Group #14280567 — subgroups

Subgroups — C₃×#10603811 #14280567

Order 1920.

392 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 172 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	C₃×#65678	C₂	1	2	yes	maximal
2	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×#170⋊C₈	C₂	1	4	yes	maximal, complemented
4	#10603811	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₈×D₅	C₄	1	2	yes	—
6	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
7	C₃×#4004	C₄	1	4	yes	—
8	C₃×#4003	C₄	1	4	yes	—
9	C₃×C₄×#170	C₂²	1	4	yes	—
10	C₃×C₄×C₅×C₈	C₄	1	1	yes	characteristic
11	C₃×C₈×Dic₅	C₂²	1	2	yes	—
12	C₃×C₄×#168	C₄	1	1	yes	characteristic
13	C₃×#1452	—	5	1	no	maximal, Hall
14	#65678	C₂×C₃	1	2	yes	—
15	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic
16	#170⋊C₈	C₂×C₃	1	4	yes	complemented
17	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
18	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
19	C₂×C₃×#170	C₂×C₄	1	8	yes	—
20	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
21	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
22	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
23	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
24	C₂×C₃×#168	C₂×C₄	1	2	yes	—
25	C₃×C₈×D₅	—	2	4	no	—
26	C₃×#431	—	5	2	no	—
27	C₂×C₃×C₄×C₈	—	5	1	no	—
28	C₃×#322	—	5	4	no	—
29	C₂×C₈×D₅	C₃×C₄	1	2	yes	—
30	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
31	#4004	C₃×C₄	1	4	yes	—
32	#4003	C₃×C₄	1	4	yes	—
33	C₄×#170	C₂²×C₃	1	4	yes	—
34	C₄×C₅×C₈	C₃×C₄	1	1	yes	characteristic
35	C₈×Dic₅	C₂²×C₃	1	2	yes	—
36	C₄×#168	C₃×C₄	1	1	yes	characteristic
37	#1452	—	5	1	no	Sylow
38	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
39	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
40	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
42	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
43	C₃×C₄×D₅	—	2	4	no	—
44	C₃×C₄×D₅	M₁₆	1	4	yes	—
45	C₃×#170	—	2	8	no	—
46	C₃×C₅×C₈	—	2	2	no	—
47	C₃×#168	—	2	2	no	—
48	C₂²×C₃×C₈	—	5	2	no	—
49	C₂×C₃×C₄²	—	5	1	no	—
50	C₃×C₄⋊C₈	—	5	4	no	—
51	C₃×C₂²⋊C₈	—	5	4	no	—
52	C₃×C₄×C₈	—	5	4	no	—
53	C₃×C₄×C₈	—	5	2	no	—
54	C₃×C₄×C₈	—	5	1	no	—
55	C₃×C₄×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
56	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
57	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
58	C₂×#170	C₂×C₃×C₄	1	8	yes	—
59	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
60	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
61	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
62	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
63	C₂×#168	C₂×C₃×C₄	1	2	yes	—
64	C₈×D₅	—	2	4	no	—
65	#431	—	5	2	no	—
66	C₂×C₄×C₈	—	5	1	no	—
67	#322	—	5	4	no	—
68	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₃×D₅	—	2	2	no	—
70	C₂×C₃×D₅	#97	1	2	yes	—
71	C₃×C₄×C₅	—	2	2	no	—
72	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
73	C₃×Dic₅	#97	1	2	yes	—
74	C₃×Dic₅	#131	1	4	yes	—
