Group #34190768 — subgroups

Subgroups — #34190768

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	#23773201	C₂	1	2	yes	maximal
2	#23764335	C₂	1	1	yes	maximal, characteristic
3	#23761855	C₂	1	2	yes	maximal
4	#23761275	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#3249	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
7	#19098867	—	2	4	no	—
8	#19098855	—	2	2	no	—
9	#19098845	—	2	2	no	—
10	#19098606	—	2	2	no	—
11	#19098587	C₂²	1	2	yes	—
12	#19098571	—	2	2	no	—
13	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
14	#19098317	—	2	2	no	—
15	Q₈⋊(C₇₉⋊C₈)	—	2	4	no	—
16	#533×C₇₉	C₂²	1	2	yes	—
17	#477×C₇₉	—	2	2	no	—
18	#467×C₇₉	—	2	2	no	—
19	#462×C₇₉	—	2	2	no	—
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×Dic₁₅₈	D₄	1	1	yes	characteristic
22	C₂×#11929608	—	2	2	no	—
23	C₂²×C₇₉⋊C₈	—	2	1	no	—
24	C₄×Dic₁₅₈	—	2	2	no	—
25	C₄×Dic₁₅₈	—	2	2	no	—
26	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
27	C₂×Dic₇₉⋊C₄	—	2	1	no	—
28	C₂×C₄×Dic₇₉	—	2	1	no	—
29	#14579094	—	2	4	no	—
30	#14579092	—	2	4	no	—
31	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
33	#14579084	—	2	4	no	—
34	#14579084	—	2	4	no	—
35	C₄×C₇₉⋊C₈	—	2	2	no	—
36	C₂×Q₁₆×C₇₉	—	2	2	no	—
37	C₂²×C₈×C₇₉	D₄	1	2	yes	—
38	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
39	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
40	#125×C₇₉	—	2	2	no	—
41	C₂²⋊Q₈×C₇₉	—	2	2	no	—
42	C₂²⋊Q₈×C₇₉	—	2	2	no	—
43	C₄×Q₈×C₇₉	—	2	2	no	—
44	C₄×Q₈×C₇₉	—	2	2	no	—
45	#117×C₇₉	—	2	2	no	—
46	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
47	#107×C₇₉	—	2	2	no	—
48	C₄⋊C₈×C₇₉	—	2	2	no	—
49	#103×C₇₉	—	2	4	no	—
50	C₂×Dic₁₅₈	—	2	2	no	—
51	C₂×Dic₁₅₈	—	2	1	no	—
52	C₂×Dic₁₅₈	—	2	2	no	—
53	C₂×Dic₁₅₈	Q₁₆	1	2	yes	complemented
54	C₂²×Dic₇₉	—	2	1	no	—
55	C₂²×Dic₇₉	—	2	1	no	—
56	#11929608	—	4	2	no	—
57	#11929608	—	4	2	no	—
58	C₂×C₇₉⋊C₈	—	2	2	no	—
59	C₂×C₇₉⋊C₈	—	2	4	no	—
60	C₂×C₇₉⋊C₈	—	4	1	no	—
61	C₂×C₇₉⋊C₈	—	4	1	no	—
62	C₄⋊Dic₇₉	—	2	2	no	—
63	Dic₇₉⋊C₄	—	4	2	no	—
64	C₄×Dic₇₉	—	4	1	no	—
65	C₄×Dic₇₉	—	4	1	no	—
66	C₂×Q₈×C₇₉	—	2	2	no	—
67	C₂×Q₈×C₇₉	—	2	2	no	—
68	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
71	Q₁₆×C₇₉	—	8	2	no	—
72	C₂×C₈×C₇₉	—	2	2	no	—
