Group #28506139 — subgroups

Subgroups — #28506139

Order 15104.

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

normal subgroups only

This group has 490 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, complemented
2	#21425812	C₂	1	2	yes	maximal, complemented
3	#21424142	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422197	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3058	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	#16837203	—	2	4	no	—
12	#16837159	—	2	1	no	—
13	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
15	C₅₉×#535	—	2	1	no	—
16	C₅₉×#469	C₄	1	4	yes	complemented
17	C₅₉×#466	—	2	2	no	—
18	C₅₉×#427	C₂²	1	1	yes	characteristic
19	C₅₉×#418	—	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	complemented
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×D₄×C₅₉	—	2	1	no	—
31	C₂×D₈×C₅₉	—	2	2	no	—
32	C₂×D₈×C₅₉	—	2	1	no	—
33	C₂×D₈×C₅₉	—	2	2	no	—
34	C₂×D₈×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	#127×C₅₉	—	4	1	no	—
42	#124×C₅₉	—	4	1	no	—
43	#121×C₅₉	—	2	4	no	—
44	#120×C₅₉	—	4	2	no	—
45	#117×C₅₉	—	2	1	no	—
46	#107×C₅₉	—	2	1	no	—
47	#106×C₅₉	C₂×C₄	1	2	yes	—
48	#102×C₅₉	—	2	4	no	—
49	C₂⁴×C₅₉	—	4	1	no	—
50	#41×C₅₉	—	2	2	no	—
51	#41×C₅₉	—	2	2	no	—
52	C₂×Q₈×C₅₉	SD₁₆	1	1	yes	characteristic
53	C₂×D₄×C₅₉	—	2	2	no	—
54	C₂×D₄×C₅₉	—	4	4	no	—
55	C₂×D₄×C₅₉	—	4	2	no	—
56	C₂×D₄×C₅₉	—	4	1	no	—
57	C₂×D₄×C₅₉	—	4	2	no	—
58	C₂×D₄×C₅₉	D₈	1	2	yes	—
59	C₂×D₄×C₅₉	SD₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
62	D₈×C₅₉	—	2	4	no	—
63	D₈×C₅₉	—	4	1	no	—
64	D₈×C₅₉	—	4	1	no	—
65	M₁₆×C₅₉	—	2	2	no	—
66	M₁₆×C₅₉	—	2	4	no	—
67	C₂×C₈×C₅₉	—	2	2	no	—
68	C₂×C₈×C₅₉	—	2	2	no	—
69	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₅₉	#41	1	2	yes	—
74	C₄⋊C₄×C₅₉	—	2	2	no	—
75	C₂²⋊C₄×C₅₉	—	4	1	no	—
76	C₂²⋊C₄×C₅₉	—	4	4	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	—	4	2	no	—
83	C₂³×C₅₉	—	8	2	no	—
84	C₂³×C₅₉	—	16	2	no	—
85	C₂³×C₅₉	#102	1	2	yes	—
86	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
87	Q₈×C₅₉	—	2	2	no	—
88	D₄×C₅₉	—	2	4	no	—
89	D₄×C₅₉	—	2	2	no	—
90	D₄×C₅₉	—	4	2	no	—
91	D₄×C₅₉	—	4	2	no	—
92	D₄×C₅₉	—	8	2	no	—
93	D₄×C₅₉	—	16	4	no	—
94	C₂×C₄×C₅₉	—	2	2	no	—
95	C₂×C₄×C₅₉	—	2	2	no	—
96	C₂×C₄×C₅₉	—	4	2	no	—
97	C₂×C₄×C₅₉	#102	1	2	yes	—
98	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₅₉	#121	1	2	yes	—
100	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₅₉	#135	1	2	yes	—
102	C₂×Dic₅₉	—	8	2	no	—
103	C₈×C₅₉	—	2	2	no	—
104	C₈×C₅₉	C₄×D₄	1	2	yes	—
105	C₈×C₅₉	#120	1	1	yes	characteristic
106	C₈×C₅₉	#123	1	1	yes	characteristic
107	#13074	—	59	1	no	maximal, Sylow
108	C₂²×C₅₉	—	2	2	no	—
109	C₂²×C₅₉	—	4	1	no	—
110	C₂²×C₅₉	—	4	2	no	—
111	C₂²×C₅₉	—	8	4	no	—
112	C₂²×C₅₉	—	8	2	no	—
113	C₂²×C₅₉	—	16	4	no	—
114	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
115	C₂²×C₅₉	#466	1	2	yes	—
116	C₄×C₅₉	—	2	2	no	—
117	C₄×C₅₉	—	8	2	no	—
118	C₄×C₅₉	#386	1	1	yes	characteristic
119	C₄×C₅₉	#416	1	1	yes	characteristic
120	C₄×C₅₉	#465	1	2	yes	—
121	Dic₅₉	—	16	2	no	—
122	#3407	—	59	1	no	—
123	#3058	D₅₉	1	1	yes	characteristic
124	#2140	—	59	2	no	—
125	#1812	—	59	1	no	—
126	#1384	—	59	2	no	—
127	C₂×C₅₉	—	2	2	no	—
128	C₂×C₅₉	—	2	1	no	—
129	C₂×C₅₉	—	4	2	no	—
130	C₂×C₅₉	—	16	2	no	—
