Group #34190805 — subgroups

Subgroups — #34190805

Order 20224.

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

normal subgroups only

This group has 574 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×#19098968	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098774	C₂	1	2	yes	maximal
3	#23764336	C₂	1	1	yes	maximal, characteristic
4	C₂×#19098310	C₂	1	2	yes	maximal
5	C₇₉×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₁₆	—	2	2	no	—
7	C₂×#14579161	C₂²	1	2	yes	—
8	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
9	#19098968	—	2	4	no	—
10	#19098774	—	2	4	no	—
11	#19098774	—	2	4	no	—
12	C₂×#14579095	—	2	2	no	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#14579086	—	2	2	no	—
15	#19098317	—	2	2	no	—
16	#19098310	—	2	4	no	—
17	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₅₈	—	2	2	no	—
20	C₂²×Dic₁₅₈	D₄	1	1	yes	characteristic
21	C₂×Dic₃₁₆	—	2	8	no	—
22	C₂×Dic₃₁₆	—	4	4	no	—
23	C₂×Dic₃₁₆	—	4	4	no	—
24	C₂²×C₇₉⋊C₈	—	2	1	no	—
25	#14579161	—	2	2	no	—
26	#14579161	—	2	2	no	—
27	#14579161	—	2	2	no	—
28	#14579161	D₄	1	4	yes	—
29	C₄×Dic₁₅₈	—	2	2	no	—
30	C₄×Dic₁₅₈	—	2	2	no	—
31	C₂×C₄⋊Dic₇₉	—	2	2	no	—
32	C₂×C₄⋊Dic₇₉	—	2	2	no	—
33	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
34	C₂×Dic₇₉⋊C₄	—	2	1	no	—
35	C₂×C₄×Dic₇₉	—	2	1	no	—
36	#14579095	—	2	8	no	—
37	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
38	#14579086	—	2	8	no	—
39	C₂²×C₈×C₇₉	—	2	2	no	—
40	C₂²×C₈×C₇₉	D₄	1	2	yes	—
41	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₉	—	2	2	no	—
43	C₄⋊C₈×C₇₉	D₄	1	4	yes	—
44	C₄×C₈×C₇₉	—	2	2	no	—
45	C₂×Dic₁₅₈	—	2	2	no	—
46	C₂×Dic₁₅₈	—	2	4	no	—
47	C₂×Dic₁₅₈	—	2	1	no	—
48	C₂×Dic₁₅₈	—	2	2	no	—
49	C₂×Dic₁₅₈	—	4	2	no	—
50	C₂×Dic₁₅₈	—	4	2	no	—
51	C₂×Dic₁₅₈	—	4	2	no	—
52	C₂×Dic₁₅₈	—	4	2	no	—
53	C₂×Dic₁₅₈	—	4	2	no	—
54	C₂×Dic₁₅₈	D₈	1	2	yes	—
55	C₂²×Dic₇₉	—	2	1	no	—
56	C₂²×Dic₇₉	—	2	1	no	—
57	C₂²×Dic₇₉	—	4	2	no	—
58	Dic₃₁₆	—	4	16	no	—
59	C₂×C₇₉⋊C₈	—	4	1	no	—
60	C₂×C₇₉⋊C₈	—	4	2	no	—
61	C₄⋊Dic₇₉	—	2	2	no	—
62	C₄⋊Dic₇₉	—	2	4	no	—
63	C₄⋊Dic₇₉	—	2	4	no	—
64	C₄⋊Dic₇₉	—	4	2	no	—
65	C₄⋊Dic₇₉	—	4	2	no	—
66	Dic₇₉⋊C₄	—	4	2	no	—
67	C₄×Dic₇₉	—	4	1	no	—
68	C₄×Dic₇₉	—	4	1	no	—
69	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
72	C₂×C₈×C₇₉	—	2	2	no	—
73	C₂×C₈×C₇₉	—	2	4	no	—
74	C₂×C₈×C₇₉	—	2	2	no	—
75	C₂×C₈×C₇₉	—	4	2	no	—
76	C₂×C₈×C₇₉	—	4	2	no	—
77	C₂×C₈×C₇₉	Q₁₆	1	4	yes	complemented
78	C₄²×C₇₉	C₂×D₄	1	2	yes	—
79	C₄²×C₇₉	C₂×D₄	1	2	yes	—
80	C₂³×C₇₉	#121	1	1	yes	characteristic
81	C₂×C₄×C₇₉	—	2	2	no	—
