Group #14298929 — subgroups

Subgroups — #14298929

Order 1920.

360 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 140 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×C₅×#815	C₂	1	1	yes	maximal, characteristic
2	#11748440	C₂	1	2	yes	maximal
3	#11746373	C₂	1	1	yes	maximal, characteristic
4	C₃×#64772	C₂	1	1	yes	maximal, characteristic
5	#11745983	C₂	1	2	yes	maximal
6	#10600634	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×#6710	C₂²	1	2	yes	—
9	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
10	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×#681	C₂²	1	2	yes	—
12	C₅×#815	C₄	1	4	yes	—
13	Dic₃⋊#168	—	2	4	no	—
14	#68929	—	5	1	no	maximal, Hall
15	C₂×C₅×#97	—	3	1	no	—
16	#65213	—	3	2	no	—
17	#64772	—	3	2	no	—
18	#64772	—	3	1	no	—
19	#64772	D₃	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
21	C₂²×C₅×Dic₃	Q₈	1	2	yes	—
22	C₂×C₃×C₅×C₈	—	2	2	no	—
23	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
24	#6710	—	2	2	no	—
25	#6710	—	2	2	no	—
26	C₂×C₃⋊#168	—	2	2	no	—
27	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
28	C₄×C₅×Dic₃	D₄	1	2	yes	—
29	C₂×C₅×C₃⋊C₈	—	2	2	no	—
30	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
31	C₃×#681	—	2	2	no	—
32	C₃×#681	—	2	2	no	—
33	C₂×C₃×#168	—	2	2	no	—
34	#5118	—	5	2	no	—
35	C₂×#815	D₅	1	1	yes	characteristic
36	C₃×#341	—	5	1	no	—
37	#4558	—	5	2	no	—
38	#4552	—	5	1	no	—
39	C₂²×C₅×C₈	—	3	1	no	—
40	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
41	C₂×C₄²×C₅	—	3	1	no	—
42	C₂×#681	—	3	2	no	—
43	C₂×#681	C₂×D₃	1	2	yes	—
44	C₅×#97	—	3	4	no	—
45	C₄⋊#168	—	6	4	no	—
46	#1838	—	15	1	no	Sylow
47	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	#41	1	2	yes	—
51	C₂×C₃×C₄×C₅	#41	1	2	yes	—
52	C₂×C₅×Dic₃	—	4	2	no	—
53	C₂×C₅×Dic₃	C₄⋊C₄	1	4	yes	—
54	C₃×C₅×C₈	—	2	2	no	—
55	C₃⋊#168	—	4	2	no	—
56	C₃×#168	—	4	2	no	—
57	C₅×C₃⋊C₈	—	2	2	no	—
58	C₂×C₃×M₁₆	—	5	2	no	—
59	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
60	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
61	C₂×#208	—	5	2	no	—
62	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
63	#815	Dic₅	1	4	yes	—
64	Dic₃⋊C₈	—	10	4	no	—
65	C₂²×C₄×C₅	—	3	2	no	—
66	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
67	C₂×C₅×C₈	—	2	2	no	—
68	C₂×C₅×C₈	—	3	2	no	—
69	C₂×C₅×C₈	—	6	2	no	—
70	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
71	C₄²×C₅	—	3	2	no	—
72	C₄²×C₅	—	3	2	no	—
73	#681	—	2	2	no	—
74	#681	—	2	2	no	—
75	#681	—	6	2	no	—
76	#681	—	6	2	no	—
77	C₂×#168	—	2	2	no	—
78	C₂×#168	—	6	2	no	—
79	#423	—	15	2	no	—
80	C₂×#97	—	3	1	no	—
81	#341	—	5	1	no	—
82	#341	—	15	2	no	—
83	#341	—	15	1	no	—
84	C₂²×C₃×C₅	—	2	2	no	—
85	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₃×C₅	#125	1	2	yes	—
87	C₃×C₄×C₅	#117	1	1	yes	characteristic
88	C₃×C₄×C₅	#117	1	1	yes	characteristic
89	C₃×C₄×C₅	#124	1	2	yes	—
90	C₅×Dic₃	—	2	4	no	—
91	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
92	C₂²×Dic₃	Dic₁₀	1	2	yes	—
93	C₃×M₁₆	—	10	2	no	—
94	C₃×M₁₆	—	10	2	no	—
95	C₂×C₃×C₈	—	2	2	no	—
96	C₂×C₃×C₈	—	10	2	no	—
97	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	—
