Group #34190892 — subgroups

Subgroups — #34190892

Order 20224.

510 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂×#19098855	C₂	1	2	yes	maximal
2	#23764336	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098312	C₂	1	2	yes	maximal
4	#23761235	C₂	1	1	yes	maximal, characteristic
5	C₂×#500×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
7	#19098855	—	2	4	no	—
8	#19098855	—	2	4	no	—
9	C₂×#14579094	—	2	2	no	—
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#14579084	—	2	2	no	—
13	#19098317	—	2	2	no	—
14	#19098312	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
16	#500×C₇₉	—	2	4	no	—
17	C₂×#107×C₇₉	—	2	2	no	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₅₈	D₄	1	1	yes	characteristic
20	C₂²×C₇₉⋊C₈	—	2	2	no	—
21	C₂²×C₇₉⋊C₈	—	2	1	no	—
22	C₄×Dic₁₅₈	—	2	2	no	—
23	C₄×Dic₁₅₈	—	2	2	no	—
24	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
25	C₂×Dic₇₉⋊C₄	—	2	1	no	—
26	C₂×C₄×Dic₇₉	—	2	1	no	—
27	#14579094	—	2	8	no	—
28	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
31	#14579084	—	2	8	no	—
32	C₂²×Q₈×C₇₉	—	2	2	no	—
33	C₂²×C₈×C₇₉	D₄	1	2	yes	—
34	C₄⋊Q₈×C₇₉	—	2	2	no	—
35	C₄⋊Q₈×C₇₉	—	2	2	no	—
36	C₄⋊Q₈×C₇₉	—	2	2	no	—
37	C₄⋊Q₈×C₇₉	D₄	1	4	yes	—
38	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
40	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
41	#107×C₇₉	—	2	8	no	—
42	C₄×C₈×C₇₉	—	2	2	no	—
43	C₂×Dic₁₅₈	—	2	2	no	—
44	C₂×Dic₁₅₈	—	2	1	no	—
45	C₂×Dic₁₅₈	—	2	2	no	—
46	C₂×Dic₁₅₈	Q₁₆	1	2	yes	—
47	C₂²×Dic₇₉	—	2	1	no	—
48	C₂²×Dic₇₉	—	2	1	no	—
49	C₂×C₇₉⋊C₈	—	2	4	no	—
50	C₂×C₇₉⋊C₈	—	4	1	no	—
51	C₂×C₇₉⋊C₈	—	4	2	no	—
52	C₂×C₇₉⋊C₈	—	4	2	no	—
53	C₂×C₇₉⋊C₈	—	4	2	no	—
54	C₄⋊Dic₇₉	—	2	2	no	—
55	Dic₇₉⋊C₄	—	4	2	no	—
56	C₄×Dic₇₉	—	4	1	no	—
57	C₄×Dic₇₉	—	4	1	no	—
58	C₂×Q₈×C₇₉	—	2	4	no	—
59	C₂×Q₈×C₇₉	—	4	2	no	—
60	C₂×Q₈×C₇₉	—	8	4	no	—
61	C₂²×C₄×C₇₉	—	4	2	no	—
62	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
65	C₂×C₈×C₇₉	—	2	2	no	—
66	C₂×C₈×C₇₉	—	2	2	no	—
67	C₂×C₈×C₇₉	Q₁₆	1	4	yes	—
68	C₄⋊C₄×C₇₉	—	2	4	no	—
69	C₄⋊C₄×C₇₉	—	2	4	no	—
70	C₄⋊C₄×C₇₉	—	4	2	no	—
71	C₄⋊C₄×C₇₉	—	4	2	no	—
72	C₄²×C₇₉	C₂×D₄	1	2	yes	—
73	C₄²×C₇₉	C₂×D₄	1	2	yes	—
74	C₂³×C₇₉	#121	1	1	yes	characteristic
75	Q₈×C₇₉	—	8	4	no	—
