Group #21425241 — subgroups

Subgroups — #21425241

Order 7552.

294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14273718	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14273649	C₂	1	1	yes	maximal, characteristic
3	C₂×#14273647	C₂	1	1	yes	maximal, characteristic
4	#16837303	C₂	1	1	yes	maximal, characteristic
5	#16837164	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837156	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₂₃₆	C₂²	1	1	yes	characteristic
9	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
10	#14273718	—	2	2	no	—
11	#14273718	—	2	2	no	—
12	C₂×C₄⋊Dic₅₉	—	2	1	no	—
13	C₂×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₅₉⋊C₄	—	2	1	no	—
15	C₂×(C₂×D₅₉)⋊C₄	—	2	1	no	—
16	C₂×(C₂×D₅₉)⋊C₄	—	2	1	no	—
17	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
18	#14273649	—	2	2	no	—
19	#14273647	—	2	2	no	—
20	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
23	C₂³×D₅₉	—	2	1	no	—
24	C₂²×C₄×C₅₉	—	2	1	no	—
25	C₂²×C₄×C₅₉	—	2	1	no	—
26	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₅₉	—	2	1	no	—
28	C₂²×Dic₅₉	D₄	1	1	yes	characteristic
29	C₂²×Dic₅₉	D₄	1	1	yes	characteristic
30	C₂×D₂₃₆	—	2	1	no	—
31	C₂×D₂₃₆	—	2	1	no	—
32	C₂×D₂₃₆	—	2	1	no	—
33	C₂×D₂₃₆	—	2	1	no	—
34	C₂×D₂₃₆	—	2	1	no	—
35	C₂×D₂₃₆	Q₈	1	2	yes	—
36	C₂×C₈×C₅₉	—	2	1	no	—
37	C₂×C₈×C₅₉	—	2	1	no	—
38	C₂×C₈×C₅₉	—	2	1	no	—
39	C₄⋊C₄×C₅₉	—	2	1	no	—
40	C₄⋊C₄×C₅₉	—	2	1	no	—
41	C₄⋊C₄×C₅₉	—	2	1	no	—
42	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
43	(C₂×D₅₉)⋊C₄	—	4	2	no	—
44	(C₂×D₅₉)⋊C₄	—	4	2	no	—
45	C₄⋊Dic₅₉	—	2	4	no	—
46	C₄⋊Dic₅₉	—	2	1	no	—
47	C₄⋊Dic₅₉	D₄	1	2	yes	—
48	Dic₅₉⋊C₄	—	2	4	no	—
49	C₄×Dic₅₉	—	2	1	no	—
50	C₄×Dic₅₉	—	2	1	no	—
51	C₂×C₅₉⋊C₈	—	2	1	no	—
52	C₂×C₅₉⋊C₈	—	2	1	no	—
53	C₂×C₅₉⋊C₈	—	2	1	no	—
54	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×D₅₉	—	2	2	no	—
56	C₂²×D₅₉	—	4	1	no	—
57	C₂²×D₅₉	—	4	1	no	—
58	C₂²×D₅₉	—	4	1	no	—
59	C₂²×D₅₉	—	4	1	no	—
60	C₂²×D₅₉	—	4	1	no	—
61	C₂²×D₅₉	—	4	1	no	—
62	C₂×C₄×C₅₉	—	2	2	no	—
63	C₂×C₄×C₅₉	—	4	1	no	—
64	C₂×C₄×C₅₉	—	4	1	no	—
65	C₂×C₄×C₅₉	—	4	1	no	—
66	C₂×C₄×C₅₉	—	4	1	no	—
67	C₂×C₄×C₅₉	—	4	1	no	—
68	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
71	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
72	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
73	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
74	C₂×Dic₅₉	—	2	1	no	—
75	C₂×Dic₅₉	—	2	1	no	—
76	C₂×Dic₅₉	—	2	2	no	—
