Group #21437129 — subgroups

Subgroups — #21437129

Order 7552.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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	#16838131	C₂	1	1	yes	maximal, characteristic, complemented
2	#16838125	C₂	1	1	yes	maximal, characteristic
3	#16837796	C₂	1	2	yes	maximal
4	#16837782	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837625	C₂	1	2	yes	maximal
6	#16837613	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837613	C₂	1	2	yes	maximal, complemented
8	#16837608	C₂	1	1	yes	maximal, characteristic
9	#16837510	C₂	1	2	yes	maximal, complemented
10	C₄×#11745660	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Dic₂₃₆	C₂²	1	2	yes	—
13	C₂×Dic₂₃₆	C₂²	1	2	yes	—
14	C₂×Dic₂₃₆	C₂²	1	2	yes	—
15	C₂×#11745660	C₂²	1	1	yes	characteristic
16	C₂×#11745660	C₂²	1	2	yes	—
17	#14273727	C₂²	1	1	yes	characteristic
18	#14273727	C₂²	1	1	yes	characteristic
19	#14273727	C₂²	1	2	yes	—
20	#14273722	—	2	2	no	—
21	#14273718	—	2	1	no	—
22	#14273718	—	2	2	no	—
23	#14273715	C₂²	1	2	yes	—
24	#14273703	—	2	1	no	—
25	Q₈×Dic₅₉	—	2	1	no	—
26	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
27	C₄×Dic₁₁₈	C₂²	1	2	yes	—
28	C₄×Dic₁₁₈	C₂²	1	2	yes	—
29	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
30	#14273685	—	2	1	no	—
31	#14273659	C₂²	1	1	yes	characteristic
32	#14273652	C₂²	1	1	yes	characteristic
33	#14273652	C₂²	1	2	yes	—
34	#14273652	C₂²	1	2	yes	—
35	#14273649	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
39	#97×C₅₉	C₂²	1	2	yes	—
40	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
42	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₅₉	—	2	1	no	—
44	C₂×Dic₁₁₈	C₂³	1	2	yes	—
45	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
46	C₂×Dic₁₁₈	C₂³	1	2	yes	—
47	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
48	C₂×C₈×C₅₉	C₂³	1	2	yes	—
49	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
50	C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
51	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
52	C₄²×C₅₉	C₂³	1	1	yes	characteristic
53	C₄²×C₅₉	C₂³	1	2	yes	—
54	(C₂×D₅₉)⋊C₄	—	2	2	no	—
55	(C₂×D₅₉)⋊C₄	—	2	1	no	—
56	(C₂×D₅₉)⋊C₄	—	2	2	no	—
57	C₄⋊Dic₅₉	—	2	1	no	—
58	C₄⋊Dic₅₉	—	2	2	no	—
59	C₄⋊Dic₅₉	—	2	1	no	—
60	C₄⋊Dic₅₉	—	2	2	no	—
61	C₄⋊Dic₅₉	—	2	1	no	—
62	C₄⋊Dic₅₉	—	2	1	no	—
63	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
64	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
65	Dic₅₉⋊C₄	—	2	2	no	—
66	Dic₅₉⋊C₄	—	2	2	no	—
67	Dic₅₉⋊C₄	—	2	1	no	—
68	C₄×Dic₅₉	—	2	2	no	—
69	C₄×Dic₅₉	—	2	2	no	—
70	C₄×Dic₅₉	—	2	1	no	—
71	Dic₂₃₆	—	2	4	no	—
72	Dic₂₃₆	—	4	2	no	—
73	Dic₂₃₆	—	4	2	no	—
74	#11745660	—	2	2	no	—
75	#11745660	—	4	2	no	—
76	C₂²×D₅₉	—	2	1	no	—
77	Q₈×C₅₉	—	2	2	no	—
78	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
83	C₂×Dic₅₉	—	2	1	no	—
84	C₂×Dic₅₉	—	2	1	no	—
85	C₂×Dic₅₉	—	2	1	no	—
86	C₂×Dic₅₉	—	2	2	no	—
87	C₂×Dic₅₉	—	2	2	no	—
88	D₂₃₆	—	2	1	no	—
89	D₂₃₆	—	2	1	no	—
90	C₄×D₅₉	—	4	2	no	—
91	Dic₁₁₈	—	2	1	no	—
92	Dic₁₁₈	—	2	2	no	—
93	Dic₁₁₈	—	2	2	no	—
94	Dic₁₁₈	—	2	2	no	—
95	Dic₁₁₈	—	2	2	no	—
96	Dic₁₁₈	—	2	1	no	—
97	C₈×C₅₉	—	2	2	no	—
98	C₈×C₅₉	—	2	1	no	—
99	C₈×C₅₉	#41	1	2	yes	—
100	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
101	C₂×D₅₉	—	4	1	no	—
102	C₂×D₅₉	—	4	1	no	—
103	C₂×D₅₉	—	4	1	no	—
104	C₄×C₅₉	—	2	2	no	—
105	C₄×C₅₉	—	2	2	no	—
106	C₄×C₅₉	—	2	1	no	—
107	C₄×C₅₉	#137	1	2	yes	—
108	C₄×C₅₉	C₂×#41	1	1	yes	characteristic
109	C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
110	Dic₅₉	—	4	1	no	—
111	Dic₅₉	—	4	2	no	—
112	Dic₅₉	—	4	2	no	—
113	Dic₅₉	—	4	1	no	—
