Group #28505250 — subgroups

Subgroups — #28505250

Order 15104.

414 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 127 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×#16837440	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837226	C₂	1	2	yes	maximal, complemented
3	#21425707	C₂	1	1	yes	maximal, characteristic
4	#21422196	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1810	C₂	1	1	yes	maximal, characteristic
6	C₂×#14273686	—	2	1	no	—
7	C₂×#14273667	C₂²	1	2	yes	—
8	#16837440	—	2	4	no	—
9	C₂×#14273661	—	2	1	no	—
10	C₂×#14273659	C₂²	1	2	yes	—
11	#16837226	—	2	4	no	—
12	C₂²⋊(C₅₉⋊C₁₆)	C₄	1	4	yes	complemented
13	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#407	—	2	1	no	—
17	C₅₉×#341	—	2	1	no	—
18	#14273686	—	2	4	no	—
19	#14273686	—	4	2	no	—
20	C₂×C₄⋊Dic₅₉	—	2	2	no	—
21	C₂×C₂²⋊Dic₅₉	—	4	1	no	—
22	C₂×C₄×Dic₅₉	—	4	1	no	—
23	#14273667	—	2	2	no	—
24	#14273667	—	2	2	no	—
25	C₂×C₅₉⋊C₁₆	C₂×C₄	1	4	yes	—
26	#14273661	—	2	4	no	—
27	#14273659	—	2	2	no	—
28	#14273659	D₄	1	4	yes	—
29	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₅₉	—	2	1	no	—
31	C₂×M₁₆×C₅₉	—	2	1	no	—
32	C₂²×C₈×C₅₉	—	2	2	no	—
33	C₂²×C₈×C₅₉	—	2	2	no	—
34	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₅₉	Q₈	1	2	yes	—
37	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
38	#108×C₅₉	—	2	2	no	—
39	#108×C₅₉	—	2	2	no	—
40	C₂²⋊C₈×C₅₉	—	4	2	no	—
41	C₂⁴×C₅₉	SD₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₅₉	—	2	1	no	—
43	C₂²×C₄×C₅₉	—	2	1	no	—
44	C₂²×C₄×C₅₉	—	2	1	no	—
45	C₂²×C₄×C₅₉	—	2	1	no	—
46	C₂²×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₅₉	SD₁₆	1	1	yes	characteristic
48	C₂²×C₄×C₅₉	SD₁₆	1	2	yes	—
49	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₅₉	—	4	2	no	—
51	M₁₆×C₅₉	—	4	1	no	—
52	M₁₆×C₅₉	—	4	1	no	—
53	M₁₆×C₅₉	—	4	1	no	—
54	M₁₆×C₅₉	—	4	1	no	—
55	C₂×C₈×C₅₉	—	2	1	no	—
56	C₂×C₈×C₅₉	—	2	1	no	—
57	C₂×C₈×C₅₉	—	2	4	no	—
58	C₂×C₈×C₅₉	—	2	4	no	—
59	C₂×C₈×C₅₉	—	4	1	no	—
60	C₂×C₈×C₅₉	—	4	1	no	—
61	C₂×C₈×C₅₉	C₄⋊C₄	1	2	yes	—
62	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
64	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₈×C₅₉	#41	1	2	yes	—
66	C₂²⋊Dic₅₉	—	4	4	no	—
67	C₄⋊Dic₅₉	—	2	4	no	—
68	C₄⋊Dic₅₉	—	4	2	no	—
69	C₄×Dic₅₉	—	4	4	no	—
70	C₅₉⋊C₁₆	—	2	4	no	—
71	C₂³×C₅₉	—	2	1	no	—
72	C₂³×C₅₉	—	2	1	no	—
73	C₂³×C₅₉	—	4	2	no	—
74	C₂³×C₅₉	#106	1	2	yes	—
75	C₂³×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₅₉	—	2	1	no	—
77	C₂×C₄×C₅₉	—	2	1	no	—
78	C₂×C₄×C₅₉	—	2	2	no	—
79	C₂×C₄×C₅₉	—	2	2	no	—
80	C₂×C₄×C₅₉	—	2	2	no	—
81	C₂×C₄×C₅₉	—	2	2	no	—
82	C₂×C₄×C₅₉	#106	1	2	yes	—
83	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
85	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
86	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
89	C₂×Dic₅₉	—	4	4	no	—
90	C₂×Dic₅₉	—	8	4	no	—
91	C₈×C₅₉	—	2	2	no	—
92	C₈×C₅₉	—	8	1	no	—
93	C₈×C₅₉	—	8	1	no	—
94	C₈×C₅₉	C₄×D₄	1	2	yes	—
95	C₈×C₅₉	C₂²⋊Q₈	1	2	yes	—
96	#12930	—	59	1	no	maximal, Sylow
97	C₂²×C₅₉	—	2	2	no	—
98	C₂²×C₅₉	—	2	2	no	—
99	C₂²×C₅₉	—	2	4	no	—
100	C₂²×C₅₉	—	4	2	no	—
101	C₂²×C₅₉	—	4	2	no	—
102	C₂²×C₅₉	C₂×#106	1	1	yes	characteristic
103	C₂²×C₅₉	#450	1	1	yes	characteristic
104	C₂²×C₅₉	#483	1	1	yes	characteristic
105	C₄×C₅₉	—	2	2	no	—
106	C₄×C₅₉	#385	1	1	yes	characteristic
107	C₄×C₅₉	#428	1	1	yes	characteristic