82	C₂×C₄×C₇₉	#120	1	2	yes	—
83	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#121	1	2	yes	—
85	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
86	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
88	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
89	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
90	C₂×C₄×C₇₉	#137	1	2	yes	—
91	C₂×Dic₇₉	—	2	2	no	—
92	C₂×Dic₇₉	—	4	1	no	—
93	C₂×Dic₇₉	—	4	1	no	—
94	C₂×Dic₇₉	—	4	1	no	—
95	C₂×Dic₇₉	—	4	4	no	—
96	C₂×Dic₇₉	—	4	2	no	—
97	C₂×Dic₇₉	—	8	2	no	—
98	C₂×Dic₇₉	—	8	2	no	—
99	Dic₁₅₈	—	2	4	no	—
100	Dic₁₅₈	—	4	2	no	—
101	Dic₁₅₈	—	4	4	no	—
102	Dic₁₅₈	—	4	4	no	—
103	Dic₁₅₈	—	8	2	no	—
104	Dic₁₅₈	—	8	2	no	—
105	C₈×C₇₉	—	2	4	no	—
106	C₈×C₇₉	—	4	4	no	—
107	C₇₉⋊C₈	—	8	1	no	—
108	C₂²×C₇₉	#392	1	1	yes	characteristic
109	C₂²×C₇₉	#462	1	2	yes	—
110	C₂²×C₇₉	#466	1	1	yes	characteristic
111	C₂²×C₇₉	#469	1	1	yes	characteristic
112	C₂²×C₇₉	#473	1	2	yes	—
113	C₄×C₇₉	—	2	2	no	—
114	C₄×C₇₉	#447	1	2	yes	—
115	C₄×C₇₉	#449	1	2	yes	—
116	C₄×C₇₉	#451	1	2	yes	—
117	C₄×C₇₉	#494	1	1	yes	characteristic
118	C₄×C₇₉	#497	1	1	yes	characteristic
119	Dic₇₉	—	4	2	no	—
120	Dic₇₉	—	8	4	no	—
121	Dic₇₉	—	8	1	no	—
122	#10265	—	79	1	no	maximal, Sylow
123	C₂×C₇₉	#1674	1	2	yes	—
124	C₂×C₇₉	#1694	1	2	yes	—
125	C₂×C₇₉	#1999	1	1	yes	characteristic
126	C₂×C₇₉	#2016	1	1	yes	characteristic
127	C₂×C₇₉	#2020	1	1	yes	characteristic
128	C₂×#500	—	79	1	no	—
129	C₂×#462	—	79	2	no	—
130	#1984	—	79	1	no	—
131	C₂×#332	—	79	2	no	—
132	#1277	D₇₉	1	1	yes	characteristic
133	C₇₉	#10265	1	1	yes	characteristic, complemented, Sylow
134	C₂²×Q₁₆	—	158	2	no	—
135	C₂×C₄⋊Q₈	—	79	2	no	—
136	C₂×C₄×Q₈	—	79	1	no	—
137	#500	—	158	4	no	—
138	#462	—	158	4	no	—
139	#462	—	158	4	no	—
140	C₂×#107	—	158	2	no	—
141	C₂×C₄⋊C₈	—	79	1	no	—
142	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
143	C₂×#103	—	158	2	no	—
144	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
145	#336	—	158	2	no	—
146	#332	—	158	4	no	—
147	C₂²×Q₈	—	79	1	no	—
148	C₂²×Q₈	—	158	2	no	—
149	C₂×Q₁₆	—	316	4	no	—
150	C₂×Q₁₆	—	316	4	no	—
151	C₂×Q₁₆	—	158	8	no	—
152	C₂²×C₈	—	2	2	no	—
153	C₂²×C₈	—	158	1	no	—
154	C₂²×C₈	D₃₁₆	1	2	yes	—
155	C₄⋊Q₈	—	79	4	no	—
156	C₄⋊Q₈	—	158	2	no	—
157	C₄⋊Q₈	—	158	2	no	—
158	C₄⋊Q₈	—	158	2	no	—
159	C₄×Q₈	—	158	2	no	—
160	C₄×Q₈	—	158	2	no	—
161	C₂×C₄⋊C₄	—	79	1	no	—
162	C₂×C₄⋊C₄	—	158	1	no	—
163	C₂×C₄⋊C₄	—	158	2	no	—
164	C₂×C₄⋊C₄	—	158	2	no	—
165	C₂×C₄²	—	158	1	no	—
166	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
