Group #28506144 — subgroups

Subgroups — #28506144

Order 15104.

458 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 131 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	#21437199	C₂	1	1	yes	maximal, characteristic
2	#21425816	C₂	1	2	yes	maximal, complemented
3	#21424142	C₂	1	1	yes	maximal, characteristic
4	#21422197	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3059	C₂	1	1	yes	maximal, characteristic
6	#16837819	—	2	4	no	—
7	C₂×#14273667	—	2	2	no	—
8	C₂×#14273667	C₂²	1	2	yes	—
9	#16837440	C₂²	1	2	yes	—
10	#16837376	—	2	1	no	—
11	#16837206	—	2	4	no	—
12	#16837159	—	2	1	no	—
13	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
15	C₅₉×#536	—	2	1	no	—
16	C₅₉×#470	C₄	1	4	yes	complemented
17	C₅₉×#467	—	2	2	no	—
18	C₅₉×#427	C₂²	1	1	yes	characteristic
19	C₅₉×#419	—	2	1	no	—
20	#14273686	—	2	2	no	—
21	#14273667	—	2	4	no	—
22	#14273667	—	2	2	no	—
23	#14273667	—	2	2	no	—
24	C₂×C₅₉⋊C₁₆	—	2	4	no	—
25	C₂×C₅₉⋊C₁₆	D₄	1	4	yes	—
26	#14273661	—	2	2	no	—
27	#14273659	—	2	2	no	—
28	#14273642	—	4	2	no	—
29	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
30	C₂²×Q₈×C₅₉	—	2	1	no	—
31	C₂×Q₁₆×C₅₉	—	2	2	no	—
32	C₂×Q₁₆×C₅₉	—	2	1	no	—
33	C₂×Q₁₆×C₅₉	—	2	2	no	—
34	C₂×Q₁₆×C₅₉	C₂×C₄	1	2	yes	—
35	#131×C₅₉	—	2	2	no	—
36	#131×C₅₉	—	2	2	no	—
37	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₅₉	D₄	1	2	yes	—
40	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
41	C₄⋊Q₈×C₅₉	—	4	1	no	—
42	#124×C₅₉	—	4	1	no	—
43	#123×C₅₉	—	4	2	no	—
44	C₂²⋊Q₈×C₅₉	—	2	4	no	—
45	#117×C₅₉	—	2	1	no	—
46	#107×C₅₉	—	2	1	no	—
47	#106×C₅₉	C₂×C₄	1	2	yes	—
48	#103×C₅₉	—	2	4	no	—
49	#41×C₅₉	—	2	2	no	—
50	#41×C₅₉	—	2	2	no	—
51	C₂×Q₈×C₅₉	—	2	2	no	—
52	C₂×Q₈×C₅₉	—	4	1	no	—
53	C₂×Q₈×C₅₉	—	4	2	no	—
54	C₂×Q₈×C₅₉	—	4	2	no	—
55	C₂×Q₈×C₅₉	SD₁₆	1	1	yes	characteristic
56	C₂×D₄×C₅₉	D₈	1	2	yes	—
57	C₂×D₄×C₅₉	SD₁₆	1	1	yes	characteristic
58	C₂²×C₄×C₅₉	—	4	1	no	—
59	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₅₉	—	2	4	no	—
62	Q₁₆×C₅₉	—	4	1	no	—
63	Q₁₆×C₅₉	—	4	1	no	—
64	M₁₆×C₅₉	—	2	2	no	—
65	M₁₆×C₅₉	—	2	4	no	—
66	C₂×C₈×C₅₉	—	2	2	no	—
67	C₂×C₈×C₅₉	—	2	2	no	—
68	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
69	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
71	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₅₉	#41	1	2	yes	—
73	C₄⋊C₄×C₅₉	—	2	2	no	—
74	C₄⋊C₄×C₅₉	—	4	4	no	—
75	C₂²⋊C₄×C₅₉	—	4	4	no	—
76	C₂²⋊C₄×C₅₉	—	4	1	no	—
77	C₄²×C₅₉	—	4	1	no	—
78	C₂²⋊Dic₅₉	—	4	2	no	—
79	C₄⋊Dic₅₉	—	4	2	no	—
80	C₄×Dic₅₉	—	4	2	no	—
81	C₅₉⋊C₁₆	—	2	4	no	—
82	C₂³×C₅₉	#102	1	2	yes	—
83	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
84	Q₈×C₅₉	—	2	2	no	—
85	Q₈×C₅₉	—	4	2	no	—
86	Q₈×C₅₉	—	4	2	no	—
87	Q₈×C₅₉	—	8	2	no	—
88	D₄×C₅₉	—	2	4	no	—
89	D₄×C₅₉	—	2	2	no	—
90	C₂×C₄×C₅₉	—	2	2	no	—
91	C₂×C₄×C₅₉	—	2	2	no	—
92	C₂×C₄×C₅₉	—	4	2	no	—
93	C₂×C₄×C₅₉	—	4	2	no	—
94	C₂×C₄×C₅₉	—	8	2	no	—
95	C₂×C₄×C₅₉	#102	1	2	yes	—
96	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₅₉	#121	1	2	yes	—
98	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
99	C₂×C₄×C₅₉	#135	1	2	yes	—
100	C₂×Dic₅₉	—	8	2	no	—
101	C₈×C₅₉	—	2	2	no	—
102	C₈×C₅₉	C₄×D₄	1	2	yes	—
103	C₈×C₅₉	#120	1	1	yes	characteristic
104	C₈×C₅₉	#123	1	1	yes	characteristic
105	#13075	—	59	1	no	maximal, Sylow
106	C₂²×C₅₉	—	2	2	no	—
107	C₂²×C₅₉	—	4	1	no	—
108	C₂²×C₅₉	—	4	2	no	—
109	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
110	C₂²×C₅₉	#466	1	2	yes	—
111	C₄×C₅₉	—	2	2	no	—
112	C₄×C₅₉	—	8	2	no	—
113	C₄×C₅₉	—	8	2	no	—