108	C₄×C₅₉	#448	1	1	yes	characteristic
109	C₄×C₅₉	#481	1	1	yes	characteristic
110	Dic₅₉	—	8	4	no	—
111	C₂×#427	—	59	1	no	—
112	C₂×#365	—	59	2	no	—
113	#2112	—	59	1	no	—
114	#1810	D₅₉	1	1	yes	characteristic
115	#1383	—	59	2	no	—
116	C₂×C₅₉	—	2	1	no	—
117	C₂×C₅₉	—	2	1	no	—
118	C₂×C₅₉	—	4	2	no	—
119	C₂×C₅₉	#1853	1	1	yes	characteristic
120	C₂×C₅₉	#2155	1	2	yes	—
121	C₂³×C₈	C₂×D₅₉	1	1	yes	characteristic
122	C₂×#117	—	118	1	no	—
123	C₂×M₃₂	—	59	2	no	—
124	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
125	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
126	#427	—	118	4	no	—
127	C₂×#107	—	118	1	no	—
128	C₂×#106	—	59	2	no	—
129	#407	—	2	1	no	—
130	#365	—	118	4	no	—
131	C₂²⋊C₁₆	—	59	4	no	—
132	#341	—	2	1	no	—
133	C₅₉	#12930	1	1	yes	characteristic, complemented, Sylow
134	C₂³×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
135	C₂×M₁₆	—	2	1	no	—
136	C₂×M₁₆	—	2	1	no	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	Dic₁₁₈	1	2	yes	—
140	C₂²×C₈	C₄×D₅₉	1	2	yes	—
141	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
143	#117	—	118	4	no	—
144	#117	—	236	2	no	—
145	C₂×C₄⋊C₄	—	118	2	no	—
146	C₂×C₂²⋊C₄	—	236	1	no	—
147	C₂×C₄²	—	236	1	no	—
148	M₃₂	—	118	2	no	—
149	M₃₂	—	118	2	no	—
150	C₂×C₁₆	—	59	4	no	—
151	#108	—	2	2	no	—
152	#108	—	2	2	no	—
153	#107	—	118	4	no	—
154	#106	—	59	4	no	—
155	#106	—	118	2	no	—
156	C₂²⋊C₈	—	4	2	no	—
157	C₂⁴	#11745671	1	1	yes	characteristic
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	236	2	no	—
163	C₂²×C₄	Dic₅₉⋊C₄	1	2	yes	—
164	C₂²×C₄	#11745670	1	2	yes	—
165	C₂²×C₄	#11745671	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
167	M₁₆	—	4	1	no	—
168	M₁₆	—	4	1	no	—
169	M₁₆	—	4	1	no	—
170	M₁₆	—	4	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	Dic₅₉⋊C₄	1	2	yes	—
178	C₂×C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
179	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
180	C₂×C₈	D₄×D₅₉	1	2	yes	—
181	C₂×C₈	#11745687	1	2	yes	—
182	C₄⋊C₄	—	118	4	no	—
183	C₄⋊C₄	—	236	2	no	—
184	C₂²⋊C₄	—	236	4	no	—
185	C₄²	—	236	4	no	—
186	C₁₆	—	118	4	no	—
187	C₂³	—	2	1	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	4	2	no	—
190	C₂³	#14273658	1	2	yes	—
191	C₂³	C₂×#11745671	1	1	yes	characteristic
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	472	4	no	—
199	C₂×C₄	—	236	4	no	—
200	C₂×C₄	#14273658	1	2	yes	—
201	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
202	C₂×C₄	#14273695	1	1	yes	characteristic
203	C₂×C₄	#14273708	1	1	yes	characteristic
204	C₂×C₄	C₂×#11745670	1	1	yes	characteristic
205	C₂×C₄	#14273752	1	1	yes	characteristic
206	C₂×C₄	#14273757	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	8	1	no	—
209	C₈	—	8	1	no	—
210	C₈	(C₂²⋊D₅₉)⋊C₄	1	2	yes	—
211	C₈	#14273704	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	C₂×#14273658	1	1	yes	characteristic
218	C₂²	#16837552	1	1	yes	characteristic
219	C₂²	#16837730	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	472	4	no	—
222	C₄	#16837274	1	1	yes	characteristic
223	C₄	#16837445	1	1	yes	characteristic
224	C₄	#16837540	1	1	yes	characteristic
225	C₄	#16837718	1	1	yes	characteristic
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	—	4	2	no	—
229	C₂	#21424288	1	1	yes	characteristic
230	C₂	#21425870	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837440

