Group #34190770 — subgroups

Subgroups — #34190770

Order 20224.

474 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 103 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	#23774745	C₂	1	1	yes	maximal, characteristic
2	#23773205	C₂	1	2	yes	maximal
3	#23761856	C₂	1	2	yes	maximal
4	#23761275	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#1984	C₂	1	1	yes	maximal, characteristic
6	#19099120	C₂²	1	2	yes	—
7	#19098870	—	2	4	no	—
8	#19098859	—	2	2	no	—
9	#19098858	—	2	2	no	—
10	#19098848	—	2	2	no	—
11	#19098804	—	2	2	no	—
12	#19098774	—	2	2	no	—
13	#19098603	—	2	2	no	—
14	#19098587	C₂²	1	2	yes	—
15	#19098572	—	2	2	no	—
16	#19098295	—	2	4	no	—
17	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	#336×C₇₉	—	2	2	no	—
21	C₂×Dic₃₁₆	—	2	2	no	—
22	C₂×#11929608	—	2	2	no	—
23	#14579161	D₄	1	2	yes	—
24	#14579161	D₄	1	2	yes	—
25	#14579153	—	2	2	no	—
26	#14579140	—	2	2	no	—
27	#14579140	—	2	2	no	—
28	C₄×Dic₁₅₈	—	2	2	no	—
29	C₄×Dic₁₅₈	—	2	2	no	—
30	#14579120	—	2	2	no	—
31	#14579095	—	2	2	no	—
32	#14579094	—	2	4	no	—
33	#14579092	—	2	4	no	—
34	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
35	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
36	#14579086	—	2	4	no	—
37	#14579085	—	2	4	no	—
38	#14579085	—	2	4	no	—
39	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₉	—	2	1	no	—
41	C₂²×C₈×C₇₉	D₄	1	2	yes	—
42	C₄×Q₈×C₇₉	—	2	2	no	—
43	C₄×Q₈×C₇₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₇₉	—	2	1	no	—
47	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
48	C₄⋊C₈×C₇₉	—	2	2	no	—
49	C₄×C₈×C₇₉	—	2	2	no	—
50	C₂×Dic₁₅₈	—	2	2	no	—
51	C₂×Dic₁₅₈	—	2	2	no	—
52	Dic₃₁₆	—	8	2	no	—
53	#11929608	—	4	2	no	—
54	#11929608	—	4	2	no	—
55	C₂×C₇₉⋊C₈	—	2	4	no	—
56	C₄⋊Dic₇₉	—	2	2	no	—
57	C₄⋊Dic₇₉	—	2	2	no	—
58	C₄⋊Dic₇₉	—	2	2	no	—
59	C₄⋊Dic₇₉	—	2	2	no	—
60	Dic₇₉⋊C₄	—	4	2	no	—
61	Dic₇₉⋊C₄	—	4	2	no	—
62	C₂²⋊Dic₇₉	—	4	2	no	—
63	C₄×Dic₇₉	—	4	2	no	—
64	C₂×Q₈×C₇₉	—	2	1	no	—
65	C₂×Q₈×C₇₉	—	2	2	no	—
66	C₂×Q₈×C₇₉	—	2	2	no	—
67	C₂×Q₈×C₇₉	Q₁₆	1	2	yes	complemented
68	C₂²×C₄×C₇₉	—	2	1	no	—
69	C₂²×C₄×C₇₉	—	2	1	no	—
70	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
73	C₂×C₈×C₇₉	—	2	2	no	—
74	C₂×C₈×C₇₉	—	2	2	no	—
75	C₂×C₈×C₇₉	—	4	2	no	—
76	C₂×C₈×C₇₉	—	4	1	no	—
77	C₂×C₈×C₇₉	—	4	1	no	—
78	C₄⋊C₄×C₇₉	—	2	2	no	—
79	C₄⋊C₄×C₇₉	—	4	2	no	—
80	C₄²×C₇₉	—	4	1	no	—
81	C₄²×C₇₉	—	4	1	no	—
82	C₄²×C₇₉	C₂×D₄	1	2	yes	—
83	C₄²×C₇₉	C₂×D₄	1	2	yes	—