114	C₄×C₅₉	#386	1	1	yes	characteristic
115	C₄×C₅₉	#416	1	1	yes	characteristic
116	C₄×C₅₉	#465	1	2	yes	—
117	Dic₅₉	—	16	2	no	—
118	#3407	—	59	1	no	—
119	#3059	D₅₉	1	1	yes	characteristic
120	#2141	—	59	2	no	—
121	#1812	—	59	1	no	—
122	#1384	—	59	2	no	—
123	C₂×C₅₉	—	2	2	no	—
124	C₂×C₅₉	—	2	1	no	—
125	C₂×C₅₉	—	4	2	no	—
126	C₂×C₅₉	#1893	1	1	yes	characteristic
127	C₂²×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
128	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
129	#536	—	2	1	no	—
130	#504	—	118	4	no	—
131	C₂×M₃₂	—	59	2	no	—
132	C₂×M₃₂	—	118	2	no	—
133	#470	Dic₅₉	1	4	yes	complemented
134	#467	—	2	2	no	—
135	#427	—	59	2	no	—
136	#427	C₂×D₅₉	1	1	yes	characteristic
137	#419	—	2	1	no	—
138	#410	—	118	1	no	—
139	#358	—	118	4	no	—
140	H(3,ℤ/4)	—	118	1	no	—
141	C₅₉	#13075	1	1	yes	characteristic, complemented, Sylow
142	C₂×#41	C₂²⋊D₅₉	1	1	yes	characteristic
143	C₂²×Q₈	—	2	1	no	—
144	C₂×Q₁₆	—	2	2	no	—
145	C₂×Q₁₆	—	2	2	no	—
146	C₂×Q₁₆	—	2	1	no	—
147	C₂×Q₁₆	C₂×Dic₅₉	1	2	yes	—
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	C₂×M₁₆	C₂×Dic₅₉	1	2	yes	—
151	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
152	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
153	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
154	C₄⋊Q₈	—	4	1	no	—
155	#124	—	4	1	no	—
156	#123	—	4	2	no	—
157	C₂²⋊Q₈	—	2	4	no	—
158	#117	—	2	1	no	—
159	#117	—	118	2	no	—
160	M₃₂	—	118	4	no	—
161	M₃₂	—	118	2	no	—
162	M₃₂	—	118	2	no	—
163	C₂×C₁₆	—	59	4	no	—
164	C₂×C₁₆	—	118	4	no	—
165	#107	—	2	1	no	—
166	#107	—	118	2	no	—
167	#106	—	118	2	no	—
168	#106	C₂×Dic₅₉	1	2	yes	—
169	#103	—	2	4	no	—
170	#99	—	236	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	#11745670	1	1	yes	characteristic
178	C₂×D₄	#11745669	1	2	yes	—
179	C₂×D₄	#11745670	1	1	yes	characteristic
180	C₂²×C₄	—	4	1	no	—
181	C₂²×C₄	C₂²⋊Dic₅₉	1	2	yes	—
182	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
183	Q₁₆	—	2	4	no	—
184	Q₁₆	—	4	1	no	—
185	Q₁₆	—	4	1	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	4	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	C₂²⋊Dic₅₉	1	2	yes	—
191	C₂×C₈	D₄×D₅₉	1	2	yes	—
192	C₂×C₈	#11745687	1	2	yes	—
193	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
194	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	4	4	no	—
197	C₄⋊C₄	—	236	2	no	—
198	C₂²⋊C₄	—	4	4	no	—
199	C₂²⋊C₄	—	4	1	no	—
200	C₂²⋊C₄	—	236	2	no	—
201	C₄²	—	4	1	no	—
202	C₄²	—	236	2	no	—
203	C₁₆	—	118	4	no	—
204	C₂³	#14273648	1	2	yes	—
205	C₂³	C₂×#11745669	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	4	2	no	—
209	Q₈	—	8	2	no	—
210	D₄	—	2	4	no	—
211	D₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	472	2	no	—
218	C₂×C₄	#14273648	1	2	yes	—
219	C₂×C₄	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
220	C₂×C₄	#14273699	1	2	yes	—
221	C₂×C₄	C₂×#11745670	1	1	yes	characteristic
222	C₂×C₄	#14273747	1	2	yes	—
223	C₈	—	2	2	no	—
224	C₈	D₄×Dic₅₉	1	2	yes	—
225	C₈	#14273695	1	1	yes	characteristic
226	C₈	#14273708	1	1	yes	characteristic
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂×#14273648	1	1	yes	characteristic
231	C₂²	#16837636	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	8	2	no	—
234	C₄	—	8	2	no	—
235	C₄	—	944	2	no	—
236	C₄	#16837282	1	1	yes	characteristic
237	C₄	#16837398	1	1	yes	characteristic
238	C₄	#16837629	1	2	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#21424525	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21437199