77	C₂×Dic₅₉	—	2	1	no	—
78	C₂×Dic₅₉	—	2	1	no	—
79	C₂×Dic₅₉	—	2	1	no	—
80	C₂×Dic₅₉	—	2	1	no	—
81	C₂×Dic₅₉	—	4	1	no	—
82	C₂×Dic₅₉	—	4	1	no	—
83	D₂₃₆	—	2	2	no	—
84	D₂₃₆	—	2	2	no	—
85	D₂₃₆	—	4	1	no	—
86	D₂₃₆	—	4	1	no	—
87	C₈×C₅₉	—	4	1	no	—
88	C₅₉⋊C₈	—	4	1	no	—
89	C₂²×C₅₉	#120	1	1	yes	characteristic
90	C₂²×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂²×C₅₉	#124	1	1	yes	characteristic
92	C₂²×C₅₉	#135	1	1	yes	characteristic
93	C₂²×C₅₉	#135	1	1	yes	characteristic
94	C₂²×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂²×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×D₅₉	—	4	2	no	—
97	C₂×D₅₉	—	4	2	no	—
98	C₂×D₅₉	—	4	2	no	—
99	C₂×D₅₉	—	8	1	no	—
100	C₂×D₅₉	—	8	1	no	—
101	C₂×D₅₉	—	8	1	no	—
102	C₂×D₅₉	—	8	1	no	—
103	C₄×C₅₉	—	4	2	no	—
104	C₄×C₅₉	—	8	1	no	—
105	C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
106	C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
107	C₄×C₅₉	#124	1	1	yes	characteristic
108	C₄×C₅₉	#124	1	1	yes	characteristic
109	Dic₅₉	—	4	1	no	—
110	Dic₅₉	—	4	1	no	—
111	Dic₅₉	—	4	2	no	—
112	#2025	—	59	1	no	maximal, Sylow
113	C₂×C₅₉	#393	1	1	yes	characteristic
114	C₂×C₅₉	#449	1	1	yes	characteristic
115	C₂×C₅₉	#449	1	1	yes	characteristic
116	C₂×C₅₉	#478	1	1	yes	characteristic
117	C₂×C₅₉	#478	1	1	yes	characteristic
118	C₂×C₅₉	#488	1	1	yes	characteristic
119	C₂×C₅₉	#490	1	1	yes	characteristic
120	D₅₉	—	8	2	no	—
121	C₂×#125	—	59	1	no	—
122	C₂×#102	—	59	1	no	—
123	C₂×#102	—	59	1	no	—
124	#390	—	59	1	no	—
125	#340	—	59	1	no	—
126	#340	D₅₉	1	1	yes	characteristic, complemented
127	#336	—	59	1	no	—
128	C₅₉	#2025	1	1	yes	characteristic, complemented, Sylow
129	C₂²×D₄	—	59	1	no	—
130	C₂²×C₈	—	59	1	no	—
131	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
132	#125	—	118	2	no	—
133	#125	—	118	2	no	—
134	C₂×C₄⋊C₄	—	59	1	no	—
135	C₂×C₄⋊C₄	—	118	1	no	—
136	C₂×C₄⋊C₄	—	118	1	no	—
137	C₂×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
138	C₂×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
139	C₂×C₂²⋊C₄	—	118	1	no	—
140	C₂×C₂²⋊C₄	—	118	1	no	—
141	C₂×C₄²	—	59	1	no	—
142	#102	—	118	2	no	—
143	#102	—	118	2	no	—
144	C₂⁴	—	118	1	no	—
145	C₂×D₄	—	59	2	no	—
146	C₂×D₄	—	118	1	no	—
147	C₂×D₄	—	118	1	no	—
148	C₂×D₄	—	118	1	no	—
149	C₂×D₄	—	118	1	no	—
150	C₂×D₄	—	118	1	no	—
151	C₂²×C₄	—	2	1	no	—
152	C₂²×C₄	—	2	1	no	—
153	C₂²×C₄	—	59	1	no	—
154	C₂²×C₄	—	59	1	no	—
155	C₂²×C₄	—	118	1	no	—