C₂

yes

maximal, characteristic

C₂×#16837226

C₂

yes

maximal, complemented

#21425707

C₂

yes

maximal, characteristic

#21422196

C₂

yes

maximal, complemented

C₅₉×#1810

C₂

yes

maximal, characteristic

C₂×#14273686

—

C₂×#14273667

C₂²

yes

—

#16837440

—

C₂×#14273661

—

C₂×#14273659

C₂²

yes

—

#16837226

—

C₂²⋊(C₅₉⋊C₁₆)

C₄

yes

complemented

C₂³×C₈×C₅₉

C₂²

yes

characteristic

C₂×#108×C₅₉

C₂²

yes

characteristic

C₂×#108×C₅₉

C₂²

yes

characteristic

C₅₉×#407

—

C₅₉×#341

—

#14273686

—

#14273686

—

C₂×C₄⋊Dic₅₉

—

C₂×C₂²⋊Dic₅₉

—

C₂×C₄×Dic₅₉

—

#14273667

—

#14273667

—

C₂×C₅₉⋊C₁₆

C₂×C₄

yes

—

#14273661

—

#14273659

—

#14273659

D₄

yes

—

C₂³×C₄×C₅₉

D₄

yes

characteristic

C₂×M₁₆×C₅₉

—

C₂×M₁₆×C₅₉

—

C₂²×C₈×C₅₉

—

C₂²×C₈×C₅₉

—

C₂²×C₈×C₅₉

C₂×C₄

yes

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

Q₈

yes

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

#108×C₅₉

—

#108×C₅₉

—

C₂²⋊C₈×C₅₉

—

C₂⁴×C₅₉

SD₁₆

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₄⋊C₄

yes

—

C₂²×C₄×C₅₉

SD₁₆

yes

characteristic

C₂²×C₄×C₅₉

SD₁₆

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₄⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₅₉