98	C₄×Dic₃	D₂₀	1	2	yes	—
99	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
100	#208	—	10	2	no	—
101	#208	—	10	2	no	—
102	C₂×C₃⋊C₈	—	2	2	no	—
103	C₂×C₃⋊C₈	—	10	2	no	—
104	C₂×C₃⋊C₈	C₂×Dic₅	1	2	yes	—
105	C₂³×C₅	D₃×Q₈	1	1	yes	characteristic
106	C₂×C₄×C₅	—	3	4	no	—
107	C₂×C₄×C₅	—	12	2	no	—
108	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
109	C₂×C₄×C₅	#235	1	2	yes	—
110	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
111	C₂×C₄×C₅	#237	1	2	yes	—
112	C₅×C₈	—	2	2	no	—
113	C₅×C₈	—	6	2	no	—
114	#168	—	4	2	no	—
115	#168	—	12	2	no	—
116	C₂×M₁₆	—	5	2	no	—
117	C₂×M₁₆	—	15	2	no	—
118	C₂²×C₈	—	3	1	no	—
119	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
120	C₂×C₄²	—	3	1	no	—
121	C₄⋊C₈	—	30	4	no	—
122	#97	—	3	4	no	—
123	C₂×C₃×C₅	—	2	2	no	—
124	C₂×C₃×C₅	#382	1	1	yes	characteristic
125	C₂×C₃×C₅	#430	1	2	yes	—
126	C₂³×C₃	C₂×Dic₁₀	1	1	yes	characteristic
127	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
128	C₂×C₃×C₄	#709	1	2	yes	—
129	C₂×C₃×C₄	#709	1	2	yes	—
130	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
131	C₂×Dic₃	—	4	2	no	—
132	C₂×Dic₃	C₄⋊Dic₅	1	4	yes	—
133	C₃×C₈	—	2	2	no	—
134	C₃×C₈	—	20	2	no	—
135	C₃⋊C₈	—	2	2	no	—
136	C₃⋊C₈	—	20	2	no	—
137	C₂²×C₅	—	2	2	no	—
138	C₂²×C₅	#889	1	2	yes	—
139	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
140	C₄×C₅	—	6	4	no	—
141	C₄×C₅	#872	1	1	yes	characteristic
142	C₄×C₅	#877	1	1	yes	characteristic
143	C₄×C₅	#885	1	2	yes	—
144	C₂²×C₄	—	3	2	no	—
145	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
146	M₁₆	—	10	2	no	—
147	M₁₆	—	10	2	no	—
148	M₁₆	—	30	2	no	—
149	M₁₆	—	30	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	3	2	no	—
152	C₂×C₈	—	6	2	no	—
153	C₂×C₈	—	10	2	no	—
154	C₂×C₈	—	30	2	no	—
155	C₂×C₈	D₃×Dic₅	1	2	yes	—
156	C₄²	—	3	2	no	—
157	C₄²	—	3	2	no	—
158	C₃×C₅	#1838	1	1	yes	characteristic, complemented, Hall
159	C₂²×C₃	—	2	2	no	—
160	C₂²×C₃	#4016	1	2	yes	—
161	C₂²×C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic
162	C₃×C₄	#4021	1	2	yes	—
163	C₃×C₄	#4072	1	1	yes	characteristic
164	C₃×C₄	#4072	1	1	yes	characteristic
165	Dic₃	—	2	4	no	—
166	C₂×C₅	—	2	2	no	—
167	C₂×C₅	#4650	1	1	yes	characteristic
168	C₂×C₅	#4893	1	2	yes	—
169	C₂³	D₃×Dic₁₀	1	1	yes	characteristic
170	C₂×C₄	—	3	4	no	—
171	C₂×C₄	—	12	2	no	—
172	C₂×C₄	#6771	1	2	yes	—
173	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
174	C₂×C₄	#6779	1	2	yes	—
175	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
176	C₈	—	2	2	no	—
177	C₈	—	6	2	no	—
178	C₈	—	20	2	no	—
179	C₈	—	60	2	no	—
180	C₂×C₃	—	2	2	no	—
181	C₂×C₃	#65225	1	1	yes	characteristic
182	C₂×C₃	#65414	1	2	yes	—
183	C₅	#68929	1	1	yes	characteristic, complemented, Sylow
184	C₂²	—	2	2	no	—
185	C₂²	#91379	1	2	yes	—
186	C₂²	D₃×C₄⋊Dic₅	1	1	yes	characteristic
187	C₄	—	6	4	no	—
188	C₄	#91353	1	2	yes	—
189	C₄	#91371	1	1	yes	characteristic
190	C₄	#91529	1	1	yes	characteristic
191	C₃	#10600634	1	1	yes	characteristic, complemented, Sylow
192	C₂	—	2	2	no	—
193	C₂	#11748059	1	2	yes	—
194	C₂	#11748600	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×#815

