Group #28491312 — subgroups

Subgroups — #28491312

Order 15104.

510 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 139 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×#16837694	C₂	1	2	yes	maximal
2	#21425032	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837151	C₂	1	2	yes	maximal
4	#21421931	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅₉×#500	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
7	#16837694	—	2	4	no	—
8	#16837694	—	2	4	no	—
9	C₂×#14273660	—	2	2	no	—
10	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#14273650	—	2	2	no	—
13	#16837156	—	2	2	no	—
14	#16837151	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
16	C₅₉×#500	—	2	4	no	—
17	C₂×#107×C₅₉	—	2	2	no	—
18	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₁₈	D₄	1	1	yes	characteristic
20	C₂²×C₅₉⋊C₈	—	2	2	no	—
21	C₂²×C₅₉⋊C₈	—	2	1	no	—
22	C₄×Dic₁₁₈	—	2	2	no	—
23	C₄×Dic₁₁₈	—	2	2	no	—
24	C₂×C₄⋊Dic₅₉	D₄	1	1	yes	characteristic
25	C₂×Dic₅₉⋊C₄	—	2	1	no	—
26	C₂×C₄×Dic₅₉	—	2	1	no	—
27	#14273660	—	2	8	no	—
28	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₅₉⋊C₈)	D₄	1	4	yes	—
31	#14273650	—	2	8	no	—
32	C₂²×Q₈×C₅₉	—	2	2	no	—
33	C₂²×C₈×C₅₉	D₄	1	2	yes	—
34	C₄⋊Q₈×C₅₉	—	2	2	no	—
35	C₄⋊Q₈×C₅₉	—	2	2	no	—
36	C₄⋊Q₈×C₅₉	—	2	2	no	—
37	C₄⋊Q₈×C₅₉	D₄	1	4	yes	—
38	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
40	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
41	#107×C₅₉	—	2	8	no	—
42	C₄×C₈×C₅₉	—	2	2	no	—
43	C₂×Q₈×C₅₉	—	2	4	no	—
44	C₂×Q₈×C₅₉	—	4	2	no	—
45	C₂×Q₈×C₅₉	—	8	4	no	—
46	C₂²×C₄×C₅₉	—	4	2	no	—
47	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
50	C₂²×Dic₅₉	—	2	1	no	—
51	C₂²×Dic₅₉	—	2	1	no	—
52	C₂×Dic₁₁₈	—	2	2	no	—
53	C₂×Dic₁₁₈	—	2	2	no	—
54	C₂×Dic₁₁₈	—	2	1	no	—
55	C₂×Dic₁₁₈	Q₁₆	1	2	yes	—
56	C₂×C₈×C₅₉	—	2	2	no	—
57	C₂×C₈×C₅₉	—	2	2	no	—
58	C₂×C₈×C₅₉	Q₁₆	1	4	yes	—
59	C₄⋊C₄×C₅₉	—	2	4	no	—
60	C₄⋊C₄×C₅₉	—	2	4	no	—
61	C₄⋊C₄×C₅₉	—	4	2	no	—
62	C₄⋊C₄×C₅₉	—	4	2	no	—
63	C₄²×C₅₉	C₂×D₄	1	2	yes	—
64	C₄²×C₅₉	C₂×D₄	1	2	yes	—
65	C₄⋊Dic₅₉	—	2	2	no	—
66	Dic₅₉⋊C₄	—	4	2	no	—
67	C₄×Dic₅₉	—	4	1	no	—
68	C₄×Dic₅₉	—	4	1	no	—
69	C₂×C₅₉⋊C₈	—	2	4	no	—
70	C₂×C₅₉⋊C₈	—	4	2	no	—
71	C₂×C₅₉⋊C₈	—	4	2	no	—
72	C₂×C₅₉⋊C₈	—	4	1	no	—
73	C₂×C₅₉⋊C₈	—	4	2	no	—
74	C₂³×C₅₉	#121	1	1	yes	characteristic
75	Q₈×C₅₉	—	8	4	no	—
76	Q₈×C₅₉	—	8	4	no	—
77	C₂×C₄×C₅₉	—	2	2	no	—
78	C₂×C₄×C₅₉	—	4	4	no	—
79	C₂×C₄×C₅₉	—	8	4	no	—
80	C₂×C₄×C₅₉	#120	1	2	yes	—
81	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
82	C₂×C₄×C₅₉	#121	1	2	yes	—
83	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
84	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
85	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
87	C₂×C₄×C₅₉	#137	1	2	yes	—
88	C₂×C₄×C₅₉	#137	1	2	yes	—
89	C₂×Dic₅₉	—	2	2	no	—
90	C₂×Dic₅₉	—	4	1	no	—
91	C₂×Dic₅₉	—	4	1	no	—
92	C₂×Dic₅₉	—	4	1	no	—
93	C₂×Dic₅₉	—	4	2	no	—
94	Dic₁₁₈	—	2	4	no	—
95	Dic₁₁₈	—	4	2	no	—
96	C₈×C₅₉	—	2	4	no	—
97	C₅₉⋊C₈	—	4	4	no	—
98	C₅₉⋊C₈	—	8	1	no	—
99	#10279	—	59	1	no	maximal, Sylow
100	C₂²×C₅₉	#392	1	1	yes	characteristic
101	C₂²×C₅₉	#462	1	2	yes	—
102	C₂²×C₅₉	#467	1	1	yes	characteristic
103	C₂²×C₅₉	#470	1	1	yes	characteristic
104	C₂²×C₅₉	#472	1	2	yes	—
105	C₄×C₅₉	—	2	2	no	—
106	C₄×C₅₉	—	8	4	no	—
107	C₄×C₅₉	#451	1	2	yes	—
108	C₄×C₅₉	#451	1	2	yes	—
109	C₄×C₅₉	#452	1	2	yes	—
110	C₄×C₅₉	#494	1	1	yes	characteristic
111	C₄×C₅₉	#497	1	1	yes	characteristic
