Group #28741660 — subgroups

Subgroups — #28741660

Order 15104.

1102 conjugacy classes of subgroups; only the 391 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 391 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	#21432707	C₂	1	1	yes	maximal, characteristic, complemented
3	#21425845	C₂	1	6	yes	maximal, complemented
4	C₂×#16837218	C₂	1	6	yes	maximal, complemented
5	C₂×C₅₉×#578	C₂	1	1	yes	maximal, characteristic
6	#16838169	—	2	1	no	—
7	#16837819	—	2	4	no	—
8	C₂×#14273667	C₂²	1	6	yes	—
9	#16837451	—	2	3	no	—
10	C₂×#14273663	C₂²	1	6	yes	—
11	#16837218	C₂²	1	12	yes	—
12	#16837215	C₂²	1	4	yes	—
13	C₂×2₋¹⁺⁴×C₅₉	—	2	1	no	—
14	C₅₉×#578	—	2	4	no	—
15	C₅₉×#578	C₄	1	8	yes	—
16	C₂×#137×C₅₉	—	2	3	no	—
17	C₂×#135×C₅₉	C₂²	1	3	yes	—
18	C₂²×Q₁₆×C₅₉	C₂²	1	3	yes	—
19	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
20	#14273734	—	4	4	no	—
21	C₂×#11745664	—	2	6	no	—
22	#14273667	—	2	6	no	—
23	#14273667	C₂³	1	4	yes	—
24	C₂×C₅₉⋊C₁₆	—	2	6	no	—
25	#14273663	—	2	6	no	—
26	#14273663	C₂³	1	4	yes	—
27	2₋¹⁺⁴×C₅₉	—	2	8	no	—
28	2₋¹⁺⁴×C₅₉	—	4	4	no	—
29	C₂×#41×C₅₉	—	2	3	no	—
30	C₂×#41×C₅₉	—	4	3	no	—
31	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
32	C₂²×Q₈×C₅₉	—	2	3	no	—
33	C₂²×Q₈×C₅₉	—	4	1	no	—
34	#137×C₅₉	—	2	24	no	—
35	#135×C₅₉	—	2	6	no	—
36	#135×C₅₉	C₂×C₄	1	12	yes	—
37	C₂×Q₁₆×C₅₉	—	2	3	no	—
38	C₂×Q₁₆×C₅₉	—	2	6	no	—
39	C₂×Q₁₆×C₅₉	C₂×C₄	1	12	yes	—
40	C₂×Q₁₆×C₅₉	C₂³	1	3	yes	—
41	C₂×SD₁₆×C₅₉	—	2	3	no	—
42	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
43	#131×C₅₉	C₂×C₄	1	4	yes	—
44	#131×C₅₉	D₄	1	4	yes	—
45	C₂×M₁₆×C₅₉	D₄	1	3	yes	—
46	C₂²×C₈×C₅₉	C₂³	1	3	yes	—
47	#41×C₅₉	—	2	12	no	—
48	#41×C₅₉	—	4	24	no	—
49	#41×C₅₉	—	4	6	no	—
50	#41×C₅₉	C₂²⋊C₄	1	4	yes	—
51	#41×C₅₉	D₈	1	4	yes	—
52	C₂×Q₈×C₅₉	—	2	12	no	—
53	C₂×Q₈×C₅₉	—	2	3	no	—
54	C₂×Q₈×C₅₉	—	4	8	no	—
55	C₂×Q₈×C₅₉	—	4	6	no	—
56	C₂×Q₈×C₅₉	—	4	3	no	—
57	C₂×Q₈×C₅₉	SD₁₆	1	1	yes	characteristic
58	C₂×D₄×C₅₉	—	2	1	no	—
59	C₂×D₄×C₅₉	—	4	3	no	—
60	C₂×D₄×C₅₉	SD₁₆	1	3	yes	—
61	C₂²×C₄×C₅₉	—	4	3	no	—
62	C₂²×C₄×C₅₉	—	4	3	no	—
63	C₂²×C₄×C₅₉	C₂×D₄	1	3	yes	—
64	Q₁₆×C₅₉	—	2	12	no	—
65	Q₁₆×C₅₉	—	2	3	no	—
66	Q₁₆×C₅₉	C₂²×C₄	1	6	yes	—
67	SD₁₆×C₅₉	—	2	12	no	—
68	D₈×C₅₉	—	2	1	no	—
69	D₈×C₅₉	C₂²×C₄	1	2	yes	—
70	M₁₆×C₅₉	C₂²⋊C₄	1	12	yes	—