C₂

yes

maximal, characteristic

#11748440

C₂

yes

maximal

#11746373

C₂

yes

maximal, characteristic

C₃×#64772

C₂

yes

maximal, characteristic

#11745983

C₂

yes

maximal

#10600634

—

maximal, Hall

C₂²×C₃×C₅×C₈

C₂²

yes

characteristic

C₂×#6710

C₂²

yes

—

C₂×C₄×C₅×Dic₃

C₂²

yes

characteristic

C₂²×C₅×C₃⋊C₈

C₂²

yes

characteristic

C₂×C₃×#681

C₂²

yes

—

C₅×#815

C₄

yes

—

Dic₃⋊#168

—

#68929

—

maximal, Hall

C₂×C₅×#97

—

—

—

—

D₃

yes

characteristic

C₂²×C₃×C₄×C₅

C₂³

yes

characteristic

C₂²×C₅×Dic₃

Q₈

yes

—

C₂×C₃×C₅×C₈

—

C₂×C₃×C₅×C₈

C₂×C₄

yes

—

#6710

—

#6710

—

C₂×C₃⋊#168

—

C₄×C₅×Dic₃

C₂×C₄

yes

—

C₄×C₅×Dic₃

D₄

yes

—

C₂×C₅×C₃⋊C₈

—

C₂×C₅×C₃⋊C₈

C₂×C₄

yes

—

C₃×#681

—

C₃×#681

—

C₂×C₃×#168

—

#5118

—

C₂×#815

D₅

yes

—

—

—

C₂²×C₅×C₈

—

C₂²×C₅×C₈

C₂×D₃

yes

characteristic

C₂×C₄²×C₅

—

C₂×#681

—

C₂×#681

C₂×D₃

yes

—

C₅×#97

—

C₄⋊#168

—

#1838

—

Sylow

C₂³×C₃×C₅

C₂×Q₈

yes

characteristic

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₃×C₄×C₅

#41

yes

—

C₂×C₃×C₄×C₅

#41

yes

—

C₂×C₅×Dic₃

—

C₂×C₅×Dic₃

C₄⋊C₄

yes

—

C₃×C₅×C₈

—

C₃⋊#168

—

C₃×#168

—

C₅×C₃⋊C₈

—

C₂×C₃×M₁₆

—

C₂²×C₃×C₈

C₂×D₅

yes

characteristic

C₂×C₄×Dic₃

C₂×D₅

yes

characteristic

C₂×#208

—

C₂²×C₃⋊C₈

C₂×D₅

yes

characteristic

#815

Dic₅

yes

—

Dic₃⋊C₈

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²×D₃

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄×D₃

yes

—

C₄²×C₅

—

C₄²×C₅

—

—

—

—

—

—

—

—

C₂×#97

—

#341

—

#341

—

#341

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃×C₅

#125

yes

—

C₃×C₄×C₅

yes

C₃×C₄×C₅

yes

C₃×C₄×C₅

yes

—

C₅×Dic₃

—

C₂²×C₃×C₄

C₂²×D₅

yes

characteristic

C₂²×Dic₃

Dic₁₀

yes

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×Dic₅

yes

—

C₄×Dic₃

D₂₀

yes

—

C₄×Dic₃

C₂×Dic₅

yes

—

100

#208

—

101

#208

—

102

C₂×C₃⋊C₈

—

103

C₂×C₃⋊C₈

—

104

C₂×C₃⋊C₈

C₂×Dic₅

yes

—

105

C₂³×C₅

D₃×Q₈

yes

characteristic

106

C₂×C₄×C₅

—

107

C₂×C₄×C₅

—

108

C₂×C₄×C₅

C₂×C₄×D₃

yes

characteristic

109

C₂×C₄×C₅

#235

yes

—

110

C₂×C₄×C₅

D₃×D₄

yes

characteristic

111

C₂×C₄×C₅

#237

yes

—

112

C₅×C₈

—

113

C₅×C₈

—

114

#168

—

115

#168

—

116

C₂×M₁₆

—

117

C₂×M₁₆

—

118

C₂²×C₈

—

119

C₂²×C₈

D₃×D₅

yes

characteristic

120

C₂×C₄²

—

121

C₄⋊C₈

—

122

#97

—

123

C₂×C₃×C₅

—

124

C₂×C₃×C₅

#382

yes

characteristic

125

C₂×C₃×C₅

#430

yes

—

126

C₂³×C₃

C₂×Dic₁₀

yes

characteristic

127

C₂×C₃×C₄

C₂×D₂₀

yes

characteristic

128

C₂×C₃×C₄

#709

yes

—

129

C₂×C₃×C₄

#709

yes

—

130

C₂×C₃×C₄

