Group #23774112 — subgroups

Subgroups — #23774112

Order 10112.

366 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 115 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	#19099118	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099092	C₂	1	1	yes	maximal, characteristic
3	#19098969	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098958	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098932	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098803	C₂	1	2	yes	maximal, complemented
7	#19098791	C₂	1	2	yes	maximal
8	#19098667	C₂	1	2	yes	maximal, complemented
9	#19098660	C₂	1	2	yes	maximal, complemented
10	#97×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#489×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11929614	C₂²	1	2	yes	—
13	C₂×#11929612	C₂²	1	2	yes	—
14	C₂×C₈×D₇₉	C₂²	1	2	yes	—
15	#14579161	C₂²	1	1	yes	characteristic
16	#14579154	—	2	1	no	—
17	#14579153	C₂²	1	1	yes	characteristic
18	#14579152	—	2	1	no	—
19	#14579143	—	2	1	no	—
20	#14579141	C₂²	1	2	yes	—
21	#14579137	—	2	1	no	—
22	#14579137	C₂²	1	1	yes	characteristic
23	#14579132	C₂²	1	1	yes	characteristic
24	Q₈×Dic₇₉	—	2	1	no	—
25	Q₈×Dic₇₉	C₂²	1	1	yes	characteristic
26	#14579126	C₂²	1	2	yes	—
27	D₄×Dic₇₉	C₂²	1	1	yes	characteristic
28	(C₂²⋊D₇₉)⋊C₄	—	2	1	no	—
29	#14579119	—	2	1	no	—
30	#14579117	—	2	1	no	—
31	C₄²×D₇₉	C₂²	1	1	yes	characteristic
32	#14579094	C₂²	1	2	yes	—
33	#14579092	C₂²	1	2	yes	—
34	#14579086	C₂²	1	2	yes	—
35	#14579086	C₂²	1	2	yes	—
36	#14579072	C₂²	1	1	yes	characteristic
37	#14579071	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
39	#124×C₇₉	C₂²	1	1	yes	characteristic
40	#103×C₇₉	C₂²	1	2	yes	—
41	#102×C₇₉	C₂²	1	2	yes	—
42	#97×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×Dic₁₅₈	C₂³	1	2	yes	—
44	C₂×C₂²⋊D₇₉	—	2	1	no	—
45	C₂²×Dic₇₉	—	2	1	no	—
46	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
47	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
48	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
49	#11929614	—	2	4	no	—
50	#11929612	—	2	4	no	—
51	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
52	C₈×D₇₉	—	2	4	no	—
53	C₄⋊Dic₇₉	—	2	2	no	—
54	C₄⋊Dic₇₉	—	2	1	no	—
55	C₄⋊Dic₇₉	—	2	1	no	—
56	C₄⋊Dic₇₉	—	2	1	no	—
57	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
58	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
59	Dic₇₉⋊C₄	—	2	1	no	—
60	Dic₇₉⋊C₄	—	2	2	no	—
61	Dic₇₉⋊C₄	—	2	1	no	—
62	Dic₇₉⋊C₄	—	2	1	no	—
63	C₂²⋊Dic₇₉	—	2	1	no	—
64	C₂²⋊Dic₇₉	—	2	1	no	—
65	(C₂×D₇₉)⋊C₄	—	2	2	no	—
66	(C₂×D₇₉)⋊C₄	—	2	1	no	—
67	C₄×Dic₇₉	—	2	1	no	—
68	C₄×Dic₇₉	—	2	2	no	—
69	C₄×Dic₇₉	D₄	1	1	yes	characteristic
70	C₄×Dic₇₉	D₄	1	1	yes	characteristic
71	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
72	C₂×Q₈×C₇₉	—	2	1	no	—
73	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₈×C₇₉	C₂³	1	2	yes	—
76	C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
78	C₂²⋊C₄×C₇₉	—	2	1	no	—
79	C₂²⋊C₄×C₇₉	—	2	1	no	—
80	C₄²×C₇₉	C₂³	1	1	yes	characteristic
81	C₂³×C₇₉	—	2	1	no	—
82	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₇₉	—	2	2	no	—
84	Q₈×C₇₉	—	4	2	no	—
85	D₄×C₇₉	—	2	2	no	—
86	C₂×C₄×C₇₉	—	2	1	no	—
87	C₂×C₄×C₇₉	—	2	2	no	—
88	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
91	C₂²⋊D₇₉	—	4	2	no	—
92	C₂×Dic₇₉	—	2	2	no	—
93	C₂×Dic₇₉	—	2	1	no	—
94	C₂×Dic₇₉	—	2	1	no	—
95	C₂×Dic₇₉	—	4	2	no	—
96	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
99	C₄×D₇₉	—	2	2	no	—
100	C₄×D₇₉	—	2	2	no	—
101	C₄×D₇₉	—	4	1	no	—
102	Dic₁₅₈	—	2	2	no	—
103	Dic₁₅₈	—	2	2	no	—
104	C₈×C₇₉	—	2	2	no	—
105	C₇₉⋊C₈	#41	1	4	yes	—
106	C₂²×C₇₉	—	4	1	no	—
107	C₂²×C₇₉	—	4	1	no	—
108	C₂²×C₇₉	—	4	1	no	—
109	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
110	C₂×D₇₉	—	2	1	no	—
111	C₂×D₇₉	—	2	1	no	—
112	C₂×D₇₉	#137	1	2	yes	—