C₂

yes

maximal, characteristic

#21425816

C₂

yes

maximal, complemented

#21424142

C₂

yes

maximal, characteristic

#21422197

C₂

yes

maximal, complemented

C₅₉×#3059

C₂

yes

maximal, characteristic

#16837819

—

C₂×#14273667

—

C₂×#14273667

C₂²

yes

—

#16837440

C₂²

yes

—

#16837376

—

#16837206

—

#16837159

—

C₂²×Q₁₆×C₅₉

C₂²

yes

characteristic

C₂×#131×C₅₉

C₂²

yes

characteristic

C₅₉×#536

—

C₅₉×#470

C₄

yes

complemented

C₅₉×#467

—

C₅₉×#427

C₂²

yes

characteristic

C₅₉×#419

—

—

—

—

—

C₂×C₅₉⋊C₁₆

—

C₂×C₅₉⋊C₁₆

D₄

yes

—

#14273661

—

#14273659

—

#14273642

—

C₂×#41×C₅₉

D₄

yes

characteristic

C₂²×Q₈×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

C₂×C₄

yes

—

#131×C₅₉

—

#131×C₅₉

—

C₂×M₁₆×C₅₉

C₂×C₄

yes

—

C₂×M₁₆×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

D₄

yes

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊Q₈×C₅₉

—

#124×C₅₉

—

#123×C₅₉

—

C₂²⋊Q₈×C₅₉

—

#117×C₅₉

—

#107×C₅₉

—

#106×C₅₉

C₂×C₄

yes

—

#103×C₅₉

—

#41×C₅₉

—

#41×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

SD₁₆

yes

characteristic

C₂×D₄×C₅₉

D₈

yes

—

C₂×D₄×C₅₉

SD₁₆

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

#41

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

#102

yes

—

C₂³×C₅₉

C₂×D₈

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

#121

yes

—

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

#135

yes

—

100

C₂×Dic₅₉

—

101

C₈×C₅₉

—

102

C₈×C₅₉

C₄×D₄

yes

—

103

C₈×C₅₉

#120

yes

characteristic

104

C₈×C₅₉

yes

105

—

106

C₂²×C₅₉

—

107

C₂²×C₅₉

—

108

C₂²×C₅₉

—

109

C₂²×C₅₉

C₂×#102

yes

characteristic

110

C₂²×C₅₉

#466

yes

—

111

C₄×C₅₉

—

112

C₄×C₅₉

—

113

C₄×C₅₉

—

114

C₄×C₅₉

#386

yes

characteristic

115

C₄×C₅₉

#416

yes

characteristic

116

C₄×C₅₉

#465

yes

—

117

Dic₅₉

—

118

#3407

—

119

#3059

D₅₉

yes

characteristic

120

#2141

—

121

#1812

—

122

#1384

—

123

C₂×C₅₉

—

124

C₂×C₅₉

—

125

C₂×C₅₉

—

126

C₂×C₅₉

#1893

yes

characteristic

127

C₂²×Q₁₆

C₂×D₅₉

yes

characteristic

128

C₂×#131

C₂×D₅₉

yes

characteristic

129

#536

—

130

#504

—

118

—

131

C₂×M₃₂

—

132

C₂×M₃₂

—

118

—

133

#470

Dic₅₉

yes

complemented

134

#467

—

135

#427

—

136

#427

C₂×D₅₉

yes

characteristic

137

#419

—

138

#410

—

118

—

139

#358

—

118

—

140

H(3,ℤ/4)