84	C₂³×C₇₉	#121	1	1	yes	characteristic
85	Q₈×C₇₉	—	2	4	no	—
86	Q₈×C₇₉	—	4	2	no	—
87	C₂×C₄×C₇₉	—	2	1	no	—
88	C₂×C₄×C₇₉	—	2	1	no	—
89	C₂×C₄×C₇₉	—	2	2	no	—
90	C₂×C₄×C₇₉	—	4	1	no	—
91	C₂×C₄×C₇₉	—	4	1	no	—
92	C₂×C₄×C₇₉	—	4	1	no	—
93	C₂×C₄×C₇₉	—	4	2	no	—
94	C₂×C₄×C₇₉	—	4	1	no	—
95	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
96	C₂×C₄×C₇₉	#120	1	2	yes	—
97	C₂×C₄×C₇₉	#121	1	2	yes	—
98	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
99	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
100	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
101	C₂×C₄×C₇₉	#137	1	2	yes	—
102	C₂×Dic₇₉	—	4	2	no	—
103	C₂×Dic₇₉	—	4	2	no	—
104	Dic₁₅₈	—	4	4	no	—
105	Dic₁₅₈	—	4	2	no	—
106	Dic₁₅₈	—	4	2	no	—
107	C₈×C₇₉	—	4	2	no	—
108	C₈×C₇₉	—	4	2	no	—
109	C₇₉⋊C₈	—	4	4	no	—
110	C₂²×C₇₉	—	2	1	no	—
111	C₂²×C₇₉	—	2	1	no	—
112	C₂²×C₇₉	#392	1	1	yes	characteristic
113	C₂²×C₇₉	#467	1	1	yes	characteristic
114	C₂²×C₇₉	#470	1	1	yes	characteristic
115	C₄×C₇₉	—	2	1	no	—
116	C₄×C₇₉	—	2	2	no	—
117	C₄×C₇₉	—	4	2	no	—
118	C₄×C₇₉	—	8	1	no	—
119	C₄×C₇₉	#451	1	2	yes	—
120	C₄×C₇₉	#452	1	2	yes	—
121	C₄×C₇₉	#455	1	1	yes	characteristic
122	C₄×C₇₉	#456	1	1	yes	characteristic
123	Dic₇₉	—	8	2	no	—
124	Dic₇₉	—	8	2	no	—
125	#10259	—	79	1	no	maximal, Sylow
126	C₂×C₇₉	—	2	1	no	—
127	C₂×C₇₉	—	2	1	no	—
128	C₂×C₇₉	#2001	1	1	yes	characteristic
129	C₂×C₇₉	#2007	1	1	yes	characteristic
130	C₂×C₇₉	#2017	1	1	yes	characteristic
131	#3249	—	79	1	no	—
132	#3078	—	79	2	no	—
133	#1984	D₇₉	1	1	yes	characteristic
134	#1493	—	79	2	no	—
135	#1292	—	79	1	no	—
136	C₇₉	#10259	1	1	yes	characteristic, complemented, Sylow
137	#533	—	79	2	no	—
138	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
139	#479	—	158	4	no	—
140	#477	—	158	2	no	—
141	#477	—	158	2	no	—
142	#475	—	158	2	no	—
143	#467	—	158	2	no	—
144	#462	—	158	2	no	—
145	#428	—	158	2	no	—
146	#423	—	79	2	no	—
147	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
148	#419	—	158	2	no	—
149	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
150	#336	—	2	2	no	—
151	Q₈⋊C₈	—	158	4	no	—
152	C₂²×Q₈	D₃₁₆	1	1	yes	characteristic
153	C₂×Q₁₆	—	158	2	no	—
154	C₂×M₁₆	—	158	2	no	—
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
157	C₄⋊Q₈	—	79	2	no	—
158	C₄⋊Q₈	—	79	2	no	—
159	#125	—	158	2	no	—
160	C₂²⋊Q₈	—	158	2	no	—
161	C₂²⋊Q₈	—	158	2	no	—
162	C₄×Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	C₄×Q₈	—	158	2	no	—
