	—
149	C₄⋊C₈	—	158	2	no	—
150	#102	—	316	4	no	—
151	C₂²⋊C₈	—	316	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	158	1	no	—
154	C₂×D₄	—	79	2	no	—
155	C₂×D₄	—	158	2	no	—
156	C₂×D₄	—	158	1	no	—
157	C₂×D₄	—	158	2	no	—
158	C₂²×C₄	—	4	2	no	—
159	C₂²×C₄	—	316	1	no	—
160	C₂²×C₄	—	316	1	no	—
161	C₂²×C₄	—	316	2	no	—
162	C₂²×C₄	—	316	2	no	—
163	C₂²×C₄	—	158	1	no	—
164	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
165	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
166	C₂²×C₄	#11929623	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	316	2	no	—
171	C₂×C₈	—	316	1	no	—
172	C₂×C₈	—	316	2	no	—
173	C₂×C₈	—	316	2	no	—
174	C₂×C₈	—	316	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	8	2	no	—
180	C₄⋊C₄	—	158	2	no	—
181	C₂²⋊C₄	—	316	2	no	—
182	C₄²	#11929624	1	2	yes	—
183	C₄²	#11929625	1	2	yes	—
184	C₂³	—	316	1	no	—
185	C₂³	—	316	2	no	—
186	C₂³	—	316	1	no	—
187	C₂³	—	316	2	no	—
188	C₂³	—	158	2	no	—
189	C₂³	#14579132	1	1	yes	characteristic
190	D₄	—	316	2	no	—
191	D₄	—	158	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	8	2	no	—
194	C₂×C₄	—	8	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	316	1	no	—
197	C₂×C₄	—	316	2	no	—
198	C₂×C₄	—	632	2	no	—
199	C₂×C₄	—	632	1	no	—
200	C₂×C₄	—	632	1	no	—
201	C₂×C₄	#14579144	1	1	yes	characteristic
202	C₂×C₄	#14579146	1	2	yes	—
203	C₂×C₄	#14579150	1	1	yes	characteristic
204	C₂×C₄	#14579156	1	2	yes	—
205	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
206	C₂×C₄	#14579180	1	1	yes	characteristic
207	C₂×C₄	#14579181	1	2	yes	—
208	C₂×C₄	#14579186	1	2	yes	—
209	C₂×C₄	#14579193	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	632	1	no	—
212	C₈	—	632	2	no	—
213	C₂²	—	316	2	no	—
214	C₂²	—	316	4	no	—
215	C₂²	—	632	2	no	—
216	C₂²	—	632	1	no	—
217	C₂²	—	632	1	no	—
218	C₂²	#19098489	1	1	yes	characteristic
219	C₂²	#19098775	1	2	yes	—
220	C₂²	#19098796	1	1	yes	characteristic
221	C₂²	#19098818	1	1	yes	characteristic
222	C₂²	#19098823	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	16	2	no	—
225	C₄	—	632	1	no	—
226	C₄	#19098878	1	2	yes	—
227	C₄	#19098887	1	2	yes	—
228	C₄	#19098906	1	2	yes	—
229	C₄	#19098920	1	1	yes	characteristic
230	C₄	#19098929	1	1	yes	characteristic
231	C₂	—	632	2	no	—
232	C₂	#23762834	1	2	yes	—
233	C₂	#23762972	1	2	yes	—
234	C₂	#23764814	1	1	yes	characteristic
235	C₂	#23764824	1	1	yes	characteristic
236	C₂	#23764846	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764194