71	C₂×C₈×C₅₉	C₂²×C₄	1	6	yes	—
72	C₂×C₈×C₅₉	C₂×D₄	1	3	yes	—
73	C₂×C₈×C₅₉	C₂×D₄	1	6	yes	—
74	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
75	#11745664	—	2	4	no	—
76	#11745664	—	4	6	no	—
77	C₂×C₅₉⋊C₈	—	4	6	no	—
78	C₅₉⋊C₁₆	—	2	4	no	—
79	C₂³×C₅₉	—	4	1	no	—
80	C₂³×C₅₉	C₂×SD₁₆	1	3	yes	—
81	Q₈×C₅₉	—	2	6	no	—
82	Q₈×C₅₉	—	4	3	no	—
83	Q₈×C₅₉	—	4	12	no	—
84	Q₈×C₅₉	#102	1	4	yes	—
85	D₄×C₅₉	—	2	2	no	—
86	D₄×C₅₉	—	4	12	no	—
87	D₄×C₅₉	—	4	1	no	—
88	D₄×C₅₉	#102	1	12	yes	—
89	C₂×C₄×C₅₉	—	4	3	no	—
90	C₂×C₄×C₅₉	—	4	12	no	—
91	C₂×C₄×C₅₉	—	4	12	no	—
92	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	6	yes	—
93	C₂×C₄×C₅₉	C₂×D₈	1	6	yes	—
94	C₂×C₄×C₅₉	C₂×SD₁₆	1	3	yes	—
95	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
96	C₈×C₅₉	C₂×C₂²⋊C₄	1	6	yes	—
97	C₈×C₅₉	C₂³×C₄	1	1	yes	characteristic
98	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
99	C₅₉⋊C₈	—	4	4	no	—
100	#33393	—	59	1	no	maximal, Sylow
101	C₂²×C₅₉	—	4	3	no	—
102	C₂²×C₅₉	—	4	2	no	—
103	C₂²×C₅₉	—	8	2	no	—
104	C₂²×C₅₉	C₂×#102	1	6	yes	—
105	C₂²×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
106	C₄×C₅₉	—	4	6	no	—
107	C₄×C₅₉	C₂×#102	1	6	yes	—
108	C₄×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
109	C₄×C₅₉	C₂²×D₈	1	1	yes	characteristic
110	C₂×#578	D₅₉	1	1	yes	characteristic
111	#3407	—	59	1	no	—
112	#2916	—	59	1	no	—
113	#2148	—	59	6	no	—
114	C₂×#362	—	59	6	no	—
115	C₂×C₅₉	—	2	1	no	—
116	C₂×C₅₉	—	2	6	no	—
117	C₂×C₅₉	—	8	2	no	—
118	C₂×C₅₉	C₂²×#102	1	1	yes	characteristic
119	C₂×2₋¹⁺⁴	—	2	1	no	—
120	#578	—	2	4	no	—
121	#578	Dic₅₉	1	8	yes	—
122	C₂×#137	—	2	3	no	—
123	C₂×#135	C₂×D₅₉	1	3	yes	—
124	C₂²×Q₁₆	C₂×D₅₉	1	3	yes	—
125	#568	—	118	1	no	—
126	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
127	#504	—	118	4	no	—
128	C₂×M₃₂	—	59	6	no	—
129	#430	—	118	3	no	—
130	C₂×#108	—	59	6	no	—
131	#362	—	59	12	no	—
132	#361	—	59	4	no	—
133	C₅₉	#33393	1	1	yes	characteristic, complemented, Sylow
134	2₋¹⁺⁴	—	2	8	no	—
135	2₋¹⁺⁴	—	4	4	no	—
136	C₂×#41	—	2	3	no	—
137	C₂×#41	—	4	3	no	—
138	C₂×#41	C₂²⋊D₅₉	1	1	yes	characteristic
139	C₂²×Q₈	—	2	3	no	—
140	C₂²×Q₈	—	4	1	no	—
141	#137	—	2	24	no	—
142	#135	—	2	6	no	—
143	#135	C₂×Dic₅₉	1	12	yes	—
144	C₂×Q₁₆	—	2	3	no	—
145	C₂×Q₁₆	—	2	6	no	—
146	C₂×Q₁₆	C₂×Dic₅₉	1	12	yes	—