112	Dic₅₉	—	4	2	no	—
113	Dic₅₉	—	8	1	no	—
114	C₂×#500	D₅₉	1	1	yes	characteristic
115	C₂×#477	—	59	2	no	—
116	#1984	—	59	1	no	—
117	C₂×#333	—	59	2	no	—
118	#1277	—	59	1	no	—
119	C₂×C₅₉	#1676	1	2	yes	—
120	C₂×C₅₉	#1696	1	2	yes	—
121	C₂×C₅₉	#2001	1	1	yes	characteristic
122	C₂×C₅₉	#2016	1	1	yes	characteristic
123	C₂×C₅₉	#2018	1	1	yes	characteristic
124	C₂×C₄⋊Q₈	C₂×D₅₉	1	2	yes	—
125	C₂×C₄×Q₈	—	59	1	no	—
126	#500	—	2	4	no	—
127	#477	—	118	4	no	—
128	#477	—	118	4	no	—
129	C₂×#107	—	2	2	no	—
130	C₂×#107	—	118	2	no	—
131	C₂×C₄⋊C₈	—	59	2	no	—
132	C₂×C₄⋊C₈	—	59	1	no	—
133	C₂×#103	—	118	2	no	—
134	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
135	#336	—	118	2	no	—
136	#333	—	118	4	no	—
137	C₅₉	#10279	1	1	yes	characteristic, complemented, Sylow
138	C₂²×Q₈	—	2	2	no	—
139	C₂²×Q₈	—	59	1	no	—
140	C₂²×C₈	—	118	2	no	—
141	C₂²×C₈	—	118	1	no	—
142	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	C₂²⋊D₅₉	1	4	yes	—
147	C₄×Q₈	—	118	2	no	—
148	C₄×Q₈	—	118	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	59	1	no	—
152	C₂×C₄⋊C₄	—	118	1	no	—
153	C₂×C₄²	—	118	1	no	—
154	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
155	#107	—	2	8	no	—
156	#107	—	118	8	no	—
157	C₄⋊C₈	—	59	4	no	—
158	C₄⋊C₈	—	118	2	no	—
159	C₄⋊C₈	—	118	2	no	—
160	#103	—	118	8	no	—
161	C₄×C₈	—	2	2	no	—
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	8	4	no	—
165	C₂×Q₈	—	59	2	no	—
166	C₂×Q₈	—	118	1	no	—
167	C₂×Q₈	—	118	2	no	—
168	C₂×Q₈	—	118	2	no	—
169	C₂²×C₄	—	4	2	no	—
170	C₂²×C₄	—	118	1	no	—
171	C₂²×C₄	—	118	1	no	—
172	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
173	C₂²×C₄	#11745687	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	—	118	4	no	—
178	C₂×C₈	—	236	1	no	—
179	C₂×C₈	—	236	2	no	—
180	C₂×C₈	—	236	2	no	—
181	C₂×C₈	—	236	2	no	—
182	C₂×C₈	#11745672	1	4	yes	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	118	2	no	—
188	C₄⋊C₄	—	236	2	no	—
189	C₄²	—	236	1	no	—
190	C₄²	—	236	1	no	—
191	C₄²	D₄×D₅₉	1	2	yes	—
192	C₄²	C₂×C₂²⋊D₅₉	1	2	yes	—
193	C₂³	#14273698	1	1	yes	characteristic
194	Q₈	—	8	4	no	—
195	Q₈	—	8	4	no	—
196	Q₈	—	118	4	no	—
197	Q₈	—	236	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	8	4	no	—
201	C₂×C₄	—	118	2	no	—
202	C₂×C₄	—	236	2	no	—
203	C₂×C₄	—	236	1	no	—
204	C₂×C₄	—	236	1	no	—
205	C₂×C₄	—	236	1	no	—
206	C₂×C₄	#14273695	1	2	yes	—
207	C₂×C₄	#14273696	1	1	yes	characteristic
208	C₂×C₄	#14273699	1	2	yes	—
209	C₂×C₄	#14273723	1	1	yes	characteristic
210	C₂×C₄	Q₁₆×D₅₉	1	1	yes	characteristic
211	C₂×C₄	C₂×#11745672	1	2	yes	—
212	C₂×C₄	#14273750	1	1	yes	characteristic
213	C₂×C₄	#14273758	1	2	yes	—
214	C₂×C₄	#14273759	1	2	yes	—
215	C₈	—	2	4	no	—
216	C₈	—	472	1	no	—
217	C₈	—	236	4	no	—
218	C₂²	#16837310	1	1	yes	characteristic
219	C₂²	#16837609	1	2	yes	—
220	C₂²	#16837640	1	1	yes	characteristic
221	C₂²	#16837657	1	1	yes	characteristic
222	C₂²	#16837669	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	4	no	—
225	C₄	—	472	1	no	—
226	C₄	—	236	2	no	—
227	C₄	#16837556	1	2	yes	—
228	C₄	#16837558	1	2	yes	—
229	C₄	#16837563	1	2	yes	—
230	C₄	#16837781	1	1	yes	characteristic
231	C₄	#16837794	1	1	yes	characteristic
232	C₂	#21423497	1	2	yes	—
233	C₂	#21423621	1	2	yes	—
234	C₂	#21425103	1	1	yes	characteristic
235	C₂	#21425196	1	1	yes	characteristic
236	C₂	#21425203	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837694