76	Q₈×C₇₉	—	8	4	no	—
77	C₂×C₄×C₇₉	—	2	2	no	—
78	C₂×C₄×C₇₉	—	4	4	no	—
79	C₂×C₄×C₇₉	—	8	4	no	—
80	C₂×C₄×C₇₉	#120	1	2	yes	—
81	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
82	C₂×C₄×C₇₉	#121	1	2	yes	—
83	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
85	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
87	C₂×C₄×C₇₉	#137	1	2	yes	—
88	C₂×C₄×C₇₉	#137	1	2	yes	—
89	C₂×Dic₇₉	—	2	2	no	—
90	C₂×Dic₇₉	—	4	1	no	—
91	C₂×Dic₇₉	—	4	1	no	—
92	C₂×Dic₇₉	—	4	1	no	—
93	C₂×Dic₇₉	—	4	2	no	—
94	Dic₁₅₈	—	2	4	no	—
95	Dic₁₅₈	—	4	2	no	—
96	C₈×C₇₉	—	2	4	no	—
97	C₇₉⋊C₈	—	4	4	no	—
98	C₇₉⋊C₈	—	8	1	no	—
99	C₂²×C₇₉	#392	1	1	yes	characteristic
100	C₂²×C₇₉	#462	1	2	yes	—
101	C₂²×C₇₉	#467	1	1	yes	characteristic
102	C₂²×C₇₉	#470	1	1	yes	characteristic
103	C₂²×C₇₉	#472	1	2	yes	—
104	C₄×C₇₉	—	2	2	no	—
105	C₄×C₇₉	—	8	4	no	—
106	C₄×C₇₉	#451	1	2	yes	—
107	C₄×C₇₉	#451	1	2	yes	—
108	C₄×C₇₉	#452	1	2	yes	—
109	C₄×C₇₉	#494	1	1	yes	characteristic
110	C₄×C₇₉	#497	1	1	yes	characteristic
111	Dic₇₉	—	4	2	no	—
112	Dic₇₉	—	8	1	no	—
113	#10279	—	79	1	no	maximal, Sylow
114	C₂×C₇₉	#1676	1	2	yes	—
115	C₂×C₇₉	#1696	1	2	yes	—
116	C₂×C₇₉	#2001	1	1	yes	characteristic
117	C₂×C₇₉	#2016	1	1	yes	characteristic
118	C₂×C₇₉	#2018	1	1	yes	characteristic
119	C₂×#500	D₇₉	1	1	yes	characteristic
120	C₂×#477	—	79	2	no	—
121	#1984	—	79	1	no	—
122	C₂×#333	—	79	2	no	—
123	#1277	—	79	1	no	—
124	C₇₉	#10279	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
126	C₂×C₄×Q₈	—	79	1	no	—
127	#500	—	2	4	no	—
128	#477	—	158	4	no	—
129	#477	—	158	4	no	—
130	C₂×#107	—	2	2	no	—
131	C₂×#107	—	158	2	no	—
132	C₂×C₄⋊C₈	—	79	2	no	—
133	C₂×C₄⋊C₈	—	79	1	no	—
134	C₂×#103	—	158	2	no	—
135	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
136	#336	—	158	2	no	—
137	#333	—	158	4	no	—
138	C₂²×Q₈	—	2	2	no	—
139	C₂²×Q₈	—	79	1	no	—
140	C₂²×C₈	—	158	1	no	—
141	C₂²×C₈	—	158	2	no	—
142	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	C₂²⋊D₇₉	1	4	yes	—
147	C₄×Q₈	—	158	2	no	—
148	C₄×Q₈	—	158	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	79	1	no	—
152	C₂×C₄⋊C₄	—	158	1	no	—
153	C₂×C₄²	—	158	1	no	—
154	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
155	#107	—	2	8	no	—
156	#107	—	158	8	no	—