147	C₂×Q₁₆	C₂²×D₅₉	1	3	yes	—
148	C₂×SD₁₆	—	2	3	no	—
149	C₂×D₈	C₂²×D₅₉	1	1	yes	characteristic
150	#131	—	236	4	no	—
151	#131	C₂×Dic₅₉	1	4	yes	—
152	#131	C₂²⋊D₅₉	1	4	yes	—
153	C₂×M₁₆	—	118	6	no	—
154	C₂×M₁₆	C₂²⋊D₅₉	1	3	yes	—
155	C₂²×C₈	C₂²×D₅₉	1	3	yes	—
156	M₃₂	—	59	4	no	—
157	M₃₂	—	118	6	no	—
158	C₂×C₁₆	—	118	6	no	—
159	#108	—	59	4	no	—
160	#108	—	118	6	no	—
161	#41	—	2	12	no	—
162	#41	—	4	24	no	—
163	#41	—	4	6	no	—
164	#41	#11745669	1	4	yes	—
165	#41	C₂²⋊Dic₅₉	1	4	yes	—
166	C₂×Q₈	—	2	12	no	—
167	C₂×Q₈	—	2	3	no	—
168	C₂×Q₈	—	4	8	no	—
169	C₂×Q₈	—	4	6	no	—
170	C₂×Q₈	—	4	3	no	—
171	C₂×Q₈	#11745670	1	1	yes	characteristic
172	C₂×D₄	—	2	1	no	—
173	C₂×D₄	—	4	3	no	—
174	C₂×D₄	#11745670	1	3	yes	—
175	C₂²×C₄	—	4	3	no	—
176	C₂²×C₄	—	4	3	no	—
177	C₂²×C₄	C₂×C₂²⋊D₅₉	1	3	yes	—
178	Q₁₆	—	2	12	no	—
179	Q₁₆	—	2	3	no	—
180	Q₁₆	C₂²×Dic₅₉	1	6	yes	—
181	SD₁₆	—	2	12	no	—
182	D₈	—	2	1	no	—
183	D₈	C₂²×Dic₅₉	1	2	yes	—
184	M₁₆	—	118	4	no	—
185	M₁₆	—	236	6	no	—
186	M₁₆	C₂²⋊Dic₅₉	1	12	yes	—
187	C₂×C₈	—	236	6	no	—
188	C₂×C₈	C₂²×Dic₅₉	1	6	yes	—
189	C₂×C₈	C₂×C₂²⋊D₅₉	1	3	yes	—
190	C₂×C₈	C₂×C₂²⋊D₅₉	1	6	yes	—
191	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
192	C₁₆	—	118	4	no	—
193	C₂³	—	4	1	no	—
194	C₂³	C₂×#11745670	1	3	yes	—
195	Q₈	—	2	6	no	—
196	Q₈	—	4	12	no	—
197	Q₈	—	4	3	no	—
198	Q₈	#14273648	1	4	yes	—
199	D₄	—	2	2	no	—
200	D₄	—	4	12	no	—
201	D₄	—	4	1	no	—
202	D₄	#14273648	1	12	yes	—
203	C₂×C₄	—	4	12	no	—
204	C₂×C₄	—	4	3	no	—
205	C₂×C₄	—	4	12	no	—
206	C₂×C₄	C₂×C₂²⋊Dic₅₉	1	6	yes	—
207	C₂×C₄	C₂×#11745669	1	6	yes	—
208	C₂×C₄	C₂×#11745670	1	3	yes	—
209	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
210	C₈	—	236	4	no	—
211	C₈	C₂×C₂²⋊Dic₅₉	1	6	yes	—
212	C₈	C₂³×Dic₅₉	1	1	yes	characteristic
213	C₈	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
214	C₂²	—	4	3	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	8	2	no	—
217	C₂²	C₂×#14273648	1	6	yes	—
218	C₂²	C₂²×#11745670	1	1	yes	characteristic
219	C₄	—	4	6	no	—
220	C₄	C₂×#14273648	1	6	yes	—
221	C₄	C₂²×C₂²⋊Dic₅₉	1	1	yes	characteristic
222	C₄	C₂²×#11745669	1	1	yes	characteristic
223	C₂	—	2	1	no	—
224	C₂	—	2	6	no	—
225	C₂	—	8	2	no	—
226	C₂	C₂²×#14273648	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21437199