165	C₄×Q₈	—	158	2	no	—
166	#117	—	158	2	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
169	C₂×C₄²	—	2	1	no	—
170	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
171	#107	—	158	4	no	—
172	#107	—	158	2	no	—
173	#106	—	158	4	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	79	4	no	—
176	C₄⋊C₈	—	158	2	no	—
177	#103	—	158	4	no	—
178	#103	—	158	4	no	—
179	#103	—	158	4	no	—
180	C₄×C₈	—	2	2	no	—
181	C₂×Q₈	—	2	1	no	—
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂×Q₈	—	158	2	no	—
185	C₂×Q₈	—	158	2	no	—
186	C₂×Q₈	Dic₃₁₆	1	2	yes	complemented
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
191	C₂²×C₄	#11929624	1	1	yes	characteristic
192	Q₁₆	—	632	2	no	—
193	M₁₆	—	316	2	no	—
194	M₁₆	—	316	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	4	1	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	—	158	4	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₄⋊C₄	—	316	2	no	—
204	C₄⋊C₄	—	316	2	no	—
205	C₄⋊C₄	—	158	2	no	—
206	C₄⋊C₄	—	158	2	no	—
207	C₄⋊C₄	—	158	2	no	—
208	C₄⋊C₄	—	158	2	no	—
209	C₂²⋊C₄	—	316	2	no	—
210	C₄²	—	4	1	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	316	2	no	—
213	C₄²	D₄×D₇₉	1	2	yes	—
214	C₄²	D₄×D₇₉	1	2	yes	—
215	C₂³	#14579135	1	1	yes	characteristic
216	Q₈	—	2	4	no	—
217	Q₈	—	4	2	no	—
218	Q₈	—	316	4	no	—
219	Q₈	—	316	2	no	—
220	Q₈	—	316	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	316	2	no	—
230	C₂×C₄	—	316	2	no	—
231	C₂×C₄	#14579129	1	1	yes	characteristic
232	C₂×C₄	#14579131	1	2	yes	—
233	C₂×C₄	#14579134	1	2	yes	—
234	C₂×C₄	#14579157	1	1	yes	characteristic
235	C₂×C₄	C₂×Dic₃₁₆	1	1	yes	characteristic
236	C₂×C₄	#14579183	1	1	yes	characteristic
237	C₂×C₄	#14579194	1	2	yes	—
238	C₈	—	4	2	no	—
239	C₈	—	4	2	no	—
240	C₈	—	316	4	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	#19098472	1	1	yes	characteristic
244	C₂²	#19098804	1	1	yes	characteristic
245	C₂²	#19098821	1	1	yes	characteristic
246	C₄	—	2	2	no	—
247	C₄	—	2	1	no	—
248	C₄	—	4	2	no	—
249	C₄	—	8	1	no	—
250	C₄	—	632	2	no	—
251	C₄	—	632	2	no	—
252	C₄	#19098721	1	2	yes	—
253	C₄	#19098727	1	2	yes	—
254	C₄	#19098740	1	1	yes	characteristic
255	C₄	#19098745	1	1	yes	characteristic
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	#23764410	1	1	yes	characteristic
259	C₂	#23764446	1	1	yes	characteristic
260	C₂	#23764504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23774745