131	C₂×C₅₉	#1893	1	1	yes	characteristic
132	C₂²×D₈	C₂×D₅₉	1	1	yes	characteristic
133	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
134	#535	—	2	1	no	—
135	#504	—	118	4	no	—
136	C₂×M₃₂	—	59	2	no	—
137	C₂×M₃₂	—	118	2	no	—
138	#469	Dic₅₉	1	4	yes	complemented
139	#466	—	2	2	no	—
140	#427	—	59	2	no	—
141	#427	C₂×D₅₉	1	1	yes	characteristic
142	#418	—	2	1	no	—
143	#410	—	118	1	no	—
144	#357	—	118	4	no	—
145	H(3,ℤ/4)	—	118	1	no	—
146	C₅₉	#13074	1	1	yes	characteristic, complemented, Sylow
147	C₂×#41	C₂²⋊D₅₉	1	1	yes	characteristic
148	C₂²×D₄	—	2	1	no	—
149	C₂×D₈	—	2	2	no	—
150	C₂×D₈	—	2	2	no	—
151	C₂×D₈	—	2	1	no	—
152	C₂×D₈	C₂×Dic₅₉	1	2	yes	—
153	#131	—	2	2	no	—
154	#131	—	2	2	no	—
155	C₂×M₁₆	C₂×Dic₅₉	1	2	yes	—
156	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
158	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
159	#127	—	4	1	no	—
160	#124	—	4	1	no	—
161	#121	—	2	4	no	—
162	#120	—	4	2	no	—
163	#117	—	2	1	no	—
164	#117	—	118	2	no	—
165	M₃₂	—	118	4	no	—
166	M₃₂	—	118	2	no	—
167	M₃₂	—	118	2	no	—
168	C₂×C₁₆	—	59	4	no	—
169	C₂×C₁₆	—	118	4	no	—
170	#107	—	2	1	no	—
171	#107	—	118	2	no	—
172	#106	—	118	2	no	—
173	#106	C₂×Dic₅₉	1	2	yes	—
174	#102	—	2	4	no	—
175	#99	—	236	2	no	—
176	C₂⁴	—	4	1	no	—
177	#41	—	2	2	no	—
178	#41	—	2	2	no	—
179	C₂×Q₈	#11745670	1	1	yes	characteristic
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	—	4	4	no	—
182	C₂×D₄	—	4	2	no	—
183	C₂×D₄	—	4	1	no	—
184	C₂×D₄	—	4	2	no	—
185	C₂×D₄	#11745669	1	2	yes	—
186	C₂×D₄	#11745670	1	1	yes	characteristic
187	C₂²×C₄	C₂²⋊Dic₅₉	1	2	yes	—
188	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
189	D₈	—	2	4	no	—
190	D₈	—	4	1	no	—
191	D₈	—	4	1	no	—
192	M₁₆	—	2	2	no	—
193	M₁₆	—	2	4	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	C₂²⋊Dic₅₉	1	2	yes	—
197	C₂×C₈	D₄×D₅₉	1	2	yes	—
198	C₂×C₈	#11745687	1	2	yes	—
199	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	236	2	no	—
203	C₂²⋊C₄	—	4	1	no	—
204	C₂²⋊C₄	—	4	4	no	—
205	C₂²⋊C₄	—	236	2	no	—
206	C₄²	—	4	1	no	—
207	C₄²	—	236	2	no	—
208	C₁₆	—	118	4	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	8	2	no	—
211	C₂³	—	16	2	no	—
212	C₂³	#14273648	1	2	yes	—
213	C₂³	C₂×#11745669	1	1	yes	characteristic
214	Q₈	—	2	2	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	2	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	8	2	no	—
220	D₄	—	16	4	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	472	2	no	—
225	C₂×C₄	#14273648	1	2	yes	—
226	C₂×C₄	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
227	C₂×C₄	#14273699	1	2	yes	—
228	C₂×C₄	C₂×#11745670	1	1	yes	characteristic
229	C₂×C₄	#14273747	1	2	yes	—
230	C₈	—	2	2	no	—
231	C₈	D₄×Dic₅₉	1	2	yes	—
232	C₈	#14273695	1	1	yes	characteristic
233	C₈	#14273708	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	8	4	no	—
238	C₂²	—	8	2	no	—
239	C₂²	—	16	4	no	—
240	C₂²	C₂×#14273648	1	1	yes	characteristic
241	C₂²	#16837636	1	2	yes	—
242	C₄	—	2	2	no	—
243	C₄	—	8	2	no	—
244	C₄	—	944	2	no	—
245	C₄	#16837282	1	1	yes	characteristic
246	C₄	#16837398	1	1	yes	characteristic
247	C₄	#16837629	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	2	no	—
250	C₂	—	4	2	no	—
251	C₂	—	16	2	no	—
252	C₂	#21424525	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21437199