114	Dic₅₉	—	4	1	no	—
115	#3398	—	59	1	no	maximal, Sylow
116	C₂×C₅₉	#550	1	1	yes	characteristic
117	C₂×C₅₉	C₂×#137	1	1	yes	characteristic
118	C₂×C₅₉	#578	1	1	yes	characteristic
119	D₅₉	—	8	1	no	—
120	#557	—	59	1	no	—
121	#556	—	59	1	no	—
122	#497	—	59	2	no	—
123	#494	—	59	1	no	—
124	#464	—	59	2	no	—
125	#462	—	59	2	no	—
126	#462	—	59	1	no	—
127	#461	—	59	1	no	—
128	#446	D₅₉	1	1	yes	characteristic, complemented
129	#441	—	59	2	no	—
130	C₄×SD₁₆	—	59	1	no	—
131	C₅₉	#3398	1	1	yes	characteristic, complemented, Sylow
132	C₂×Q₁₆	—	59	2	no	—
133	C₂×Q₁₆	—	59	2	no	—
134	C₂×Q₁₆	—	59	2	no	—
135	C₂×SD₁₆	—	59	1	no	—
136	C₂×SD₁₆	—	59	2	no	—
137	C₄⋊Q₈	—	59	1	no	—
138	C₄⋊Q₈	—	59	1	no	—
139	C₄⋊Q₈	—	59	2	no	—
140	#126	—	118	2	no	—
141	#125	—	118	1	no	—
142	#125	—	118	2	no	—
143	#124	—	59	2	no	—
144	C₂²⋊Q₈	—	118	1	no	—
145	C₄×Q₈	—	59	2	no	—
146	C₄×Q₈	—	59	1	no	—
147	C₄×Q₈	—	59	2	no	—
148	C₄×Q₈	—	118	1	no	—
149	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
150	C₄×D₄	—	59	1	no	—
151	#117	—	118	1	no	—
152	#106	—	59	1	no	—
153	C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
154	C₄⋊C₈	C₂×D₅₉	1	2	yes	—
155	#103	—	59	1	no	—
156	#103	—	59	2	no	—
157	#103	—	59	2	no	—
158	#102	—	59	1	no	—
159	#97	C₂×D₅₉	1	2	yes	—
160	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
161	C₂×Q₈	—	59	2	no	—
162	C₂×Q₈	—	59	1	no	—
163	C₂×Q₈	—	59	2	no	—
164	C₂×Q₈	D₂₃₆	1	1	yes	characteristic
165	C₂×D₄	—	59	1	no	—
166	C₂²×C₄	—	118	1	no	—
167	Q₁₆	—	118	4	no	—
168	Q₁₆	—	236	2	no	—
169	Q₁₆	—	236	2	no	—
170	SD₁₆	—	118	2	no	—
171	SD₁₆	—	236	2	no	—
172	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
173	C₂×C₈	C₂²×D₅₉	1	2	yes	—
174	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
175	C₄⋊C₄	—	59	1	no	—
176	C₄⋊C₄	—	59	1	no	—
177	C₄⋊C₄	—	118	1	no	—
178	C₄⋊C₄	—	118	2	no	—
179	C₄⋊C₄	—	118	2	no	—
180	C₄⋊C₄	—	118	1	no	—
181	C₄⋊C₄	—	118	2	no	—
182	C₄⋊C₄	—	118	1	no	—
183	C₄⋊C₄	—	118	2	no	—
184	C₄⋊C₄	—	118	1	no	—
185	C₄⋊C₄	—	118	1	no	—
186	C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
187	C₄⋊C₄	D₂₃₆	1	2	yes	—
188	C₂²⋊C₄	—	118	2	no	—
189	C₂²⋊C₄	—	118	1	no	—
190	C₂²⋊C₄	—	118	2	no	—
191	C₄²	—	118	2	no	—
192	C₄²	—	118	2	no	—
193	C₄²	—	118	1	no	—
194	C₄²	C₂²×D₅₉	1	1	yes	characteristic
195	C₄²	C₂²×D₅₉	1	2	yes	—
196	C₂³	—	118	1	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	118	1	no	—
199	Q₈	—	118	2	no	—
200	Q₈	—	118	2	no	—
201	Q₈	—	118	2	no	—
202	Q₈	—	118	2	no	—
203	Q₈	—	118	1	no	—
204	D₄	—	118	1	no	—
205	D₄	—	118	1	no	—
206	C₂×C₄	—	118	1	no	—
207	C₂×C₄	—	118	1	no	—
208	C₂×C₄	—	118	2	no	—
209	C₂×C₄	—	118	1	no	—
210	C₂×C₄	—	118	2	no	—
211	C₂×C₄	—	236	2	no	—
212	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
213	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
214	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
215	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
216	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
217	C₈	—	2	2	no	—
218	C₈	—	2	1	no	—
219	C₈	#11745689	1	2	yes	—
220	C₂²	—	236	1	no	—
221	C₂²	—	236	1	no	—
222	C₂²	—	236	1	no	—
223	C₂²	C₂²×D₂₃₆	1	1	yes	characteristic
224	C₄	—	2	2	no	—
225	C₄	—	2	2	no	—
226	C₄	—	2	1	no	—
227	C₄	—	236	1	no	—
228	C₄	—	236	1	no	—
229	C₄	—	236	2	no	—
230	C₄	—	236	1	no	—
231	C₄	—	236	2	no	—
232	C₄	#14273760	1	2	yes	—
233	C₄	C₂×#11745689	1	1	yes	characteristic
234	C₄	#14273773	1	1	yes	characteristic
235	C₂	—	472	1	no	—
236	C₂	#16838074	1	1	yes	characteristic
237	C₂	C₂×#14273760	1	1	yes	characteristic
238	C₂	#16838219	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838131