113	C₄×C₇₉	—	2	1	no	—
114	C₄×C₇₉	—	2	1	no	—
115	C₄×C₇₉	—	4	1	no	—
116	C₄×C₇₉	—	4	2	no	—
117	C₄×C₇₉	C₂×#41	1	2	yes	—
118	Dic₇₉	—	2	1	no	—
119	Dic₇₉	—	2	1	no	—
120	Dic₇₉	—	2	1	no	—
121	Dic₇₉	—	4	2	no	—
122	Dic₇₉	—	4	1	no	—
123	Dic₇₉	—	4	1	no	—
124	C₂×C₇₉	—	8	1	no	—
125	C₂×C₇₉	#532	1	1	yes	characteristic
126	C₂×C₇₉	C₂×#137	1	1	yes	characteristic
127	C₂×C₇₉	#575	1	1	yes	characteristic
128	D₇₉	—	2	2	no	—
129	#3181	—	79	1	no	maximal, Sylow
130	C₇₉	#3181	1	1	yes	characteristic, complemented, Sylow
131	#533	—	79	1	no	—
132	#529	—	79	1	no	—
133	#501	—	79	1	no	—
134	#497	—	79	1	no	—
135	#491	—	79	1	no	—
136	#489	D₇₉	1	1	yes	characteristic, complemented
137	#467	—	79	2	no	—
138	#465	—	79	2	no	—
139	#441	—	79	2	no	—
140	#440	—	79	2	no	—
141	C₂×#97	—	79	1	no	—
142	C₂×Q₁₆	—	79	2	no	—
143	C₂×SD₁₆	—	79	2	no	—
144	C₂²×C₈	—	79	2	no	—
145	C₄⋊Q₈	—	79	1	no	—
146	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
147	#126	—	158	1	no	—
148	#125	—	79	1	no	—
149	#125	—	158	1	no	—
150	#124	C₂×D₇₉	1	1	yes	characteristic
151	#123	—	158	1	no	—
152	C₂²⋊Q₈	—	79	1	no	—
153	C₂²⋊Q₈	—	79	2	no	—
154	C₂²⋊Q₈	—	158	1	no	—
155	#121	—	79	1	no	—
156	C₄×Q₈	—	79	1	no	—
157	C₄×Q₈	—	79	2	no	—
158	C₄×Q₈	—	158	1	no	—
159	C₄×D₄	—	79	1	no	—
160	C₄×D₄	—	158	1	no	—
161	#117	—	158	1	no	—
162	#117	—	158	1	no	—
163	C₂×C₄²	—	79	1	no	—
164	#107	—	79	2	no	—
165	#106	—	79	2	no	—
166	#103	—	79	2	no	—
167	#103	—	79	2	no	—
168	#103	C₂×D₇₉	1	2	yes	—
169	#102	C₂×D₇₉	1	2	yes	—
170	#97	—	79	2	no	—
171	#97	—	79	1	no	—
172	#97	C₂×D₇₉	1	1	yes	characteristic
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	79	2	no	—
175	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
176	C₂×D₄	—	158	1	no	—
177	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
178	C₂²×C₄	—	79	1	no	—
179	C₂²×C₄	—	79	1	no	—
180	C₂²×C₄	—	79	1	no	—
181	C₂²×C₄	—	158	1	no	—
182	Q₁₆	—	158	4	no	—
183	SD₁₆	—	158	4	no	—
184	C₂×C₈	—	79	2	no	—
185	C₂×C₈	—	158	4	no	—
186	C₂×C₈	C₂²×D₇₉	1	2	yes	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	79	1	no	—
189	C₄⋊C₄	—	79	1	no	—
190	C₄⋊C₄	—	158	1	no	—
191	C₄⋊C₄	—	158	2	no	—
192	C₄⋊C₄	—	158	1	no	—
193	C₄⋊C₄	—	158	2	no	—
194	C₄⋊C₄	—	158	1	no	—
195	C₄⋊C₄	—	158	1	no	—
196	C₄⋊C₄	—	158	1	no	—
197	C₄⋊C₄	—	158	1	no	—
198	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	158	2	no	—
202	C₂²⋊C₄	—	158	1	no	—
203	C₂²⋊C₄	—	158	1	no	—
204	C₂²⋊C₄	—	158	1	no	—
205	C₄²	—	79	1	no	—
206	C₄²	—	79	1	no	—
207	C₄²	—	79	1	no	—
208	C₄²	—	158	1	no	—
209	C₄²	—	158	2	no	—
210	C₄²	C₂²×D₇₉	1	1	yes	characteristic
211	C₂³	—	2	1	no	—
212	C₂³	—	79	1	no	—
213	Q₈	—	2	2	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	158	2	no	—
216	Q₈	—	158	2	no	—
217	D₄	—	2	2	no	—
218	D₄	—	316	2	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	316	1	no	—
222	C₂×C₄	—	316	2	no	—
223	C₂×C₄	—	79	1	no	—
224	C₂×C₄	—	79	1	no	—
225	C₂×C₄	—	79	1	no	—
226	C₂×C₄	—	158	2	no	—
227	C₂×C₄	—	158	1	no	—
228	C₂×C₄	—	158	2	no	—
229	C₂×C₄	—	158	1	no	—
230	C₂×C₄	—	158	2	no	—
231	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
232	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
233	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
234	C₈	—	2	2	no	—
235	C₈	—	79	4	no	—
236	C₂²	—	4	1	no	—
237	C₂²	—	4	1	no	—
238	C₂²	—	4	1	no	—
239	C₂²	—	79	2	no	—
240	C₂²	—	158	1	no	—
241	C₂²	—	158	1	no	—
242	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	4	2	no	—
246	C₄	—	4	1	no	—
247	C₄	—	316	1	no	—
248	C₄	—	316	1	no	—
249	C₄	—	316	2	no	—
250	C₄	—	158	1	no	—
251	C₄	—	158	1	no	—
252	C₄	—	158	1	no	—
253	C₄	#41×D₇₉	1	2	yes	—
254	C₂	—	8	1	no	—
255	C₂	—	158	2	no	—
256	C₂	#19099112	1	1	yes	characteristic
257	C₂	#137×D₇₉	1	1	yes	characteristic
258	C₂	#19099359	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099118