C₂

yes

maximal, characteristic

#23763397

C₂

yes

maximal

#23761283

C₂

yes

maximal, complemented

#23761235

C₂

yes

maximal, characteristic, complemented

C₇₉×#1834

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₃₁₆

C₂²

yes

characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×#14579081

—

C₂×(C₂×D₇₉)⋊C₈

—

#19098325

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#384×C₇₉

C₂²

yes

—

#340×C₇₉

—

C₂²×D₃₁₆

D₄

yes

characteristic

C₂²×C₄×D₇₉

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄×D₃₁₆

—

C₄×D₃₁₆

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×(C₂×D₇₉)⋊C₄

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579081

—

(C₂×D₇₉)⋊C₈

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄×C₈×C₇₉

—

C₂³×D₇₉

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

D₈

yes

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

#41

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

#121

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#123

yes

characteristic

C₂×C₄×C₇₉

#123

yes

—

C₂×C₄×C₇₉

#124

yes

characteristic

C₂×C₄×C₇₉

#126

yes

—

C₂×C₄×C₇₉

C₂×D₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

#397

yes

characteristic

C₂²×C₇₉

#463

yes

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

—

C₂×D₇₉

—

100

C₂×D₇₉

—

101

C₂×D₇₉

—

102

C₂×D₇₉

—

103

C₂×D₇₉

—

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

#480

yes

—

107

C₄×C₇₉

#482

yes

—

108

C₄×C₇₉

#485

yes

—

109

C₄×C₇₉

#488

yes

characteristic

110

C₄×C₇₉

#490

yes

characteristic

111

Dic₇₉

—

112

#10621

—

maximal, Sylow

113

C₂×C₇₉

#1681

yes

—

114

C₂×C₇₉

#1703

yes

—

115

C₂×C₇₉

#2073

yes

characteristic

116

C₂×C₇₉

#2075

yes

characteristic

117

C₂×C₇₉

#2079

yes

characteristic

118

D₇₉

—

119

#1954

—

120

#1834

D₇₉

yes

characteristic, complemented

121

#1802

—

122

#1296

—

123

#1277

—

124

C₇₉

#10621

yes

characteristic, complemented, Sylow

125

C₂×C₄×D₄

—

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

—

128

C₂×#102

—

158

—

129

C₂×C₂²⋊C₈

—

158

—

130

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

131

#384

C₂×D₇₉

yes

—

132

#340

—

133

#340

—

158

—

134

C₂²×D₄

—

135

C₂³×C₄

—

158

—

136

C₂²×C₈

—

158

—

137

C₂²×C₈

—

158

—

138

C₂²×C₈

C₂²⋊D₇₉

yes

—

139

C₄×D₄

—

158

—

140

C₄×D₄

—

158

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₂²⋊C₄

—

158

—

146

C₂×C₄²

C₂²×D₇₉

yes

characteristic

147

C₄⋊C₈

—

158

—

148

C₄⋊C₈

—

158

—

149

C₄⋊C₈

—

158

—

150

#102

—

316

—

151

C₂²⋊C₈

—

316

—

152

C₄×C₈

—

153

C₂⁴

—

158

—

154

C₂×D₄

—

155

C₂×D₄

—

158

—

156

C₂×D₄

—

158

—

157

C₂×D₄

—

158

—

158

C₂²×C₄

—

159

C₂²×C₄

—

316

—

160

C₂²×C₄

—

316

—

161

C₂²×C₄

—

316

—

162

C₂²×C₄

—

316

—

163

C₂²×C₄

—

158

—

164

C₂²×C₄

D₄×D₇₉

yes

characteristic

165

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

166

C₂²×C₄

#11929623

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

316

—

171

C₂×C₈

—

316

—

172

C₂×C₈

—

316

—

173

C₂×C₈

—

316

—

174

C₂×C₈

—

316

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

158

—

181

C₂²⋊C₄

—

316

—

182

C₄²

#11929624

yes

—

183

C₄²

#11929625

yes

—

184

C₂³

—

316

—

185

C₂³

—

316

—

186

C₂³

—

316

—

187

C₂³

—

316

—

188

C₂³

—

158

—

189

C₂³

#14579132

yes

characteristic

190

D₄

—

316

—

191

D₄

—

158

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

316

—

197

C₂×C₄

—

316

—

198

C₂×C₄

—

632

—

199

C₂×C₄

—

632

—

200

C₂×C₄

—

632

—

201

C₂×C₄

#14579144

yes

characteristic

202

C₂×C₄

#14579146

yes

—

203

C₂×C₄

#14579150

yes

characteristic

204

C₂×C₄

#14579156

yes

—

205

C₂×C₄

D₈×D₇₉

yes

characteristic

206

C₂×C₄

#14579180

yes

characteristic

207

C₂×C₄

#14579181

yes

—

208

C₂×C₄

#14579186

yes

—

209

C₂×C₄

#14579193

yes

—

210

C₈

—

211

C₈

—

632

—

212

C₈

—

632

—

213

C₂²

—

316

—

214

C₂²

—

316

—

215

C₂²

—

632

—

216

C₂²

—

632

—

217

C₂²

—

632

—

218

C₂²

#19098489

yes

characteristic

219

C₂²

#19098775

yes

—

220

C₂²

#19098796

yes

characteristic

221

C₂²

#19098818

yes

characteristic

222

C₂²

#19098823

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

632

—

226

C₄

#19098878

yes

—

227

C₄

#19098887

yes

—

228

C₄

#19098906

yes

—

229

C₄

#19098920

yes

characteristic

230

C₄

#19098929

yes

characteristic

231

C₂

—

632

—

232

C₂

#23762834

yes

—

233

C₂

#23762972

yes

—

234

C₂

#23764814

yes

characteristic

235

C₂

#23764824

yes

characteristic

236

C₂

#23764846

yes

characteristic

	subgroup	G/H
center	C₂³	#14579132
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1834	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂²×D₃₁₆	D₄
hypercenter	#1834	D₇₉
hypocenter	C₇₉	#10621
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#14579132

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1834

C₂

socle

C₂³×C₇₉

#121

prime radical

C₂²×D₃₁₆

D₄

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
3. #23761283	C₂	semidirect
4. #23761235	C₂	semidirect
5. C₇₉×#1834	C₂	semidirect
120. #1834	D₇₉	semidirect
124. C₇₉	#10621	semidirect

H ≅ G/N

type

3. #23761283

C₂

semidirect

4. #23761235

C₂

semidirect

5. C₇₉×#1834

C₂

semidirect

120. #1834

D₇₉

semidirect

124. C₇₉

#10621

semidirect

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

subgroup	index
#23764194	2
#23763397	2
#23761283	2
#23761235	2
C₇₉×#1834	2
#10621	79

subgroup

index

C₇₉×#1834

Subgroups — #34193004

Conjugacy classes of subgroups

Complements

Maximal subgroups