75	C₂²×C₃×C₄	—	5	1	no	—
76	C₂²×C₃×C₄	—	5	2	no	—
77	C₂×C₃×C₈	—	5	8	no	—
78	C₂×C₃×C₈	—	5	2	no	—
79	C₂×C₃×C₈	—	10	4	no	—
80	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
81	C₃×C₄²	—	5	2	no	—
82	C₃×C₄²	—	5	1	no	—
83	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
84	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
85	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
86	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
87	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
88	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
89	C₄×D₅	—	2	4	no	—
90	C₄×D₅	C₃×M₁₆	1	4	yes	—
91	#170	—	2	8	no	—
92	C₅×C₈	—	2	2	no	—
93	#168	—	2	2	no	—
94	C₂²×C₈	—	5	2	no	—
95	C₂×C₄²	—	5	1	no	—
96	C₄⋊C₈	—	5	4	no	—
97	C₂²⋊C₈	—	5	4	no	—
98	C₄×C₈	—	5	4	no	—
99	C₄×C₈	—	5	2	no	—
100	C₄×C₈	—	5	1	no	—
101	C₄×C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
102	C₂×C₃×C₅	C₂×#97	1	1	yes	characteristic
103	C₂×C₃×C₅	#405	1	2	yes	—
104	C₃×D₅	—	2	2	no	—
105	C₂³×C₃	—	5	1	no	—
106	C₂×C₃×C₄	—	5	1	no	—
107	C₂×C₃×C₄	—	5	2	no	—
108	C₂×C₃×C₄	—	5	4	no	—
109	C₂×C₃×C₄	—	10	4	no	—
110	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	2	yes	—
111	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
112	C₃×C₈	—	2	2	no	—
113	C₃×C₈	—	10	8	no	—
114	C₃×C₈	—	10	2	no	—
115	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
116	C₂×D₅	—	2	2	no	—
117	C₂×D₅	C₃×#97	1	2	yes	—
118	C₄×C₅	—	2	2	no	—
119	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
120	Dic₅	C₃×#97	1	2	yes	—
121	Dic₅	C₃×#131	1	4	yes	—
122	C₂²×C₄	—	5	1	no	—
123	C₂²×C₄	—	5	2	no	—
124	C₂×C₈	—	5	8	no	—
125	C₂×C₈	—	5	2	no	—
126	C₂×C₈	—	10	4	no	—
127	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
128	C₄²	—	5	2	no	—
129	C₄²	—	5	1	no	—
130	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
131	C₃×C₅	#1452	1	1	yes	characteristic, complemented, Hall
132	C₂²×C₃	—	5	2	no	—
133	C₂²×C₃	—	10	2	no	—
134	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
135	C₃×C₄	—	2	2	no	—
136	C₃×C₄	—	5	2	no	—
137	C₃×C₄	—	5	4	no	—
138	C₃×C₄	D₅⋊M₁₆	1	2	yes	—
139	C₂×C₅	C₂×C₃×#97	1	1	yes	characteristic
140	C₂×C₅	C₃×#405	1	2	yes	—
141	D₅	—	2	2	no	—
142	C₂³	—	5	1	no	—
143	C₂×C₄	—	5	2	no	—
144	C₂×C₄	—	5	1	no	—
145	C₂×C₄	—	5	4	no	—
146	C₂×C₄	—	10	4	no	—
147	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
148	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
149	C₈	—	2	2	no	—
150	C₈	—	10	8	no	—
151	C₈	—	10	2	no	—
152	C₂×C₃	—	10	2	no	—
153	C₂×C₃	#65676	1	1	yes	characteristic
154	C₂×C₃	#65718	1	2	yes	—
155	C₅	C₃×#1452	1	1	yes	characteristic, complemented, Sylow
156	C₂²	—	5	2	no	—
157	C₂²	—	10	2	no	—
158	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	5	2	no	—
161	C₄	—	5	4	no	—
162	C₄	C₃×D₅⋊M₁₆	1	2	yes	—
163	C₃	#10603811	1	1	yes	characteristic, direct product factor, Sylow
164	C₂	—	10	2	no	—
165	C₂	C₃×#65676	1	1	yes	characteristic
166	C₂	C₃×#65718	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#65678