C₂

yes

maximal

#21425032

C₂

yes

maximal, characteristic

C₂×#16837151

C₂

yes

maximal

#21421931

C₂

yes

maximal, characteristic

C₂×C₅₉×#500

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₁₈

C₂²

yes

—

—

—

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

C₂×#14273650

—

#16837156

—

#16837151

—

C₂×C₄⋊Q₈×C₅₉

C₂²

yes

—

C₅₉×#500

—

C₂×#107×C₅₉

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂²×Dic₁₁₈

D₄

yes

characteristic

C₂²×C₅₉⋊C₈

—

C₂²×C₅₉⋊C₈

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₂×C₄⋊Dic₅₉

D₄

yes

characteristic

C₂×Dic₅₉⋊C₄

—

C₂×C₄×Dic₅₉

—

#14273660

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

#14273650

—

C₂²×Q₈×C₅₉

—

C₂²×C₈×C₅₉

D₄

yes

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

D₄

yes

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

#107×C₅₉

—

C₄×C₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

Q₁₆

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

Q₁₆

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂×D₄

yes

—

C₄²×C₅₉

C₂×D₄

yes

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#121

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#120

yes

—

C₂×C₄×C₅₉

#120

yes

characteristic

C₂×C₄×C₅₉

#121

yes

—

C₂×C₄×C₅₉

#127

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₁₆

yes

—

C₂×C₄×C₅₉

#135

yes

characteristic

C₂×C₄×C₅₉

#137

yes

—

C₂×C₄×C₅₉

#137

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

#10279

—

maximal, Sylow

100

C₂²×C₅₉

#392

yes

characteristic

101

C₂²×C₅₉

#462

yes

—

102

C₂²×C₅₉

#467

yes

characteristic

103

C₂²×C₅₉

#470

yes

characteristic

104

C₂²×C₅₉

#472

yes

—

105

C₄×C₅₉

—

106

C₄×C₅₉

—

107

C₄×C₅₉

#451

yes

—

108

C₄×C₅₉

#451

yes

—

109

C₄×C₅₉

#452

yes

—

110

C₄×C₅₉

#494

yes

characteristic

111

C₄×C₅₉

#497

yes

characteristic

112

Dic₅₉

—

113

Dic₅₉

—

114

C₂×#500

D₅₉

yes

characteristic

115

C₂×#477

—

116

#1984

—

117

C₂×#333

—

118

#1277

—

119

C₂×C₅₉

#1676

yes

—

120

C₂×C₅₉

#1696

yes

—

121

C₂×C₅₉

#2001

yes

characteristic

122

C₂×C₅₉

#2016

yes

characteristic

123

C₂×C₅₉

#2018

yes

characteristic

124

C₂×C₄⋊Q₈

C₂×D₅₉

yes

—

125

C₂×C₄×Q₈

—

126

#500

—

127

#477

—

118

—

128

#477

—

118

—

129

C₂×#107

—

130

C₂×#107

—

118

—

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

—

133

C₂×#103

—

118

—

134

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

135

#336

—

118

—

136

#333

—

118

—

137

C₅₉

#10279

yes

characteristic, complemented, Sylow

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×C₈

—

118

—

141

C₂²×C₈

—

118

—

142

C₂²×C₈

C₂²⋊D₅₉

yes

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

C₂²⋊D₅₉

yes

—

147

C₄×Q₈

—

118

—

148

C₄×Q₈

—

118

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

118

—

153

C₂×C₄²

—