167	#107	—	158	8	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	158	2	no	—
170	C₄⋊C₈	D₃₁₆	1	4	yes	—
171	#103	—	158	8	no	—
172	C₄×C₈	—	2	2	no	—
173	C₂×Q₈	—	316	2	no	—
174	C₂×Q₈	—	316	2	no	—
175	C₂×Q₈	—	316	2	no	—
176	C₂×Q₈	—	316	2	no	—
177	C₂×Q₈	—	316	2	no	—
178	C₂×Q₈	—	79	2	no	—
179	C₂×Q₈	—	158	4	no	—
180	C₂×Q₈	—	158	2	no	—
181	C₂×Q₈	—	158	2	no	—
182	C₂×Q₈	—	158	1	no	—
183	C₂²×C₄	—	316	2	no	—
184	C₂²×C₄	—	158	1	no	—
185	C₂²×C₄	—	158	1	no	—
186	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
187	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
188	C₂²×C₄	#11929625	1	1	yes	characteristic
189	Q₁₆	—	316	16	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	2	4	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	316	1	no	—
196	C₂×C₈	—	316	2	no	—
197	C₂×C₈	Dic₃₁₆	1	4	yes	complemented
198	C₄⋊C₄	—	316	2	no	—
199	C₄⋊C₄	—	316	2	no	—
200	C₄⋊C₄	—	316	2	no	—
201	C₄⋊C₄	—	158	2	no	—
202	C₄⋊C₄	—	158	4	no	—
203	C₄⋊C₄	—	158	4	no	—
204	C₄²	—	316	1	no	—
205	C₄²	—	316	1	no	—
206	C₄²	D₄×D₇₉	1	2	yes	—
207	C₄²	C₂×D₃₁₆	1	2	yes	—
208	C₂³	#14579136	1	1	yes	characteristic
209	Q₈	—	316	2	no	—
210	Q₈	—	316	4	no	—
211	Q₈	—	316	4	no	—
212	Q₈	—	632	2	no	—
213	Q₈	—	632	2	no	—
214	Q₈	—	158	4	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	316	1	no	—
217	C₂×C₄	—	316	1	no	—
218	C₂×C₄	—	316	1	no	—
219	C₂×C₄	—	316	4	no	—
220	C₂×C₄	—	316	2	no	—
221	C₂×C₄	—	632	2	no	—
222	C₂×C₄	—	632	2	no	—
223	C₂×C₄	—	158	2	no	—
224	C₂×C₄	#14579131	1	2	yes	—
225	C₂×C₄	#14579131	1	1	yes	characteristic
226	C₂×C₄	#14579136	1	2	yes	—
227	C₂×C₄	#14579158	1	1	yes	characteristic
228	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
229	C₂×C₄	C₂×Dic₃₁₆	1	2	yes	—
230	C₂×C₄	#14579184	1	1	yes	characteristic
231	C₂×C₄	#14579188	1	2	yes	—
232	C₂×C₄	#14579194	1	2	yes	—
233	C₈	—	2	4	no	—
234	C₈	—	4	4	no	—
235	C₈	—	632	1	no	—
236	C₂²	#19098473	1	1	yes	characteristic
237	C₂²	#19098774	1	2	yes	—
238	C₂²	#19098800	1	1	yes	characteristic
239	C₂²	#19098817	1	1	yes	characteristic
240	C₂²	#19098839	1	2	yes	—
241	C₄	—	2	2	no	—
242	C₄	—	316	2	no	—
243	C₄	—	632	1	no	—
244	C₄	—	632	4	no	—
245	C₄	#19098698	1	2	yes	—
246	C₄	#19098711	1	2	yes	—
247	C₄	#19098721	1	2	yes	—
248	C₄	#19098943	1	1	yes	characteristic
249	C₄	#19098957	1	1	yes	characteristic
250	C₂	#23762795	1	2	yes	—
251	C₂	#23762919	1	2	yes	—
252	C₂	#23764399	1	1	yes	characteristic
253	C₂	#23764502	1	1	yes	characteristic
254	C₂	#23764522	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098968