C₂

yes

maximal, characteristic, complemented

#19099092

C₂

yes

maximal, characteristic

#19098969

C₂

yes

maximal, characteristic, complemented

#19098958

C₂

yes

maximal, characteristic, complemented

#19098932

C₂

yes

maximal, characteristic, complemented

#19098803

C₂

yes

maximal, complemented

#19098791

C₂

yes

maximal

#19098667

C₂

yes

maximal, complemented

#19098660

C₂

yes

maximal, complemented

#97×D₇₉

C₂

yes

maximal, characteristic, complemented

#489×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929614

C₂²

yes

—

C₂×#11929612

C₂²

yes

—

C₂×C₈×D₇₉

C₂²

yes

—

#14579161

C₂²

yes

characteristic

#14579154

—

#14579153

C₂²

yes

—

—

C₂²

yes

—

#14579137

—

#14579137

C₂²

yes

characteristic

#14579132

C₂²

yes

characteristic

Q₈×Dic₇₉

—

Q₈×Dic₇₉

C₂²

yes

characteristic

#14579126

C₂²

yes

—

D₄×Dic₇₉

C₂²

yes

characteristic

(C₂²⋊D₇₉)⋊C₄

—

#14579119

—

#14579117

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579094

C₂²

yes

—

#14579092

C₂²

yes

—

#14579086

C₂²

yes

—

#14579086

C₂²

yes

—

#14579072

C₂²

yes

characteristic

#14579071

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#124×C₇₉

C₂²

yes

characteristic

#103×C₇₉

C₂²

yes

—

#102×C₇₉

C₂²

yes

—

#97×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

C₂³

yes

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

C₂³

yes

characteristic

#11929614

—

#11929612

—

C₂×C₇₉⋊C₈

C₂³

yes

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

C₄⋊Dic₇₉

C₂³

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂³

yes

characteristic

C₂×D₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₄×D₇₉

—

100

C₄×D₇₉

—

101

C₄×D₇₉

—

102

Dic₁₅₈

—

103

Dic₁₅₈

—

104

C₈×C₇₉

—

105

C₇₉⋊C₈

#41

yes

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

—

108

C₂²×C₇₉

—

109

C₂²×C₇₉

C₂²×D₄

yes

characteristic

110

C₂×D₇₉

—

111

C₂×D₇₉

—

112

C₂×D₇₉

#137

yes

—

113

C₄×C₇₉

—

114

C₄×C₇₉

—

115

C₄×C₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

C₂×#41

yes

—

118

Dic₇₉

—

119

Dic₇₉

—

120

Dic₇₉

—

121

Dic₇₉

—

122

Dic₇₉

—

123

Dic₇₉

—

124

C₂×C₇₉

—

125

C₂×C₇₉

#532

yes

characteristic

126

C₂×C₇₉

C₂×#137

yes

characteristic

127

C₂×C₇₉

#575

yes

characteristic

128

D₇₉

—

129

#3181

—

maximal, Sylow

130

C₇₉

#3181

yes

characteristic, complemented, Sylow

131

#533

—

132

#529

—

133

#501

—

134

#497

—

135

#491

—

136

#489

D₇₉

yes

characteristic, complemented

137

#467

—

138

#465

—

139

#441

—

140

#440

—

141

C₂×#97

—

142

C₂×Q₁₆

—

143

C₂×SD₁₆

—

144

C₂²×C₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

147

#126

—

158

—

148

#125

—

149

#125

—

158

—

150

#124

C₂×D₇₉

yes

characteristic

151

#123

—

158

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

—

154

C₂²⋊Q₈

—

158

—

155

#121

—

156

C₄×Q₈

—

157

C₄×Q₈

—

158

C₄×Q₈

—

158

—

159

C₄×D₄

—

160

C₄×D₄

—

158

—

161

#117

—

158

—

162

#117

—

158

—

163