157	C₄⋊C₈	—	79	4	no	—
158	C₄⋊C₈	—	158	2	no	—
159	C₄⋊C₈	—	158	2	no	—
160	#103	—	158	8	no	—
161	C₄×C₈	—	2	2	no	—
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	8	4	no	—
165	C₂×Q₈	—	79	2	no	—
166	C₂×Q₈	—	158	2	no	—
167	C₂×Q₈	—	158	2	no	—
168	C₂×Q₈	—	158	1	no	—
169	C₂²×C₄	—	4	2	no	—
170	C₂²×C₄	—	158	1	no	—
171	C₂²×C₄	—	158	1	no	—
172	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
174	C₂²×C₄	#11929623	1	1	yes	characteristic
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	—	316	2	no	—
178	C₂×C₈	—	316	2	no	—
179	C₂×C₈	—	316	1	no	—
180	C₂×C₈	—	316	2	no	—
181	C₂×C₈	—	158	4	no	—
182	C₂×C₈	#11929614	1	4	yes	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	316	2	no	—
188	C₄⋊C₄	—	158	2	no	—
189	C₄²	—	316	1	no	—
190	C₄²	—	316	1	no	—
191	C₄²	D₄×D₇₉	1	2	yes	—
192	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
193	C₂³	#14579132	1	1	yes	characteristic
194	Q₈	—	8	4	no	—
195	Q₈	—	8	4	no	—
196	Q₈	—	316	2	no	—
197	Q₈	—	158	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	8	4	no	—
201	C₂×C₄	—	316	1	no	—
202	C₂×C₄	—	316	1	no	—
203	C₂×C₄	—	316	1	no	—
204	C₂×C₄	—	316	2	no	—
205	C₂×C₄	—	158	2	no	—
206	C₂×C₄	#14579129	1	2	yes	—
207	C₂×C₄	#14579130	1	1	yes	characteristic
208	C₂×C₄	#14579133	1	2	yes	—
209	C₂×C₄	#14579157	1	1	yes	characteristic
210	C₂×C₄	Q₁₆×D₇₉	1	1	yes	characteristic
211	C₂×C₄	C₂×#11929614	1	2	yes	—
212	C₂×C₄	#14579184	1	1	yes	characteristic
213	C₂×C₄	#14579192	1	2	yes	—
214	C₂×C₄	#14579193	1	2	yes	—
215	C₈	—	2	4	no	—
216	C₈	—	316	4	no	—
217	C₈	—	632	1	no	—
218	C₂²	#19098471	1	1	yes	characteristic
219	C₂²	#19098770	1	2	yes	—
220	C₂²	#19098801	1	1	yes	characteristic
221	C₂²	#19098818	1	1	yes	characteristic
222	C₂²	#19098830	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	4	no	—
225	C₄	—	316	2	no	—
226	C₄	—	632	1	no	—
227	C₄	#19098717	1	2	yes	—
228	C₄	#19098719	1	2	yes	—
229	C₄	#19098724	1	2	yes	—
230	C₄	#19098942	1	1	yes	characteristic
231	C₄	#19098955	1	1	yes	characteristic
232	C₂	#23762801	1	2	yes	—
233	C₂	#23762925	1	2	yes	—
234	C₂	#23764407	1	1	yes	characteristic
235	C₂	#23764500	1	1	yes	characteristic
236	C₂	#23764507	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098855