C₂

yes

maximal, characteristic

C₂×#19098774

C₂

yes

maximal

#23764336

C₂

yes

maximal, characteristic

C₂×#19098310

C₂

yes

maximal

C₇₉×#1277

C₂

yes

maximal, characteristic

C₂²×Dic₃₁₆

—

C₂×#14579161

C₂²

yes

—

C₂×C₄×Dic₁₅₈

C₂²

yes

—

—

—

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

—

—

C₂×C₄⋊C₈×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

—

C₂²×Dic₁₅₈

D₄

yes

characteristic

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂²×C₇₉⋊C₈

—

—

—

—

D₄

yes

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579095

—

C₄⋊(C₇₉⋊C₈)

—

#14579086

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₈

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

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

—

C₂×C₈×C₇₉

Q₁₆

yes

complemented

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#121

yes

characteristic

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×D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

C₂×C₄×C₇₉

#135

yes

characteristic

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

100

Dic₁₅₈

—

101

Dic₁₅₈

—

102

Dic₁₅₈

—

103

Dic₁₅₈

—

104

Dic₁₅₈

—

105

C₈×C₇₉

—

106

C₈×C₇₉

—

107

C₇₉⋊C₈

—

108

C₂²×C₇₉

#392

yes

characteristic

109

C₂²×C₇₉

#462

yes

—

110

C₂²×C₇₉

#466

yes

characteristic

111

C₂²×C₇₉

#469

yes

characteristic

112

C₂²×C₇₉

#473

yes

—

113

C₄×C₇₉

—

114

C₄×C₇₉

#447

yes

—

115

C₄×C₇₉

#449

yes

—

116

C₄×C₇₉

#451

yes

—

117

C₄×C₇₉

#494

yes

characteristic

118

C₄×C₇₉

#497

yes

characteristic

119

Dic₇₉

—

120

Dic₇₉

—

121

Dic₇₉

—

122

#10265

—

maximal, Sylow

123

C₂×C₇₉

#1674

yes

—

124

C₂×C₇₉

#1694

yes

—

125

C₂×C₇₉

#1999

yes

characteristic

126

C₂×C₇₉

#2016

yes

characteristic

127

C₂×C₇₉

#2020

yes

characteristic

128

C₂×#500

—

129

C₂×#462

—

130

#1984

—

131

C₂×#332

—

132

#1277

D₇₉

yes

characteristic

133

C₇₉

#10265

yes

characteristic, complemented, Sylow

134

C₂²×Q₁₆

—

158

—

135

C₂×C₄⋊Q₈

—

136

C₂×C₄×Q₈

—

137

#500

—

158

—

138

#462

—

158

—

139

#462

—

158

—

140

C₂×#107

—

158

—

141

C₂×C₄⋊C₈

—

142

C₂×C₄⋊C₈

C₂×D₇₉

yes

—

143

C₂×#103

—

158

—

144

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

145

#336

—

158

—

146

#332

—

158

—

147

C₂²×Q₈

—

148

C₂²×Q₈

—

158

—

149

C₂×Q₁₆

—

316

—

150

C₂×Q₁₆

—

316

—

151

C₂×Q₁₆

—

158

—

152

C₂²×C₈

—

153

C₂²×C₈

—

158

—

154

C₂²×C₈

D₃₁₆

yes

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

158

—

157

C₄⋊Q₈

—

158

—

158

C₄⋊Q₈

—

158

—

159

C₄×Q₈

—

158

—

160

C₄×Q₈

—

158

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

158

—

163

C₂×C₄⋊C₄

—

158

—

164

C₂×C₄⋊C₄

—

158

—

165

C₂×C₄²

—

158

—

166

C₂×C₄²

C₂²×D₇₉

yes

characteristic

167

#107

—

158

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

158

—

170

C₄⋊C₈

D₃₁₆

yes

—

171

#103

—

158

—

172

C₄×C₈