73	C₂×C₈×C₇₉	—	4	2	no	—
74	C₄⋊C₄×C₇₉	—	2	2	no	—
75	C₄⋊C₄×C₇₉	—	2	2	no	—
76	C₄⋊C₄×C₇₉	—	2	2	no	—
77	C₄⋊C₄×C₇₉	—	2	2	no	—
78	C₄⋊C₄×C₇₉	—	4	2	no	—
79	C₄⋊C₄×C₇₉	—	4	2	no	—
80	C₂²⋊C₄×C₇₉	—	4	2	no	—
81	C₄²×C₇₉	—	4	2	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	—	4	4	no	—
86	Q₈×C₇₉	—	4	2	no	—
87	Q₈×C₇₉	—	4	2	no	—
88	C₂×C₄×C₇₉	—	2	1	no	—
89	C₂×C₄×C₇₉	—	2	1	no	—
90	C₂×C₄×C₇₉	—	4	1	no	—
91	C₂×C₄×C₇₉	—	4	2	no	—
92	C₂×C₄×C₇₉	—	4	2	no	—
93	C₂×C₄×C₇₉	#120	1	2	yes	—
94	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
95	C₂×C₄×C₇₉	#121	1	2	yes	—
96	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
97	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
98	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
99	C₂×C₄×C₇₉	#137	1	2	yes	—
100	C₂×Dic₇₉	—	2	2	no	—
101	C₂×Dic₇₉	—	4	1	no	—
102	C₂×Dic₇₉	—	4	1	no	—
103	C₂×Dic₇₉	—	4	2	no	—
104	C₂×Dic₇₉	—	4	1	no	—
105	Dic₁₅₈	—	2	4	no	—
106	Dic₁₅₈	—	4	2	no	—
107	C₈×C₇₉	—	4	2	no	—
108	C₇₉⋊C₈	—	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	—	8	2	no	—
118	C₄×C₇₉	—	8	2	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	—	4	2	no	—
124	Dic₇₉	—	8	1	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	D₇₉	1	1	yes	characteristic
132	#3078	—	79	2	no	—
133	#1984	—	79	1	no	—
134	#1493	—	79	2	no	—
135	#1292	—	79	1	no	—
136	C₇₉	#10259	1	1	yes	characteristic, complemented, Sylow
137	#533	C₂×D₇₉	1	2	yes	—
138	C₂×C₄×Q₈	—	79	1	no	—
139	#479	—	158	4	no	—
140	#477	—	2	2	no	—
141	#477	—	158	2	no	—
142	#475	—	158	2	no	—
143	#467	—	2	2	no	—
144	#462	—	2	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	—	79	1	no	—
150	#336	—	158	2	no	—
151	Q₈⋊C₈	—	158	4	no	—
152	C₂²×Q₈	—	79	1	no	—
153	C₂×Q₁₆	—	2	2	no	—
154	C₂×M₁₆	—	158	2	no	—
155	C₂²×C₈	—	158	1	no	—
156	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
157	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
158	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
159	#125	—	2	2	no	—
160	C₂²⋊Q₈	—	2	2	no	—
161	C₂²⋊Q₈	—	2	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	—	2	2	no	—
167	C₂×C₄⋊C₄	—	79	1	no	—
168	C₂×C₄⋊C₄	—	158	1	no	—
169	C₂×C₄²	—	158	1	no	—
170	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