C₂

yes

maximal, characteristic, complemented

#16838125

C₂

yes

maximal, characteristic

#16837796

C₂

yes

maximal

#16837782

C₂

yes

maximal, characteristic, complemented

#16837625

C₂

yes

maximal

#16837613

C₂

yes

maximal, characteristic, complemented

#16837613

C₂

yes

maximal, complemented

#16837608

C₂

yes

maximal, characteristic

#16837510

C₂

yes

maximal, complemented

C₄×#11745660

C₂

yes

maximal, characteristic

C₅₉×#446

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₃₆

C₂²

yes

—

C₂×Dic₂₃₆

C₂²

yes

—

C₂×Dic₂₃₆

C₂²

yes

—

C₂×#11745660

C₂²

yes

characteristic

C₂×#11745660

C₂²

yes

—

#14273727

C₂²

yes

characteristic

#14273727

C₂²

yes

characteristic

#14273727

C₂²

yes

—

—

—

—

C₂²

yes

—

#14273703

—

Q₈×Dic₅₉

—

C₄×Dic₁₁₈

C₂²

yes

characteristic

C₄×Dic₁₁₈

C₂²

yes

—

C₄×Dic₁₁₈

C₂²

yes

—

C₄×D₂₃₆

C₂²

yes

characteristic

#14273685

—

#14273659

C₂²

yes

characteristic

#14273652

C₂²

yes

characteristic

#14273652

C₂²

yes

—

#14273652

C₂²

yes

—

#14273649

C₂²

yes

characteristic

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

C₂²

yes

—

#97×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

D₄

yes

characteristic

C₂×D₂₃₆

C₂³

yes

characteristic

C₂×C₄×D₅₉

—

C₂×Dic₁₁₈

C₂³

yes

—

C₂×Dic₁₁₈

C₂³

yes

characteristic

C₂×Dic₁₁₈

C₂³

yes

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

—

C₄²×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂³

yes

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

characteristic

C₄⋊Dic₅₉

C₂³

yes

characteristic

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

#11745660

—

#11745660

—

C₂²×D₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

D₂₃₆

—

C₄×D₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

#41

yes

—

100

C₂²×C₅₉

C₂²×D₄

yes

characteristic

101

C₂×D₅₉

—

102

C₂×D₅₉

—

103

C₂×D₅₉

—

104

C₄×C₅₉

—

105

C₄×C₅₉

—

106

C₄×C₅₉

—

107

C₄×C₅₉

#137

yes

—

108

C₄×C₅₉

C₂×#41

yes

characteristic

109

C₄×C₅₉

H(5,𝔽₂)