C₂

yes

maximal, characteristic, complemented

#21432707

C₂

yes

maximal, characteristic, complemented

#21425845

C₂

yes

maximal, complemented

C₂×#16837218

C₂

yes

maximal, complemented

C₂×C₅₉×#578

C₂

yes

maximal, characteristic

#16838169

—

#16837819

—

C₂×#14273667

C₂²

yes

—

#16837451

—

C₂×#14273663

C₂²

yes

—

#16837218

C₂²

yes

—

#16837215

C₂²

yes

—

C₂×2₋¹⁺⁴×C₅₉

—

C₅₉×#578

—

C₅₉×#578

C₄

yes

—

C₂×#137×C₅₉

—

C₂×#135×C₅₉

C₂²

yes

—

C₂²×Q₁₆×C₅₉

C₂²

yes

—

C₂×#131×C₅₉

C₂²

yes

—

—

—

C₂³

yes

—

C₂×C₅₉⋊C₁₆

—

#14273663

—

#14273663

C₂³

yes

—

2₋¹⁺⁴×C₅₉

—

2₋¹⁺⁴×C₅₉

—

C₂×#41×C₅₉

—

C₂×#41×C₅₉

—

C₂×#41×C₅₉

D₄

yes

characteristic

C₂²×Q₈×C₅₉

—

C₂²×Q₈×C₅₉

—

#137×C₅₉

—

#135×C₅₉

—

#135×C₅₉

C₂×C₄

yes

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

C₂×C₄

yes

—

C₂×Q₁₆×C₅₉

C₂³

yes

—

C₂×SD₁₆×C₅₉

—

C₂×D₈×C₅₉

C₂³

yes

characteristic

#131×C₅₉

C₂×C₄

yes

—

#131×C₅₉

D₄

yes

—

C₂×M₁₆×C₅₉

D₄

yes

—

C₂²×C₈×C₅₉

C₂³

yes

—

#41×C₅₉

—

#41×C₅₉

—

#41×C₅₉

—

#41×C₅₉

C₂²⋊C₄

yes

—

#41×C₅₉

D₈

yes

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

SD₁₆

yes

characteristic

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

SD₁₆

yes

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

C₂²×C₄

yes

—

SD₁₆×C₅₉

—

D₈×C₅₉

—

D₈×C₅₉

C₂²×C₄

yes

—

M₁₆×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

—

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂⁴

yes

characteristic

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂×SD₁₆

yes

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

#102

yes

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₅₉

C₂×D₈

yes

—

C₂×C₄×C₅₉

C₂×SD₁₆

yes

—

C₂×C₄×C₅₉

C₂²×D₄

yes

characteristic

C₈×C₅₉

C₂×C₂²⋊C₄

yes

—

C₈×C₅₉

C₂³×C₄

yes

characteristic

C₈×C₅₉

C₂²×D₄

yes

characteristic

C₅₉⋊C₈

—

100

#33393

—

maximal, Sylow

101

C₂²×C₅₉

—

102

C₂²×C₅₉

—

103

C₂²×C₅₉

—

104

C₂²×C₅₉

C₂×#102

yes

—

105

C₂²×C₅₉

C₂²×SD₁₆

yes

characteristic

106

C₄×C₅₉

—

107

C₄×C₅₉

C₂×#102

yes

—

108

C₄×C₅₉

C₂²×C₂²⋊C₄

yes

characteristic

109

C₄×C₅₉

C₂²×D₈

yes

characteristic

110

C₂×#578

D₅₉

yes

characteristic

111

#3407

—

112

#2916

—

113

#2148

—

114

C₂×#362

—

115

C₂×C₅₉

—

116

C₂×C₅₉

—

117

C₂×C₅₉

—

118

C₂×C₅₉

C₂²×#102

yes

characteristic

119

C₂×2₋¹⁺⁴

—

120

#578

—

121

#578

Dic₅₉

yes

—

122

C₂×#137

—

123

C₂×#135

C₂×D₅₉

yes

—

124

C₂²×Q₁₆

C₂×D₅₉

yes

—

125

#568

—

118

—

126

C₂×#131

C₂×D₅₉

yes

characteristic

127

#504

—

118

—

128

C₂×M₃₂

—

129

#430

—

118

—

130

C₂×#108

—

131

#362

—

132

#361

—

133

C₅₉

#33393

yes

characteristic, complemented, Sylow

134

2₋¹⁺⁴

—

135

2₋¹⁺⁴

—

136

C₂×#41

—

137

C₂×#41

—

138

C₂×#41

C₂²⋊D₅₉

yes

characteristic

139

C₂²×Q₈

—

140

C₂²×Q₈

—

141

#137

—

142

#135

—

143

#135

C₂×Dic₅₉

yes

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

C₂×Dic₅₉

yes

—

147