171	#107	—	2	2	no	—
172	#107	—	158	4	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	—	2	4	no	—
178	#103	—	158	4	no	—
179	#103	—	158	4	no	—
180	C₄×C₈	—	158	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	79	2	no	—
184	C₂×Q₈	—	158	2	no	—
185	C₂×Q₈	—	158	2	no	—
186	C₂×Q₈	—	158	1	no	—
187	C₂²×C₄	—	158	1	no	—
188	C₂²×C₄	—	158	1	no	—
189	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
191	C₂²×C₄	#11929623	1	1	yes	characteristic
192	Q₁₆	—	8	2	no	—
193	M₁₆	—	316	2	no	—
194	M₁₆	—	316	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	316	1	no	—
198	C₂×C₈	—	316	1	no	—
199	C₂×C₈	—	158	2	no	—
200	C₂×C₈	—	158	4	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	316	2	no	—
208	C₄⋊C₄	—	158	2	no	—
209	C₂²⋊C₄	—	4	2	no	—
210	C₄²	—	4	2	no	—
211	C₄²	—	316	1	no	—
212	C₄²	—	316	1	no	—
213	C₄²	D₄×D₇₉	1	2	yes	—
214	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
215	C₂³	#14579132	1	1	yes	characteristic
216	Q₈	—	4	4	no	—
217	Q₈	—	4	2	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	316	2	no	—
220	Q₈	—	158	4	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	316	1	no	—
227	C₂×C₄	—	316	1	no	—
228	C₂×C₄	—	316	2	no	—
229	C₂×C₄	—	316	1	no	—
230	C₂×C₄	—	158	2	no	—
231	C₂×C₄	#14579129	1	2	yes	—
232	C₂×C₄	#14579130	1	1	yes	characteristic
233	C₂×C₄	#14579133	1	2	yes	—
234	C₂×C₄	#14579157	1	1	yes	characteristic
235	C₂×C₄	Q₁₆×D₇₉	1	1	yes	characteristic
236	C₂×C₄	#14579184	1	1	yes	characteristic
237	C₂×C₄	#14579193	1	2	yes	—
238	C₈	—	4	2	no	—
239	C₈	—	316	2	no	—
240	C₈	—	316	4	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	#19098471	1	1	yes	characteristic
244	C₂²	#19098801	1	1	yes	characteristic
245	C₂²	#19098818	1	1	yes	characteristic
246	C₄	—	2	2	no	—
247	C₄	—	2	1	no	—
248	C₄	—	8	2	no	—
249	C₄	—	8	2	no	—
250	C₄	—	316	2	no	—
251	C₄	—	632	1	no	—
252	C₄	#19098717	1	2	yes	—
253	C₄	#19098724	1	2	yes	—
254	C₄	#19098741	1	1	yes	characteristic
255	C₄	#19098746	1	1	yes	characteristic
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	#23764407	1	1	yes	characteristic
259	C₂	#23764447	1	1	yes	characteristic
260	C₂	#23764503	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773201