C₂

yes

maximal

#23764336

C₂

yes

maximal, characteristic

C₂×#19098312

C₂

yes

maximal

#23761235

C₂

yes

maximal, characteristic

C₂×#500×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₅₈

C₂²

yes

—

—

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂×#14579084

—

#19098317

—

#19098312

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

—

#500×C₇₉

—

C₂×#107×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

D₄

yes

characteristic

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579094

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579084

—

C₂²×Q₈×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#107×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

Q₁₆

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×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

Q₁₆

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×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

#120

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#127

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

C₂×C₄×C₇₉

#135

yes

characteristic

C₂×C₄×C₇₉

#137

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

#392

yes

characteristic

100

C₂²×C₇₉

#462

yes

—

101

C₂²×C₇₉

#467

yes

characteristic

102

C₂²×C₇₉

#470

yes

characteristic

103

C₂²×C₇₉

#472

yes

—

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

#451

yes

—

107

C₄×C₇₉

#451

yes

—

108

C₄×C₇₉

#452

yes

—

109

C₄×C₇₉

#494

yes

characteristic

110

C₄×C₇₉

#497

yes

characteristic

111

Dic₇₉

—

112

Dic₇₉

—

113

#10279

—

maximal, Sylow

114

C₂×C₇₉

#1676

yes

—

115

C₂×C₇₉

#1696

yes

—

116

C₂×C₇₉

#2001

yes

characteristic

117

C₂×C₇₉

#2016

yes

characteristic

118

C₂×C₇₉

#2018

yes

characteristic

119

C₂×#500

D₇₉

yes

characteristic

120

C₂×#477

—

121

#1984

—

122

C₂×#333

—

123

#1277

—

124

C₇₉

#10279

yes

characteristic, complemented, Sylow

125

C₂×C₄⋊Q₈

C₂×D₇₉

yes

—

126

C₂×C₄×Q₈

—

127

#500

—

128

#477

—

158

—

129

#477

—

158

—

130

C₂×#107

—

131

C₂×#107

—

158

—

132

C₂×C₄⋊C₈

—

133

C₂×C₄⋊C₈

—

134

C₂×#103

—

158

—

135

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

136

#336

—

158

—

137

#333

—

158

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×C₈

—

158

—

141

C₂²×C₈

—

158

—

142

C₂²×C₈

C₂²⋊D₇₉

yes

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

147

C₄×Q₈

—

158

—

148

C₄×Q₈

—

158

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

158

—

153

C₂×C₄²

—

158

—

154

C₂×C₄²

C₂²×D₇₉

yes

characteristic

155

#107

—

156

#107

—

158

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

158

—

159

C₄⋊C₈

—

158

—

160

#103

—

158

—

161

C₄×C₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

158

—

167

C₂×Q₈

—

158

—

168

C₂×Q₈

—

158

—

169

C₂²×C₄

—

170

C₂²×C₄

—

158

—

171

C₂²×C₄

—

158

—

172

C₂²×C₄

D₄×D₇₉

yes

characteristic

173

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

174

C₂²×C₄

#11929623

yes

characteristic

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

316

—

178

C₂×C₈

—

316

—

179

C₂×C₈

—

316

—

180

C₂×C₈

—

316

—

181

C₂×C₈

—

158

—

182

C₂×C₈

#11929614

yes

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

316

—

188

C₄⋊C₄

—

158

—

189

C₄²

—

316

—

190

C₄²

—

316

—

191

C₄²

D₄×D₇₉

yes

—

192

C₄²

C₂×C₂²⋊D₇₉

yes

—

193

C₂³

#14579132

yes

characteristic

194

Q₈

—

195

Q₈

—

196

Q₈

—

316

—

197

Q₈

—

158

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

316

—

202

C₂×C₄

—

316

—

203

C₂×C₄

—

316

—

204

C₂×C₄

—

316

—

205

C₂×C₄

—

158

—

206

C₂×C₄

#14579129

yes

—

207

C₂×C₄

#14579130

yes

characteristic

208

C₂×C₄

#14579133

yes

—

209

C₂×C₄

#14579157

yes

characteristic

210

C₂×C₄

Q₁₆×D₇₉

yes

characteristic

211

C₂×C₄

C₂×#11929614

yes

—

212

C₂×C₄

#14579184

yes

characteristic

213

C₂×C₄

#14579192

yes

—

214

C₂×C₄

#14579193

yes

—

215

C₈

—

216

C₈

—

316

—

217

C₈

—

632

—

218

C₂²

#19098471

yes

characteristic

219

C₂²

#19098770

yes

—

220

C₂²

#19098801

yes

characteristic

221

C₂²

#19098818

yes

characteristic

222

C₂²

#19098830

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

316

—

226

C₄

—

632

—

227

C₄

#19098717

yes

—

228

C₄

#19098719

yes

—

229

C₄

#19098724

yes

—

230

C₄

#19098942

yes

characteristic

231

C₄

#19098955

yes

characteristic

232

C₂

#23762801

yes

—

233

C₂

#23762925

yes

—

234

C₂

#23764407

yes

characteristic

235

C₂

#23764500

yes

characteristic

236

C₂

#23764507

yes

characteristic

	subgroup	G/H
center	C₂³	#14579132
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#500×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	#121
hypercenter	C₂×#500	D₇₉
hypocenter	C₇₉	#10279
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

subgroup

G/H

center

C₂³

#14579132

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×#500×C₇₉

C₂

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

N	H ≅ G/N	type
124. C₇₉	#10279	semidirect

H ≅ G/N

type

124. C₇₉

#10279

semidirect

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

subgroup	index
C₂×#19098855	2
#23764336	2
C₂×#19098312	2
#23761235	2
C₂×#500×C₇₉	2
#10279	79

subgroup

index

C₂×#500×C₇₉

Subgroups — #34190892

Conjugacy classes of subgroups

Complements

Maximal subgroups