C₂×C₄²

—

164

#107

—

165

#106

—

166

#103

—

167

#103

—

168

#103

C₂×D₇₉

yes

—

169

#102

C₂×D₇₉

yes

—

170

#97

—

171

#97

—

172

#97

C₂×D₇₉

yes

characteristic

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

C₂²×D₇₉

yes

characteristic

176

C₂×D₄

—

158

—

177

C₂×D₄

C₂²×D₇₉

yes

characteristic

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

158

—

182

Q₁₆

—

158

—

183

SD₁₆

—

158

—

184

C₂×C₈

—

185

C₂×C₈

—

158

—

186

C₂×C₈

C₂²×D₇₉

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

158

—

191

C₄⋊C₄

—

158

—

192

C₄⋊C₄

—

158

—

193

C₄⋊C₄

—

158

—

194

C₄⋊C₄

—

158

—

195

C₄⋊C₄

—

158

—

196

C₄⋊C₄

—

158

—

197

C₄⋊C₄

—

158

—

198

C₄⋊C₄

C₂²×D₇₉

yes

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

158

—

202

C₂²⋊C₄

—

158

—

203

C₂²⋊C₄

—

158

—

204

C₂²⋊C₄

—

158

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

158

—

209

C₄²

—

158

—

210

C₄²

C₂²×D₇₉

yes

characteristic

211

C₂³

—

212

C₂³

—

213

Q₈

—

214

Q₈

—

215

Q₈

—

158

—

216

Q₈

—

158

—

217

D₄

—

218

D₄

—

316

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

316

—

222

C₂×C₄

—

316

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

158

—

227

C₂×C₄

—

158

—

228

C₂×C₄

—

158

—

229

C₂×C₄

—

158

—

230

C₂×C₄

—

158

—

231

C₂×C₄

D₄×D₇₉

yes

characteristic

232

C₂×C₄

D₄×D₇₉

yes

characteristic

233

C₂×C₄

C₂³×D₇₉

yes

characteristic

234

C₈

—

235

C₈

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

158

—

241

C₂²

—

158

—

242

C₂²

C₂×D₄×D₇₉

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

316

—

248

C₄

—

316

—

249

C₄

—

316

—

250

C₄

—

158

—

251

C₄

—

158

—

252

C₄

—

158

—

253

C₄

#41×D₇₉

yes

—

254

C₂

—

255

C₂

—

158

—

256

C₂

#19099112

yes

characteristic

257

C₂

#137×D₇₉

yes

characteristic

258

C₂

#19099359

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#489×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	#14579132	C₂²
hypercenter	#489	D₇₉
hypocenter	C₇₉	#3181
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #489

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#489×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

C₂²

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #489

N	H ≅ G/N	type
1. #19099118	C₂	semidirect
3. #19098969	C₂	semidirect
4. #19098958	C₂	semidirect
5. #19098932	C₂	semidirect
6. #19098803	C₂	semidirect
8. #19098667	C₂	semidirect
9. #19098660	C₂	semidirect
10. #97×D₇₉	C₂	semidirect
11. #489×C₇₉	C₂	semidirect
130. C₇₉	#3181	semidirect
136. #489	D₇₉	semidirect

H ≅ G/N

type

1. #19099118

C₂

semidirect

3. #19098969

C₂

semidirect

4. #19098958

C₂

semidirect

5. #19098932

C₂

semidirect

6. #19098803

C₂

semidirect

8. #19098667

C₂

semidirect

9. #19098660

C₂

semidirect

10. #97×D₇₉

C₂

semidirect

11. #489×C₇₉

C₂

semidirect

130. C₇₉

#3181

semidirect

136. #489

D₇₉

semidirect

Subgroups — #23774112

Conjugacy classes of subgroups

Complements