yes

characteristic

110

Dic₅₉

—

111

Dic₅₉

—

112

Dic₅₉

—

113

Dic₅₉

—

114

Dic₅₉

—

115

#3398

—

maximal, Sylow

116

C₂×C₅₉

#550

yes

characteristic

117

C₂×C₅₉

C₂×#137

yes

characteristic

118

C₂×C₅₉

#578

yes

characteristic

119

D₅₉

—

120

#557

—

121

#556

—

122

#497

—

123

#494

—

124

#464

—

125

#462

—

126

#462

—

127

#461

—

128

#446

D₅₉

yes

characteristic, complemented

129

#441

—

130

C₄×SD₁₆

—

131

C₅₉

#3398

yes

characteristic, complemented, Sylow

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

—

135

C₂×SD₁₆

—

136

C₂×SD₁₆

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

#126

—

118

—

141

#125

—

118

—

142

#125

—

118

—

143

#124

—

144

C₂²⋊Q₈

—

118

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

118

—

149

C₄×Q₈

C₂×D₅₉

yes

characteristic

150

C₄×D₄

—

151

#117

—

118

—

152

#106

—

153

C₄⋊C₈

C₂×D₅₉

yes

characteristic

154

C₄⋊C₈

C₂×D₅₉

yes

—

155

#103

—

156

#103

—

157

#103

—

158

#102

—

159

#97

C₂×D₅₉

yes

—

160

C₄×C₈

C₂×D₅₉

yes

characteristic

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

D₂₃₆

yes

characteristic

165

C₂×D₄

—

166

C₂²×C₄

—

118

—

167

Q₁₆

—

118

—

168

Q₁₆

—

236

—

169

Q₁₆

—

236

—

170

SD₁₆

—

118

—

171

SD₁₆

—

236

—

172

C₂×C₈

C₂²×D₅₉

yes

characteristic

173

C₂×C₈

C₂²×D₅₉

yes

—

174

C₂×C₈

C₂²×D₅₉

yes

characteristic

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

118

—

178

C₄⋊C₄

—

118

—

179

C₄⋊C₄

—

118

—

180

C₄⋊C₄

—

118

—

181

C₄⋊C₄

—

118

—

182

C₄⋊C₄

—

118

—

183

C₄⋊C₄

—

118

—

184

C₄⋊C₄

—

118

—

185

C₄⋊C₄

—

118

—

186

C₄⋊C₄

D₂₃₆

yes

characteristic

187

C₄⋊C₄

D₂₃₆

yes

—

188

C₂²⋊C₄

—

118

—

189

C₂²⋊C₄

—

118

—

190

C₂²⋊C₄

—

118

—

191

C₄²

—

118

—

192

C₄²

—

118

—

193

C₄²

—

118

—

194

C₄²

C₂²×D₅₉

yes

characteristic

195

C₄²

C₂²×D₅₉

yes

—

196

C₂³

—

118

—

197

Q₈

—

198

Q₈

—

118

—

199

Q₈

—

118

—

200

Q₈

—

118

—

201

Q₈

—

118

—

202

Q₈

—

118

—

203

Q₈

—

118

—

204

D₄

—

118

—

205

D₄

—

118

—

206

C₂×C₄

—

118

—

207

C₂×C₄

—

118

—

208

C₂×C₄

—

118

—

209

C₂×C₄

—

118

—

210

C₂×C₄

—

118

—

211

C₂×C₄

—

236

—

212

C₂×C₄

C₂×D₂₃₆

yes

—

213

C₂×C₄

C₂×D₂₃₆

yes

—

214

C₂×C₄

C₂×D₂₃₆

yes

characteristic

215

C₂×C₄

C₂×D₂₃₆

yes

characteristic

216

C₂×C₄

C₂³×D₅₉

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

#11745689

yes

—

220

C₂²

—

236

—

221

C₂²

—

236

—

222

C₂²

—

236

—

223

C₂²

C₂²×D₂₃₆

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

236

—

228

C₄

—

236

—

229

C₄

—

236

—

230

C₄

—

236

—

231

C₄

—

236

—

232

C₄

#14273760

yes

—

233

C₄

C₂×#11745689

yes

characteristic

234

C₄

#14273773

yes

characteristic

235

C₂

—

472

—

236

C₂

#16838074

yes

characteristic

237

C₂

C₂×#14273760

yes

characteristic

238

C₂

#16838219

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#446	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#446	D₅₉
hypocenter	C₅₉	#3398
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

subgroup

G/H

center

C₂²

C₂²×D₂₃₆

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#446

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

N	H ≅ G/N	type
1. #16838131	C₂	semidirect
4. #16837782	C₂	semidirect
6. #16837613	C₂	semidirect
7. #16837613	C₂	semidirect
9. #16837510	C₂	semidirect
11. C₅₉×#446	C₂	semidirect
128. #446	D₅₉	semidirect
131. C₅₉	#3398	semidirect

H ≅ G/N

type

1. #16838131

C₂

semidirect

4. #16837782

C₂

semidirect

6. #16837613

C₂

semidirect

7. #16837613

C₂

semidirect

9. #16837510

C₂

semidirect

11. C₅₉×#446

C₂

semidirect

128. #446

D₅₉

semidirect

131. C₅₉

#3398

semidirect

Subgroups — #21437129

Conjugacy classes of subgroups

Complements