C₂

yes

maximal, characteristic, complemented

#21425812

C₂

yes

maximal, complemented

#21424142

C₂

yes

maximal, characteristic, complemented

#21422197

C₂

yes

maximal, complemented

C₅₉×#3058

C₂

yes

maximal, characteristic

#16837819

—

C₂×#14273667

—

C₂×#14273667

C₂²

yes

—

#16837440

C₂²

yes

—

#16837376

—

#16837203

—

#16837159

—

C₂²×D₈×C₅₉

C₂²

yes

characteristic

C₂×#131×C₅₉

C₂²

yes

characteristic

C₅₉×#535

—

C₅₉×#469

C₄

yes

complemented

C₅₉×#466

—

C₅₉×#427

C₂²

yes

characteristic

C₅₉×#418

—

—

—

—

—

C₂×C₅₉⋊C₁₆

—

C₂×C₅₉⋊C₁₆

D₄

yes

—

—

—

C₂×#41×C₅₉

D₄

yes

characteristic

C₂²×D₄×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×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

#127×C₅₉

—

#124×C₅₉

—

#121×C₅₉

—

#120×C₅₉

—

#117×C₅₉

—

#107×C₅₉

—

#106×C₅₉

C₂×C₄

yes

—

#102×C₅₉

—

C₂⁴×C₅₉

—

#41×C₅₉

—

#41×C₅₉

—

C₂×Q₈×C₅₉

SD₁₆

yes

characteristic

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

D₈

yes

—

C₂×D₄×C₅₉

SD₁₆

yes

characteristic

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

D₈×C₅₉

—

D₈×C₅₉

—

D₈×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

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

#102

yes

—

C₂³×C₅₉

C₂×D₈

yes

characteristic

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×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

—

100

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₅₉

#135

yes

—

102

C₂×Dic₅₉

—

103

C₈×C₅₉

—

104

C₈×C₅₉

C₄×D₄

yes

—

105

C₈×C₅₉

#120

yes

characteristic

106

C₈×C₅₉

yes

107

—

108

C₂²×C₅₉

—

109

C₂²×C₅₉

—

110

C₂²×C₅₉

—

111

C₂²×C₅₉

—

112

C₂²×C₅₉

—

113

C₂²×C₅₉

—

114

C₂²×C₅₉

C₂×#102

yes

characteristic

115

C₂²×C₅₉

#466

yes

—

116

C₄×C₅₉

—

117

C₄×C₅₉

—

118

C₄×C₅₉

#386

yes

characteristic

119

C₄×C₅₉

#416

yes

characteristic

120

C₄×C₅₉

#465

yes

—

121

Dic₅₉

—

122

#3407

—

123

#3058

D₅₉

yes

characteristic

124

#2140

—

125

#1812

—

126

#1384

—

127

C₂×C₅₉

—

128

C₂×C₅₉

—

129

C₂×C₅₉

—

130

C₂×C₅₉

—

131

C₂×C₅₉

#1893

yes

characteristic

132

C₂²×D₈

C₂×D₅₉

yes

characteristic

133

C₂×#131

C₂×D₅₉

yes

characteristic

134

#535

—

135

#504

—

118

—

136

C₂×M₃₂

—

137

C₂×M₃₂

—

118

—

138

#469

Dic₅₉

yes

complemented

139

#466

—

140

#427

—

141

#427

C₂×D₅₉

yes

characteristic

142

#418

—

143

#410

—

118

—

144

#357

—

118

—

145

H(3,ℤ/4)