C₂×Q₁₆

C₂²×D₅₉

yes

—

148

C₂×SD₁₆

—

149

C₂×D₈

C₂²×D₅₉

yes

characteristic

150

#131

—

236

—

151

#131

C₂×Dic₅₉

yes

—

152

#131

C₂²⋊D₅₉

yes

—

153

C₂×M₁₆

—

118

—

154

C₂×M₁₆

C₂²⋊D₅₉

yes

—

155

C₂²×C₈

C₂²×D₅₉

yes

—

156

M₃₂

—

157

M₃₂

—

118

—

158

C₂×C₁₆

—

118

—

159

#108

—

160

#108

—

118

—

161

#41

—

162

#41

—

163

#41

—

164

#41

#11745669

yes

—

165

#41

C₂²⋊Dic₅₉

yes

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

#11745670

yes

characteristic

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

#11745670

yes

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

—

178

Q₁₆

—

179

Q₁₆

—

180

Q₁₆

C₂²×Dic₅₉

yes

—

181

SD₁₆

—

182

D₈

—

183

D₈

C₂²×Dic₅₉

yes

—

184

M₁₆

—

118

—

185

M₁₆

—

236

—

186

M₁₆

C₂²⋊Dic₅₉

yes

—

187

C₂×C₈

—

236

—

188

C₂×C₈

C₂²×Dic₅₉

yes

—

189

C₂×C₈

C₂×C₂²⋊D₅₉

yes

—

190

C₂×C₈

C₂×C₂²⋊D₅₉

yes

—

191

C₂×C₈

C₂³×D₅₉

yes

characteristic

192

C₁₆

—

118

—

193

C₂³

—

194

C₂³

C₂×#11745670

yes

—

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

Q₈

#14273648

yes

—

199

D₄

—

200

D₄

—

201

D₄

—

202

D₄

#14273648

yes

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₂×C₂²⋊Dic₅₉

yes

—

207

C₂×C₄

C₂×#11745669

yes

—

208

C₂×C₄

C₂×#11745670

yes

—

209

C₂×C₄

C₂²×C₂²⋊D₅₉

yes

characteristic

210

C₈

—

236

—

211

C₈

C₂×C₂²⋊Dic₅₉

yes

—

212

C₈

C₂³×Dic₅₉

yes

characteristic

213

C₈

C₂²×C₂²⋊D₅₉

yes

characteristic

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×#14273648

yes

—

218

C₂²

C₂²×#11745670

yes

characteristic

219

C₄

—

220

C₄

C₂×#14273648

yes

—

221

C₄

C₂²×C₂²⋊Dic₅₉

yes

characteristic

222

C₄

C₂²×#11745669

yes

characteristic

223

C₂

—

224

C₂

—

225

C₂

—

226

C₂

C₂²×#14273648

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×#14273648
commutator	C₈×C₅₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₉
Fitting, prime radical	C₂×C₅₉×#578	C₂
socle	C₂×C₅₉	C₂²×#102
cosocle	C₂×C₈×C₅₉	C₂⁴
hypercenter	C₂×#578	D₅₉
hypocenter	C₅₉	#33393
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#131 ◁ C₂×#578

subgroup

G/H

center

C₂

C₂²×#14273648

commutator

C₈×C₅₉

C₂³×C₄

Frattini

C₂×C₈

C₂³×D₅₉

Fitting, prime radical

C₂×C₅₉×#578

C₂

socle

C₂×C₅₉

C₂²×#102

cosocle

C₂×C₈×C₅₉

C₂⁴

D₅₉

C₅₉

G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#131 ◁ C₂×#578

N	H ≅ G/N	type
1. #21437199	C₂	semidirect
2. #21432707	C₂	semidirect
3. #21425845	C₂	semidirect
4. C₂×#16837218	C₂	semidirect
133. C₅₉	#33393	semidirect

H ≅ G/N

type

1. #21437199

C₂

semidirect

2. #21432707

C₂

semidirect

3. #21425845

C₂

semidirect

4. C₂×#16837218

C₂

semidirect

133. C₅₉

#33393

semidirect

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

subgroup	index
#21437199	2
#21432707	2
#21425845	2
C₂×#16837218	2
C₂×C₅₉×#578	2
#33393	59

subgroup

index

C₂×C₅₉×#578

Subgroups — #28741660

Conjugacy classes of subgroups

Complements

Maximal subgroups