C₂

yes

maximal, characteristic

#23773205

C₂

yes

maximal

#23761856

C₂

yes

maximal

#23761275

C₂

yes

maximal, characteristic

C₇₉×#1984

C₂

yes

maximal, characteristic

#19099120

C₂²

yes

—

—

—

—

—

—

—

—

C₂²

yes

—

#19098572

—

#19098295

—

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#336×C₇₉

—

C₂×Dic₃₁₆

—

C₂×#11929608

—

#14579161

D₄

yes

—

#14579161

D₄

yes

—

#14579153

—

#14579140

—

#14579140

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

—

—

—

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579086

—

#14579085

—

#14579085

—

C₂²×Q₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

Dic₃₁₆

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

Q₁₆

yes

complemented

C₂²×C₄×C₇₉

—

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

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#121

yes

characteristic

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

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#127

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₁₆

yes

characteristic

100

C₂×C₄×C₇₉

#135

yes

characteristic

101

C₂×C₄×C₇₉

#137

yes

—

102

C₂×Dic₇₉

—

103

C₂×Dic₇₉

—

104

Dic₁₅₈

—

105

Dic₁₅₈

—

106

Dic₁₅₈

—

107

C₈×C₇₉

—

108

C₈×C₇₉

—

109

C₇₉⋊C₈

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

#392

yes

characteristic

113

C₂²×C₇₉

#467

yes

characteristic

114

C₂²×C₇₉

#470

yes

characteristic

115

C₄×C₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

#451

yes

—

120

C₄×C₇₉

#452

yes

—

121

C₄×C₇₉

#455

yes

characteristic

122

C₄×C₇₉

#456

yes

characteristic

123

Dic₇₉

—

124

Dic₇₉

—

125

#10259

—

maximal, Sylow

126

C₂×C₇₉

—

127

C₂×C₇₉

—

128

C₂×C₇₉

#2001

yes

characteristic

129

C₂×C₇₉

#2007

yes

characteristic

130

C₂×C₇₉

#2017

yes

characteristic

131

#3249

—

132

#3078

—

133

#1984

D₇₉

yes

characteristic

134

#1493

—

135

#1292

—

136

C₇₉

#10259

yes

characteristic, complemented, Sylow

137

#533

—

138

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

139

#479

—

158

—

140

#477

—

158

—

141

#477

—

158

—

142

#475

—

158

—

143

#467

—

158

—

144

#462

—

158

—

145

#428

—

158

—

146

#423

—

147

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

148

#419

—

158

—

149

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

150

#336

—

151

Q₈⋊C₈

—

158

—

152

C₂²×Q₈

D₃₁₆

yes

characteristic

153

C₂×Q₁₆

—

158

—

154

C₂×M₁₆

—

158

—

155

C₂²×C₈

—

156

C₂²×C₈

C₂²⋊D₇₉

yes

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

159

#125

—

158

—

160

C₂²⋊Q₈

—

158

—

161

C₂²⋊Q₈

—

158

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

—

158

—

165

C₄×Q₈

—

158

—

166

#117

—

158

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

D₃₁₆

yes

characteristic

169

C₂×C₄²

—

170

C₂×C₄²

C₂²×D₇₉

yes

characteristic

171

#107

—

158

—

172

#107

—

158

—

173

#106

—

158

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

158

—

177

#103

—

158

—

178

#103

—

158

—

179

#103

—

158

—

180

C₄×C₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

158

—

185

C₂×Q₈

—

158

—

186

C₂×Q₈

Dic₃₁₆

yes

complemented

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

190

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

191

C₂²×C₄

#11929624

yes

characteristic

192

Q₁₆

—

632

—

193

M₁₆

—

316

—

194

M₁₆

—

316

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

158

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

316

—

204

C₄⋊C₄

—

316

—

205

C₄⋊C₄

—

158

—

206

C₄⋊C₄

—

158

—

207

C₄⋊C₄

—

158

—

208

C₄⋊C₄

—

158

—

209

C₂²⋊C₄

—

316

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

316

—

213

C₄²

D₄×D₇₉

yes

—

214

C₄²

D₄×D₇₉

yes

—

215

C₂³

#14579135

yes

characteristic

216

Q₈

—

217

Q₈

—

218

Q₈

—

316

—

219

Q₈

—

316

—

220

Q₈

—

316

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

316

—

230

C₂×C₄

—

316

—

231

C₂×C₄

#14579129

yes

characteristic

232

C₂×C₄

#14579131

yes

—

233

C₂×C₄

#14579134

yes

—

234

C₂×C₄

#14579157

yes

characteristic

235

C₂×C₄

C₂×Dic₃₁₆

yes

characteristic

236

C₂×C₄

#14579183

yes

characteristic

237

C₂×C₄

#14579194

yes

—

238

C₈

—

239

C₈

—

240

C₈

—

316

—

241

C₂²

—

242

C₂²

—

243

C₂²

#19098472

yes

characteristic

244

C₂²

#19098804

yes

characteristic

245

C₂²

#19098821

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

632

—

251

C₄

—

632

—

252

C₄

#19098721

yes

—

253

C₄

#19098727

yes

—

254

C₄

#19098740

yes

characteristic

255

C₄

#19098745

yes

characteristic

256

C₂

—

257

C₂

—

258

C₂

#23764410

yes

characteristic

259

C₂

#23764446

yes

characteristic

260

C₂

#23764504

yes

characteristic

	subgroup	G/H
center	C₂²	#19098472
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1984	C₂
socle	C₂²×C₇₉	#392
prime radical	C₂³×C₇₉	#121
hypercenter	#1984	D₇₉
hypocenter	C₇₉	#10259
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂²

#19098472

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1984

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
67. C₂×Q₈×C₇₉	Q₁₆	semidirect
136. C₇₉	#10259	semidirect
186. C₂×Q₈	Dic₃₁₆	semidirect

H ≅ G/N

type

67. C₂×Q₈×C₇₉

Q₁₆

semidirect

136. C₇₉

#10259

semidirect

186. C₂×Q₈

Dic₃₁₆

semidirect

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

subgroup	index
#23774745	2
#23773205	2
#23761856	2
#23761275	2
C₇₉×#1984	2
#10259	79

subgroup

index

C₇₉×#1984

Subgroups — #34190770

Conjugacy classes of subgroups

Complements

Maximal subgroups