—

118

—

146

C₅₉

#13074

yes

characteristic, complemented, Sylow

147

C₂×#41

C₂²⋊D₅₉

yes

characteristic

148

C₂²×D₄

—

149

C₂×D₈

—

150

C₂×D₈

—

151

C₂×D₈

—

152

C₂×D₈

C₂×Dic₅₉

yes

—

153

#131

—

154

#131

—

155

C₂×M₁₆

C₂×Dic₅₉

yes

—

156

C₂×M₁₆

C₂²⋊D₅₉

yes

characteristic

157

C₂²×C₈

C₂²⋊D₅₉

yes

—

158

C₂²×C₈

C₂²×D₅₉

yes

characteristic

159

#127

—

160

#124

—

161

#121

—

162

#120

—

163

#117

—

164

#117

—

118

—

165

M₃₂

—

118

—

166

M₃₂

—

118

—

167

M₃₂

—

118

—

168

C₂×C₁₆

—

169

C₂×C₁₆

—

118

—

170

#107

—

171

#107

—

118

—

172

#106

—

118

—

173

#106

C₂×Dic₅₉

yes

—

174

#102

—

175

#99

—

236

—

176

C₂⁴

—

177

#41

—

178

#41

—

179

C₂×Q₈

#11745670

yes

characteristic

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

#11745669

yes

—

186

C₂×D₄

#11745670

yes

characteristic

187

C₂²×C₄

C₂²⋊Dic₅₉

yes

—

188

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

189

D₈

—

190

D₈

—

191

D₈

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

C₂²⋊Dic₅₉

yes

—

197

C₂×C₈

D₄×D₅₉

yes

—

198

C₂×C₈

#11745687

yes

—

199

C₂×C₈

C₂²×Dic₅₉

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

201

C₄⋊C₄

—

202

C₄⋊C₄

—

236

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

236

—

206

C₄²

—

207

C₄²

—

236

—

208

C₁₆

—

118

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

#14273648

yes

—

213

C₂³

C₂×#11745669

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

D₄

—

220

D₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

472

—

225

C₂×C₄

#14273648

yes

—

226

C₂×C₄

C₂×C₂²⋊Dic₅₉

yes

characteristic

227

C₂×C₄

#14273699

yes

—

228

C₂×C₄

C₂×#11745670

yes

characteristic

229

C₂×C₄

#14273747

yes

—

230

C₈

—

231

C₈

D₄×Dic₅₉

yes

—

232

C₈

#14273695

yes

characteristic

233

C₈

#14273708

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

C₂×#14273648

yes

characteristic

241

C₂²

#16837636

yes

—

242

C₄

—

243

C₄

—

244

C₄

—

944

—

245

C₄

#16837282

yes

characteristic

246

C₄

#16837398

yes

characteristic

247

C₄

#16837629

yes

—

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

—

252

C₂

#21424525

yes

characteristic

	subgroup	G/H
center	C₂	#21424525
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting, prime radical	C₅₉×#3058	C₂
socle	C₂×C₅₉	#1893
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#3058	D₅₉
hypocenter	C₅₉	#13074
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3058

subgroup

G/H

center

C₂

#21424525

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting, prime radical

C₅₉×#3058

C₂

socle

C₂×C₅₉

#1893

cosocle

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3058

N	H ≅ G/N	type
1. #21437199	C₂	semidirect
2. #21425812	C₂	semidirect
3. #21424142	C₂	semidirect
4. #21422197	C₂	semidirect
16. C₅₉×#469	C₄	semidirect
25. C₂×C₅₉⋊C₁₆	D₄	semidirect
138. #469	Dic₅₉	semidirect
146. C₅₉	#13074	semidirect

H ≅ G/N

type

1. #21437199

C₂

semidirect

2. #21425812

C₂

semidirect

3. #21424142

C₂

semidirect

4. #21422197

C₂

semidirect

16. C₅₉×#469

C₄

semidirect

25. C₂×C₅₉⋊C₁₆

D₄

semidirect

138. #469

Dic₅₉

semidirect

146. C₅₉

#13074

semidirect

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

subgroup	index
#21437199	2
#21425812	2
#21424142	2
#21422197	2
C₅₉×#3058	2
#13074	59

subgroup

index

C₅₉×#3058

Subgroups — #28506139

Conjugacy classes of subgroups

Complements

Maximal subgroups