—

118

—

141

C₅₉

#13075

yes

characteristic, complemented, Sylow

142

C₂×#41

C₂²⋊D₅₉

yes

characteristic

143

C₂²×Q₈

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

C₂×Dic₅₉

yes

—

148

#131

—

149

#131

—

150

C₂×M₁₆

C₂×Dic₅₉

yes

—

151

C₂×M₁₆

C₂²⋊D₅₉

yes

characteristic

152

C₂²×C₈

C₂²⋊D₅₉

yes

—

153

C₂²×C₈

C₂²×D₅₉

yes

characteristic

154

C₄⋊Q₈

—

155

#124

—

156

#123

—

157

C₂²⋊Q₈

—

158

#117

—

159

#117

—

118

—

160

M₃₂

—

118

—

161

M₃₂

—

118

—

162

M₃₂

—

118

—

163

C₂×C₁₆

—

164

C₂×C₁₆

—

118

—

165

#107

—

166

#107

—

118

—

167

#106

—

118

—

168

#106

C₂×Dic₅₉

yes

—

169

#103

—

170

#99

—

236

—

171

#41

—

172

#41

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

#11745670

yes

characteristic

178

C₂×D₄

#11745669

yes

—

179

C₂×D₄

#11745670

yes

characteristic

180

C₂²×C₄

—

181

C₂²×C₄

C₂²⋊Dic₅₉

yes

—

182

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

183

Q₁₆

—

184

Q₁₆

—

185

Q₁₆

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

C₂²⋊Dic₅₉

yes

—

191

C₂×C₈

D₄×D₅₉

yes

—

192

C₂×C₈

#11745687

yes

—

193

C₂×C₈

C₂²×Dic₅₉

yes

characteristic

194

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

236

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

236

—

201

C₄²

—

202

C₄²

—

236

—

203

C₁₆

—

118

—

204

C₂³

#14273648

yes

—

205

C₂³

C₂×#11745669

yes

characteristic

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

Q₈

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

472

—

218

C₂×C₄

#14273648

yes

—

219

C₂×C₄

C₂×C₂²⋊Dic₅₉

yes

characteristic

220

C₂×C₄

#14273699

yes

—

221

C₂×C₄

C₂×#11745670

yes

characteristic

222

C₂×C₄

#14273747

yes

—

223

C₈

—

224

C₈

D₄×Dic₅₉

yes

—

225

C₈

#14273695

yes

characteristic

226

C₈

#14273708

yes

characteristic

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂×#14273648

yes

characteristic

231

C₂²

#16837636

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

944

—

236

C₄

#16837282

yes

characteristic

237

C₄

#16837398

yes

characteristic

238

C₄

#16837629

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#21424525

yes

characteristic

	subgroup	G/H
center	C₂	#21424525
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#3059	C₂
socle	C₂×C₅₉	#1893
prime radical	C₂×#41×C₅₉	D₄
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#3059	D₅₉
hypocenter	C₅₉	#13075
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

subgroup

G/H

center

C₂

#21424525

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#3059

C₂

socle

C₂×C₅₉

#1893

prime radical

C₂×#41×C₅₉

D₄

cosocle

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

N	H ≅ G/N	type
2. #21425816	C₂	semidirect
4. #21422197	C₂	semidirect
16. C₅₉×#470	C₄	semidirect
133. #470	Dic₅₉	semidirect
141. C₅₉	#13075	semidirect

H ≅ G/N

type

2. #21425816

C₂

semidirect

4. #21422197

C₂

semidirect

16. C₅₉×#470

C₄

semidirect

133. #470

Dic₅₉

semidirect

141. C₅₉

#13075

semidirect

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

subgroup	index
#21437199	2
#21425816	2
#21424142	2
#21422197	2
C₅₉×#3059	2
#13075	59

subgroup

index

C₅₉×#3059

Subgroups — #28506144

Conjugacy classes of subgroups

Complements

Maximal subgroups