156	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
157	C₂×C₈	—	2	1	no	—
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	118	1	no	—
161	C₂×C₈	—	118	1	no	—
162	C₂×C₈	—	118	1	no	—
163	C₄⋊C₄	—	2	1	no	—
164	C₄⋊C₄	—	2	1	no	—
165	C₄⋊C₄	—	2	1	no	—
166	C₄⋊C₄	—	59	2	no	—
167	C₄⋊C₄	—	118	4	no	—
168	C₄⋊C₄	—	118	4	no	—
169	C₄⋊C₄	—	118	1	no	—
170	C₄⋊C₄	D₂₃₆	1	2	yes	—
171	C₂²⋊C₄	—	236	2	no	—
172	C₂²⋊C₄	—	236	2	no	—
173	C₄²	—	118	1	no	—
174	C₄²	—	118	1	no	—
175	C₂³	—	118	2	no	—
176	C₂³	—	236	1	no	—
177	C₂³	—	236	1	no	—
178	C₂³	—	236	1	no	—
179	C₂³	—	236	1	no	—
180	C₂³	—	236	1	no	—
181	C₂³	—	236	1	no	—
182	C₂³	D₄×D₅₉	1	1	yes	characteristic
183	D₄	—	118	2	no	—
184	D₄	—	118	2	no	—
185	D₄	—	236	1	no	—
186	D₄	—	236	1	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	—	4	1	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	118	1	no	—
194	C₂×C₄	—	118	1	no	—
195	C₂×C₄	—	118	2	no	—
196	C₂×C₄	—	118	1	no	—
197	C₂×C₄	—	118	1	no	—
198	C₂×C₄	—	118	1	no	—
199	C₂×C₄	—	118	1	no	—
200	C₂×C₄	—	236	1	no	—
201	C₂×C₄	—	236	1	no	—
202	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
203	C₂×C₄	#11745685	1	1	yes	characteristic
204	C₂×C₄	#11745685	1	1	yes	characteristic
205	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
206	C₂×C₄	#11745687	1	1	yes	characteristic
207	C₂×C₄	Q₈×D₅₉	1	1	yes	characteristic
208	C₈	—	4	1	no	—
209	C₈	—	236	1	no	—
210	C₂²	—	472	1	no	—
211	C₂²	—	472	1	no	—
212	C₂²	—	472	1	no	—
213	C₂²	—	472	1	no	—
214	C₂²	—	236	2	no	—
215	C₂²	—	236	2	no	—
216	C₂²	—	236	2	no	—
217	C₂²	#14273697	1	1	yes	characteristic
218	C₂²	#14273705	1	1	yes	characteristic
219	C₂²	#14273713	1	1	yes	characteristic
220	C₂²	#14273748	1	1	yes	characteristic
221	C₂²	#14273750	1	1	yes	characteristic
222	C₂²	#14273751	1	1	yes	characteristic
223	C₂²	#14273754	1	1	yes	characteristic
224	C₄	—	4	2	no	—
225	C₄	—	8	1	no	—
226	C₄	—	236	1	no	—
227	C₄	—	236	1	no	—
228	C₄	—	236	2	no	—
229	C₄	#14273705	1	1	yes	characteristic
230	C₄	#14273707	1	1	yes	characteristic
231	C₄	#14273713	1	1	yes	characteristic
232	C₄	#14273715	1	1	yes	characteristic
233	C₂	—	472	2	no	—
234	C₂	#16837315	1	1	yes	characteristic
235	C₂	#16837548	1	1	yes	characteristic
236	C₂	#16837550	1	1	yes	characteristic
237	C₂	#16837701	1	1	yes	characteristic
238	C₂	#16837705	1	1	yes	characteristic
239	C₂	#16837758	1	1	yes	characteristic
240	C₂	#16837765	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273718