C₂

yes

maximal

#23764335

C₂

yes

maximal, characteristic

#23761855

C₂

yes

maximal

#23761275

C₂

yes

maximal, characteristic

C₇₉×#3249

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₅₈

C₂²

yes

—

—

—

—

C₂²

yes

—

#19098571

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

#19098317

—

Q₈⋊(C₇₉⋊C₈)

—

#533×C₇₉

C₂²

yes

—

#477×C₇₉

—

#467×C₇₉

—

#462×C₇₉

—

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

D₄

yes

characteristic

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579094

—

#14579092

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579084

—

#14579084

—

C₄×C₇₉⋊C₈

—

C₂×Q₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

D₄

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

—

C₄⋊C₈×C₇₉

—

#103×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

Q₁₆

yes

complemented

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

—

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

—

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

—

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

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#121

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×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

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

100

C₂×Dic₇₉

—

101

C₂×Dic₇₉

—

102

C₂×Dic₇₉

—

103

C₂×Dic₇₉

—

104

C₂×Dic₇₉

—

105

Dic₁₅₈

—

106

Dic₁₅₈

—

107

C₈×C₇₉

—

108

C₇₉⋊C₈

—

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

D₇₉

yes

characteristic

132

#3078

—

133

#1984

—

134

#1493

—

135

#1292

—

136

C₇₉

#10259

yes

characteristic, complemented, Sylow

137

#533

C₂×D₇₉

yes

—

138

C₂×C₄×Q₈

—

139

#479

—

158

—

140

#477

—

141

#477

—

158

—

142

#475

—

158

—

143

#467

—

144

#462

—

145

#428

—

158

—

146

#423

—

147

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

148

#419

—

158

—

149

C₂×C₄×C₈

—

150

#336

—

158

—

151

Q₈⋊C₈

—

158

—

152

C₂²×Q₈

—

153

C₂×Q₁₆

—

154

C₂×M₁₆

—

158

—

155

C₂²×C₈

—

158

—

156

C₂²×C₈

C₂²⋊D₇₉

yes

—

157

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

158

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

159

#125

—

160

C₂²⋊Q₈

—

161

C₂²⋊Q₈

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

—

158

—

165

C₄×Q₈

—

158

—

166

#117

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

158

—

169

C₂×C₄²

—

158

—

170

C₂×C₄²

C₂²×D₇₉

yes

characteristic

171

#107

—

172

#107

—

158

—

173

#106

—

158

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

158

—

177

#103

—

178

#103

—

158

—

179

#103

—

158

—

180

C₄×C₈

—

158

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

158

—

185

C₂×Q₈

—

158

—

186

C₂×Q₈

—

158

—

187

C₂²×C₄

—

158

—

188

C₂²×C₄

—

158

—

189

C₂²×C₄

D₄×D₇₉

yes

characteristic

190

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

191

C₂²×C₄

#11929623

yes

characteristic

192

Q₁₆

—

193

M₁₆

—

316

—

194

M₁₆

—

316

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

316

—

198

C₂×C₈

—

316

—

199

C₂×C₈

—

158

—

200

C₂×C₈

—

158

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

316

—

208

C₄⋊C₄

—

158

—

209

C₂²⋊C₄

—

210

C₄²

—

211

C₄²

—

316

—

212

C₄²

—

316

—

213

C₄²

D₄×D₇₉

yes

—

214

C₄²

C₂×C₂²⋊D₇₉

yes

—

215

C₂³

#14579132

yes

characteristic

216

Q₈

—

217

Q₈

—

218

Q₈

—

219

Q₈

—

316

—

220

Q₈

—

158

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

316

—

227

C₂×C₄

—

316

—

228

C₂×C₄

—

316

—

229

C₂×C₄

—

316

—

230

C₂×C₄

—

158

—

231

C₂×C₄

#14579129

yes

—

232

C₂×C₄

#14579130

yes

characteristic

233

C₂×C₄

#14579133

yes

—

234

C₂×C₄

#14579157

yes

characteristic

235

C₂×C₄

Q₁₆×D₇₉

yes

characteristic

236

C₂×C₄

#14579184

yes

characteristic

237

C₂×C₄

#14579193

yes

—

238

C₈

—

239

C₈

—

316

—

240

C₈

—

316

—

241

C₂²

—

242

C₂²

—

243

C₂²

#19098471

yes

characteristic

244

C₂²

#19098801

yes

characteristic

245

C₂²

#19098818

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

316

—

251

C₄

—

632

—

252

C₄

#19098717

yes

—

253

C₄

#19098724

yes

—

254

C₄

#19098741

yes

characteristic

255

C₄

#19098746

yes

characteristic

256

C₂

—

257

C₂

—

258

C₂

#23764407

yes

characteristic

259

C₂

#23764447

yes

characteristic

260

C₂

#23764503

yes

characteristic

	subgroup	G/H
center	C₂²	#19098471
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3249	C₂
socle	C₂²×C₇₉	#392
prime radical	C₂³×C₇₉	#121
hypercenter	#3249	D₇₉
hypocenter	C₇₉	#10259
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3249

subgroup

G/H

center

C₂²

#19098471

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3249

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3249

N	H ≅ G/N	type
53. C₂×Dic₁₅₈	Q₁₆	semidirect
136. C₇₉	#10259	semidirect

H ≅ G/N

type

53. C₂×Dic₁₅₈

Q₁₆

semidirect

136. C₇₉

#10259

semidirect

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

subgroup	index
#23773201	2
#23764335	2
#23761855	2
#23761275	2
C₇₉×#3249	2
#10259	79

subgroup

index

C₇₉×#3249

Subgroups — #34190768

Conjugacy classes of subgroups

Complements

Maximal subgroups