#41

yes

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

#106

yes

—

C₂³×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#106

yes

—

C₂×C₄×C₅₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂×SD₁₆

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

C₄×D₄

yes

—

C₈×C₅₉

C₂²⋊Q₈

yes

—

#12930

—

maximal, Sylow

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

100

C₂²×C₅₉

—

101

C₂²×C₅₉

—

102

C₂²×C₅₉

C₂×#106

yes

characteristic

103

C₂²×C₅₉

#450

yes

characteristic

104

C₂²×C₅₉

#483

yes

characteristic

105

C₄×C₅₉

—

106

C₄×C₅₉

#385

yes

characteristic

107

C₄×C₅₉

#428

yes

characteristic

108

C₄×C₅₉

#448

yes

characteristic

109

C₄×C₅₉

#481

yes

characteristic

110

Dic₅₉

—

111

C₂×#427

—

112

C₂×#365

—

113

#2112

—

114

#1810

D₅₉

yes

characteristic

115

#1383

—

116

C₂×C₅₉

—

117

C₂×C₅₉

—

118

C₂×C₅₉

—

119

C₂×C₅₉

#1853

yes

characteristic

120

C₂×C₅₉

#2155

yes

—

121

C₂³×C₈

C₂×D₅₉

yes

characteristic

122

C₂×#117

—

118

—

123

C₂×M₃₂

—

124

C₂×#108

C₂×D₅₉

yes

characteristic

125

C₂×#108

C₂×D₅₉

yes

characteristic

126

#427

—

118

—

127

C₂×#107

—

118

—

128

C₂×#106

—

129

#407

—

130

#365

—

118

—

131

C₂²⋊C₁₆

—

132

#341

—

133

C₅₉

#12930

yes

characteristic, complemented, Sylow

134

C₂³×C₄

C₂²⋊D₅₉

yes

characteristic

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

Dic₁₁₈

yes

—

140

C₂²×C₈

C₄×D₅₉

yes

—

141

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

142

C₂²×C₈

C₂²×D₅₉

yes

characteristic

143

#117

—

118

—

144

#117

—

236

—

145

C₂×C₄⋊C₄

—

118

—

146

C₂×C₂²⋊C₄

—

236

—

147

C₂×C₄²

—

236

—

148

M₃₂

—

118

—

149

M₃₂

—

118

—

150

C₂×C₁₆

—

151

#108

—

152

#108

—

153

#107

—

118

—

154

#106

—

155

#106

—

118

—

156

C₂²⋊C₈

—

157

C₂⁴

#11745671

yes

characteristic

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

236

—

163

C₂²×C₄

Dic₅₉⋊C₄

yes

—

164

C₂²×C₄

#11745670

yes

—

165

C₂²×C₄

#11745671

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

167

M₁₆

—

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

Dic₅₉⋊C₄

yes

—

178

C₂×C₈

C₂×Dic₁₁₈

yes

characteristic

179

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

180

C₂×C₈

D₄×D₅₉

yes

—

181

C₂×C₈

#11745687

yes

—

182

C₄⋊C₄

—

118

—

183

C₄⋊C₄

—

236

—

184

C₂²⋊C₄

—

236

—

185

C₄²

—

236

—

186

C₁₆

—

118

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

#14273658

yes

—

191

C₂³

C₂×#11745671

yes

characteristic

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

472

—

199

C₂×C₄

—

236

—

200

C₂×C₄

#14273658

yes

—

201

C₂×C₄

C₂×Dic₅₉⋊C₄

yes

characteristic

202

C₂×C₄

#14273695

yes

characteristic

203

C₂×C₄

#14273708

yes

characteristic

204

C₂×C₄

C₂×#11745670

yes

characteristic

205

C₂×C₄

#14273752

yes

characteristic

206

C₂×C₄

#14273757

yes

characteristic

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

(C₂²⋊D₅₉)⋊C₄

yes

—

211

C₈

#14273704

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×#14273658

yes

characteristic

218

C₂²

#16837552

yes

characteristic

219

C₂²

#16837730

yes

characteristic

220

C₄

—

221

C₄

—

472

—

222

C₄

#16837274

yes

characteristic

223

C₄

#16837445

yes

characteristic

224

C₄

#16837540

yes

characteristic

225

C₄

#16837718

yes

characteristic

226

C₂

—

227

C₂

—

228

C₂

—

229

C₂

#21424288

yes

characteristic

230

C₂

#21425870

yes

—

	subgroup	G/H
center	C₂²	C₂×#14273658
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#1810	C₂
socle	C₂²×C₅₉	C₂×#106
prime radical	C₂⁴×C₅₉	SD₁₆
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#1810	D₅₉
hypocenter	C₅₉	#12930
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

subgroup

G/H

center

C₂²

C₂×#14273658

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#1810

C₂

socle

C₂²×C₅₉

C₂×#106

prime radical

C₂⁴×C₅₉

SD₁₆

cosocle

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

N	H ≅ G/N	type
2. C₂×#16837226	C₂	semidirect
4. #21422196	C₂	semidirect
12. C₂²⋊(C₅₉⋊C₁₆)	C₄	semidirect
133. C₅₉	#12930	semidirect

H ≅ G/N

type

2. C₂×#16837226

C₂

semidirect

4. #21422196

C₂

semidirect

12. C₂²⋊(C₅₉⋊C₁₆)

C₄

semidirect

133. C₅₉

#12930

semidirect

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

subgroup	index
C₂×#16837440	2
C₂×#16837226	2
#21425707	2
#21422196	2
C₅₉×#1810	2
#12930	59

subgroup

index

C₅₉×#1810

Subgroups — #28505250

Conjugacy classes of subgroups

Complements

Maximal subgroups