C₂

yes

maximal, characteristic, complemented

C₂×#14273649

C₂

yes

maximal, characteristic

C₂×#14273647

C₂

yes

maximal, characteristic

#16837303

C₂

yes

maximal, characteristic

#16837164

C₂

yes

maximal, characteristic, complemented

#16837156

C₂

yes

maximal, characteristic, complemented

C₅₉×#340

C₂

yes

maximal, characteristic, complemented

C₂²×D₂₃₆

C₂²

yes

characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

characteristic

#14273718

—

#14273718

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

C₂²

yes

characteristic

C₂×Dic₅₉⋊C₄

—

C₂×(C₂×D₅₉)⋊C₄

—

C₂×(C₂×D₅₉)⋊C₄

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

#14273649

—

#14273647

—

C₂²×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₅₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₅₉

C₂²

yes

characteristic

C₂³×D₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

D₄

yes

characteristic

C₂²×Dic₅₉

D₄

yes

characteristic

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

Q₈

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

D₄

yes

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

D₄

yes

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

#120

yes

characteristic

C₂²×C₅₉

C₂²⋊Q₈

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

100

C₂×D₅₉

—

101

C₂×D₅₉

—

102

C₂×D₅₉

—

103

C₄×C₅₉

—

104

C₄×C₅₉

—

105

C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

106

C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

107

C₄×C₅₉

#124

yes

characteristic

108

C₄×C₅₉

#124

yes

characteristic

109

Dic₅₉

—

110

Dic₅₉

—

111

Dic₅₉

—

112

#2025

—

maximal, Sylow

113

C₂×C₅₉

#393

yes

characteristic

114

C₂×C₅₉

#449

yes

characteristic

115

C₂×C₅₉

#449

yes

characteristic

116

C₂×C₅₉

#478

yes

characteristic

117

C₂×C₅₉

#478

yes

characteristic

118

C₂×C₅₉

#488

yes

characteristic

119

C₂×C₅₉

#490

yes

characteristic

120

D₅₉

—

121

C₂×#125

—

122

C₂×#102

—

123

C₂×#102

—

124

#390

—

125

#340

—

126

#340

D₅₉

yes

characteristic, complemented

127

#336

—

128

C₅₉

#2025

yes

characteristic, complemented, Sylow

129

C₂²×D₄

—

130

C₂²×C₈

—

131

C₂²×C₈

C₂×D₅₉

yes

characteristic

132

#125

—

118

—

133

#125

—

118

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

118

—

136

C₂×C₄⋊C₄

—

118

—

137

C₂×C₄⋊C₄

C₂×D₅₉

yes

characteristic

138

C₂×C₄⋊C₄

C₂×D₅₉

yes

characteristic

139

C₂×C₂²⋊C₄

—

118

—

140

C₂×C₂²⋊C₄

—

118

—

141

C₂×C₄²

—

142

#102

—

118

—

143

#102

—

118

—

144

C₂⁴

—

118

—

145

C₂×D₄

—

146

C₂×D₄

—

118

—

147

C₂×D₄

—

118

—

148

C₂×D₄

—

118

—

149

C₂×D₄

—

118

—

150

C₂×D₄

—

118

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

118

—

156

C₂²×C₄

C₂²×D₅₉

yes

characteristic

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

118

—

161

C₂×C₈

—

118

—

162

C₂×C₈

—

118

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

118

—

168

C₄⋊C₄

—

118

—

169

C₄⋊C₄

—

118

—

170

C₄⋊C₄

D₂₃₆

yes

—

171

C₂²⋊C₄

—

236

—

172

C₂²⋊C₄

—

236

—

173

C₄²

—

118

—

174

C₄²

—

118

—

175

C₂³

—

118

—

176

C₂³

—

236

—

177

C₂³

—

236

—

178

C₂³

—

236

—

179

C₂³

—

236

—

180

C₂³

—

236

—

181

C₂³

—

236

—

182

C₂³

D₄×D₅₉

yes

characteristic

183

D₄

—

118

—

184

D₄

—

118

—

185

D₄

—

236

—

186

D₄

—

236

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

118

—

194

C₂×C₄

—

118

—

195

C₂×C₄

—

118

—

196

C₂×C₄

—

118

—

197

C₂×C₄

—

118

—

198

C₂×C₄

—

118

—

199

C₂×C₄

—

118

—

200

C₂×C₄

—

236

—

201

C₂×C₄

—

236

—

202

C₂×C₄

C₂×D₂₃₆

yes

characteristic

203

C₂×C₄

#11745685

yes

characteristic

204

C₂×C₄

#11745685

yes

characteristic

205

C₂×C₄

D₄×D₅₉

yes

characteristic

206

C₂×C₄

#11745687

yes

characteristic

207

C₂×C₄

Q₈×D₅₉

yes

characteristic

208

C₈

—

209

C₈

—

236

—

210

C₂²

—

472

—

211

C₂²

—

472

—

212

C₂²

—

472

—

213

C₂²

—

472

—

214

C₂²

—

236

—

215

C₂²

—

236

—

216

C₂²

—

236

—

217

C₂²

#14273697

yes

characteristic

218

C₂²

#14273705

yes

characteristic

219

C₂²

#14273713

yes

characteristic

220

C₂²

#14273748

yes

characteristic

221

C₂²

#14273750

yes

characteristic

222

C₂²

#14273751

yes

characteristic

223

C₂²

#14273754

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

236

—

227

C₄

—

236

—

228

C₄

—

236

—

229

C₄

#14273705

yes

characteristic

230

C₄

#14273707

yes

characteristic

231

C₄

#14273713

yes

characteristic

232

C₄

#14273715

yes

characteristic

233

C₂

—

472

—

234

C₂

#16837315

yes

characteristic

235

C₂

#16837548

yes

characteristic

236

C₂

#16837550

yes

characteristic

237

C₂

#16837701

yes

characteristic

238

C₂

#16837705

yes

characteristic

239

C₂

#16837758

yes

characteristic

240

C₂

#16837765

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₅₉
commutator	C₂²×C₄×C₅₉	C₂³
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#340	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	#340	D₅₉
hypocenter	C₅₉	#2025
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₅₉

commutator

C₂²×C₄×C₅₉

C₂³

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₅₉×#340

C₂

socle

C₂³×C₅₉

C₂×D₄

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
1. C₂×#14273718	C₂	semidirect
5. #16837164	C₂	semidirect
6. #16837156	C₂	semidirect
7. C₅₉×#340	C₂	semidirect
126. #340	D₅₉	semidirect
128. C₅₉	#2025	semidirect

H ≅ G/N

type

1. C₂×#14273718

C₂

semidirect

5. #16837164

C₂

semidirect

6. #16837156

C₂

semidirect

7. C₅₉×#340

C₂

semidirect

126. #340

D₅₉

semidirect

128. C₅₉

#2025

semidirect

Subgroups — #21425241

Conjugacy classes of subgroups

Complements