—

173

C₂×Q₈

—

316

—

174

C₂×Q₈

—

316

—

175

C₂×Q₈

—

316

—

176

C₂×Q₈

—

316

—

177

C₂×Q₈

—

316

—

178

C₂×Q₈

—

179

C₂×Q₈

—

158

—

180

C₂×Q₈

—

158

—

181

C₂×Q₈

—

158

—

182

C₂×Q₈

—

158

—

183

C₂²×C₄

—

316

—

184

C₂²×C₄

—

158

—

185

C₂²×C₄

—

158

—

186

C₂²×C₄

D₄×D₇₉

yes

characteristic

187

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

188

C₂²×C₄

#11929625

yes

characteristic

189

Q₁₆

—

316

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

316

—

196

C₂×C₈

—

316

—

197

C₂×C₈

Dic₃₁₆

yes

complemented

198

C₄⋊C₄

—

316

—

199

C₄⋊C₄

—

316

—

200

C₄⋊C₄

—

316

—

201

C₄⋊C₄

—

158

—

202

C₄⋊C₄

—

158

—

203

C₄⋊C₄

—

158

—

204

C₄²

—

316

—

205

C₄²

—

316

—

206

C₄²

D₄×D₇₉

yes

—

207

C₄²

C₂×D₃₁₆

yes

—

208

C₂³

#14579136

yes

characteristic

209

Q₈

—

316

—

210

Q₈

—

316

—

211

Q₈

—

316

—

212

Q₈

—

632

—

213

Q₈

—

632

—

214

Q₈

—

158

—

215

C₂×C₄

—

216

C₂×C₄

—

316

—

217

C₂×C₄

—

316

—

218

C₂×C₄

—

316

—

219

C₂×C₄

—

316

—

220

C₂×C₄

—

316

—

221

C₂×C₄

—

632

—

222

C₂×C₄

—

632

—

223

C₂×C₄

—

158

—

224

C₂×C₄

#14579131

yes

—

225

C₂×C₄

#14579131

yes

characteristic

226

C₂×C₄

#14579136

yes

—

227

C₂×C₄

#14579158

yes

characteristic

228

C₂×C₄

D₈×D₇₉

yes

characteristic

229

C₂×C₄

C₂×Dic₃₁₆

yes

—

230

C₂×C₄

#14579184

yes

characteristic

231

C₂×C₄

#14579188

yes

—

232

C₂×C₄

#14579194

yes

—

233

C₈

—

234

C₈

—

235

C₈

—

632

—

236

C₂²

#19098473

yes

characteristic

237

C₂²

#19098774

yes

—

238

C₂²

#19098800

yes

characteristic

239

C₂²

#19098817

yes

characteristic

240

C₂²

#19098839

yes

—

241

C₄

—

242

C₄

—

316

—

243

C₄

—

632

—

244

C₄

—

632

—

245

C₄

#19098698

yes

—

246

C₄

#19098711

yes

—

247

C₄

#19098721

yes

—

248

C₄

#19098943

yes

characteristic

249

C₄

#19098957

yes

characteristic

250

C₂

#23762795

yes

—

251

C₂

#23762919

yes

—

252

C₂

#23764399

yes

characteristic

253

C₂

#23764502

yes

characteristic

254

C₂

#23764522

yes

characteristic

	subgroup	G/H
center	C₂³	#14579136
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1277	C₂
socle, prime radical	C₂³×C₇₉	#121
hypercenter	#1277	D₇₉
hypocenter	C₇₉	#10265
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂³

#14579136

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1277

C₂

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
77. C₂×C₈×C₇₉	Q₁₆	semidirect
133. C₇₉	#10265	semidirect
197. C₂×C₈	Dic₃₁₆	semidirect

H ≅ G/N

type

77. C₂×C₈×C₇₉

Q₁₆

semidirect

133. C₇₉

#10265

semidirect

197. C₂×C₈

Dic₃₁₆

semidirect

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

subgroup	index
C₂×#19098968	2
C₂×#19098774	2
#23764336	2
C₂×#19098310	2
C₇₉×#1277	2
#10265	79

subgroup

index

C₇₉×#1277

Subgroups — #34190805

Conjugacy classes of subgroups

Complements

Maximal subgroups