118

—

154

C₂×C₄²

C₂²×D₅₉

yes

characteristic

155

#107

—

156

#107

—

118

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

118

—

159

C₄⋊C₈

—

118

—

160

#103

—

118

—

161

C₄×C₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

118

—

167

C₂×Q₈

—

118

—

168

C₂×Q₈

—

118

—

169

C₂²×C₄

—

170

C₂²×C₄

—

118

—

171

C₂²×C₄

—

118

—

172

C₂²×C₄

D₄×D₅₉

yes

characteristic

173

C₂²×C₄

#11745687

yes

characteristic

174

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

118

—

178

C₂×C₈

—

236

—

179

C₂×C₈

—

236

—

180

C₂×C₈

—

236

—

181

C₂×C₈

—

236

—

182

C₂×C₈

#11745672

yes

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

118

—

188

C₄⋊C₄

—

236

—

189

C₄²

—

236

—

190

C₄²

—

236

—

191

C₄²

D₄×D₅₉

yes

—

192

C₄²

C₂×C₂²⋊D₅₉

yes

—

193

C₂³

#14273698

yes

characteristic

194

Q₈

—

195

Q₈

—

196

Q₈

—

118

—

197

Q₈

—

236

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

118

—

202

C₂×C₄

—

236

—

203

C₂×C₄

—

236

—

204

C₂×C₄

—

236

—

205

C₂×C₄

—

236

—

206

C₂×C₄

#14273695

yes

—

207

C₂×C₄

#14273696

yes

characteristic

208

C₂×C₄

#14273699

yes

—

209

C₂×C₄

#14273723

yes

characteristic

210

C₂×C₄

Q₁₆×D₅₉

yes

characteristic

211

C₂×C₄

C₂×#11745672

yes

—

212

C₂×C₄

#14273750

yes

characteristic

213

C₂×C₄

#14273758

yes

—

214

C₂×C₄

#14273759

yes

—

215

C₈

—

216

C₈

—

472

—

217

C₈

—

236

—

218

C₂²

#16837310

yes

characteristic

219

C₂²

#16837609

yes

—

220

C₂²

#16837640

yes

characteristic

221

C₂²

#16837657

yes

characteristic

222

C₂²

#16837669

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

472

—

226

C₄

—

236

—

227

C₄

#16837556

yes

—

228

C₄

#16837558

yes

—

229

C₄

#16837563

yes

—

230

C₄

#16837781

yes

characteristic

231

C₄

#16837794

yes

characteristic

232

C₂

#21423497

yes

—

233

C₂

#21423621

yes

—

234

C₂

#21425103

yes

characteristic

235

C₂

#21425196

yes

characteristic

236

C₂

#21425203

yes

characteristic

	subgroup	G/H
center	C₂³	#14273698
commutator, cosocle	C₂×C₄²×C₅₉	C₂³
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₂×C₅₉×#500	C₂
socle, prime radical	C₂³×C₅₉	#121
hypercenter	C₂×#500	D₅₉
hypocenter	C₅₉	#10279
LCS	G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

subgroup

G/H

center

C₂³

#14273698

commutator, cosocle

C₂×C₄²×C₅₉

C₂³

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₂×C₅₉×#500

C₂

C₂³×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

N	H ≅ G/N	type
137. C₅₉	#10279	semidirect

H ≅ G/N

type

137. C₅₉

#10279

semidirect

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

subgroup	index
C₂×#16837694	2
#21425032	2
C₂×#16837151	2
#21421931	2
C₂×C₅₉×#500	2
#10279	59

subgroup

index

C₂×C₅₉×#500

Subgroups — #28491312

Conjugacy classes of subgroups

Complements

Maximal subgroups