C₂²×Dic₅

yes

characteristic

131

C₂×Dic₃

—

132

C₂×Dic₃

C₄⋊Dic₅

yes

—

133

C₃×C₈

—

134

C₃×C₈

—

135

C₃⋊C₈

—

136

C₃⋊C₈

—

137

C₂²×C₅

—

138

C₂²×C₅

#889

yes

—

139

C₂²×C₅

D₃×C₄⋊C₄

yes

characteristic

140

C₄×C₅

—

141

C₄×C₅

#872

yes

characteristic

142

C₄×C₅

#877

yes

characteristic

143

C₄×C₅

#885

yes

—

144

C₂²×C₄

—

145

C₂²×C₄

C₂×D₃×D₅

yes

characteristic

146

M₁₆

—

147

M₁₆

—

148

M₁₆

—

149

M₁₆

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

D₃×Dic₅

yes

—

156

C₄²

—

157

C₄²

—

158

C₃×C₅

#1838

yes

characteristic, complemented, Hall

159

C₂²×C₃

—

160

C₂²×C₃

#4016

yes

—

161

C₂²×C₃

C₂×C₄⋊Dic₅

yes

characteristic

162

C₃×C₄

#4021

yes

—

163

C₃×C₄

#4072

yes

characteristic

164

C₃×C₄

#4072

yes

characteristic

165

Dic₃

—

166

C₂×C₅

—

167

C₂×C₅

#4650

yes

characteristic

168

C₂×C₅

#4893

yes

—

169

C₂³

D₃×Dic₁₀

yes

characteristic

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

#6771

yes

—

173

C₂×C₄

D₃×D₂₀

yes

characteristic

174

C₂×C₄

#6779

yes

—

175

C₂×C₄

C₂×D₃×Dic₅

yes

characteristic

176

C₈

—

177

C₈

—

178

C₈

—

179

C₈

—

180

C₂×C₃

—

181

C₂×C₃

#65225

yes

characteristic

182

C₂×C₃

#65414

yes

—

183

C₅

#68929

yes

characteristic, complemented, Sylow

184

C₂²

—

185

C₂²

#91379

yes

—

186

C₂²

D₃×C₄⋊Dic₅

yes

characteristic

187

C₄

—

188

C₄

#91353

yes

—

189

C₄

#91371

yes

characteristic

190

C₄

#91529

yes

characteristic

191

C₃

#10600634

yes

characteristic, complemented, Sylow

192

C₂

—

193

C₂

#11748059

yes

—

194

C₂

#11748600

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₃×D₂₀
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×C₅	C₂×Q₈
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#1838
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂×C₄

D₃×D₂₀

commutator

C₂×C₃×C₄×C₅

C₂²×C₄

Frattini

C₂²×C₄

C₂×D₃×D₅

Fitting

C₂²×C₃×C₅×C₈

C₂²

socle

C₂²×C₃×C₅

C₂×C₄⋊C₄

prime radical

C₂³×C₃×C₅

C₂×Q₈

cosocle

C₂²×C₃×C₄×C₅

C₂³

hypercenter

C₂²×C₈

D₃×D₅

hypocenter

C₃×C₅

#1838

LCS

G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
158. C₃×C₅	#1838	semidirect
183. C₅	#68929	semidirect
191. C₃	#10600634	semidirect

H ≅ G/N

type

158. C₃×C₅

#1838

semidirect

183. C₅

#68929

semidirect

191. C₃

#10600634

semidirect

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

subgroup	index
C₂×C₅×#815	2
#11748440	2
#11746373	2
C₃×#64772	2
#11745983	2
#10600634	3
#68929	5

subgroup

index

C₂×C₅×#815

Subgroups — #14298929

Conjugacy classes of subgroups

Complements

Maximal subgroups