C₂

yes

maximal

C₃×C₄×C₈×D₅

C₂

yes

maximal, characteristic

C₃×#170⋊C₈

C₂

yes

maximal, complemented

#10603811

C₃

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃×C₈×D₅

C₄

yes

—

C₃×C₄²×D₅

C₂²

yes

characteristic

C₃×#4004

C₄

yes

—

C₃×#4003

C₄

yes

—

C₃×C₄×#170

C₂²

yes

—

C₃×C₄×C₅×C₈

C₄

yes

characteristic

C₃×C₈×Dic₅

C₂²

yes

—

C₃×C₄×#168

C₄

yes

—

C₂×C₃

yes

—

C₄×C₈×D₅

C₂×C₃

yes

characteristic

#170⋊C₈

C₂×C₃

yes

complemented

C₂×C₃×C₄×D₅

C₂×C₄

yes

—

C₂×C₃×C₄×D₅

C₂×C₄

yes

characteristic

C₂×C₃×#170

C₂×C₄

yes

—

C₂×C₃×C₅×C₈

C₂×C₄

yes

—

C₃×C₄²×C₅

C₂×C₄

yes

characteristic

C₃×C₄×Dic₅

C₂×C₄

yes

—

C₃×C₄×Dic₅

C₂³

yes

characteristic

C₂×C₃×#168

C₂×C₄

yes

—

C₃×C₈×D₅

—

C₃×#431

—

C₂×C₃×C₄×C₈

—

C₃×#322

—

C₂×C₈×D₅

C₃×C₄

yes

—

C₄²×D₅

C₂²×C₃

yes

characteristic

#4004

C₃×C₄

yes

—

#4003

C₃×C₄

yes

—

C₄×#170

C₂²×C₃

yes

—

C₄×C₅×C₈

C₃×C₄

yes

characteristic

C₈×Dic₅

C₂²×C₃

yes

—

C₄×#168

C₃×C₄

yes

characteristic

#1452

—

Sylow

C₂²×C₃×D₅

C₄²

yes

characteristic

C₂×C₃×C₄×C₅

C₄²

yes

—

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×Dic₅

C₄²

yes

characteristic

C₂×C₃×Dic₅

C₂²×C₄

yes

—

C₃×C₄×D₅

—

C₃×C₄×D₅

M₁₆

yes

—

C₃×#170

—

C₃×C₅×C₈

—

C₃×#168

—

C₂²×C₃×C₈

—

C₂×C₃×C₄²

—

C₃×C₄⋊C₈

—

C₃×C₂²⋊C₈

—

C₃×C₄×C₈

—

C₃×C₄×C₈

—

C₃×C₄×C₈

—

C₃×C₄×C₈

AGL(1,𝔽₅)

yes

characteristic

C₂×C₄×D₅

C₂×C₃×C₄

yes

—

C₂×C₄×D₅

C₂×C₃×C₄

yes

characteristic

C₂×#170

C₂×C₃×C₄

yes

—

C₂×C₅×C₈

C₂×C₃×C₄

yes

—

C₄²×C₅

C₂×C₃×C₄

yes

characteristic

C₄×Dic₅

C₂×C₃×C₄

yes

—

C₄×Dic₅

C₂³×C₃

yes

characteristic

C₂×#168

C₂×C₃×C₄

yes

—

C₈×D₅

—

#431

—

C₂×C₄×C₈

—

#322

—

C₂²×C₃×C₅

C₂×C₄²

yes

characteristic

C₂×C₃×D₅

—

C₂×C₃×D₅

#97

yes

—

C₃×C₄×C₅

—

C₃×C₄×C₅

C₂×M₁₆

yes

—

C₃×Dic₅

#97

yes

—

C₃×Dic₅

#131

yes

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×AGL(1,𝔽₅)

yes

—

C₃×C₄²

—

C₃×C₄²

—

C₃×C₄²

C₂×AGL(1,𝔽₅)

yes

characteristic

C₂²×D₅

C₃×C₄²

yes

characteristic

C₂×C₄×C₅

C₃×C₄²

yes

—

C₂×C₄×C₅

C₂²×C₃×C₄

yes

characteristic

C₂×Dic₅

C₃×C₄²

yes

characteristic

C₂×Dic₅

C₂²×C₃×C₄

yes

—

C₄×D₅

—

C₄×D₅

C₃×M₁₆

yes

—

#170

—

C₅×C₈

—

#168

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

—

101

C₄×C₈

C₃×AGL(1,𝔽₅)

yes

characteristic

102

C₂×C₃×C₅

C₂×#97

yes

characteristic

103

C₂×C₃×C₅

#405

yes

—

104

C₃×D₅

—

105

C₂³×C₃

—

106

C₂×C₃×C₄

—

107

C₂×C₃×C₄

—

108

C₂×C₃×C₄

—

109

C₂×C₃×C₄

—

110

C₂×C₃×C₄

C₄×AGL(1,𝔽₅)

yes

—

111

C₂×C₃×C₄

C₂²×AGL(1,𝔽₅)

yes

characteristic

112

C₃×C₈

—

113

C₃×C₈

—

114

C₃×C₈

—

115

C₂²×C₅

C₂×C₃×C₄²

yes

characteristic

116

C₂×D₅

—

117

C₂×D₅

C₃×#97

yes

—

118

C₄×C₅

—

119

C₄×C₅

C₂×C₃×M₁₆

yes

—

120

Dic₅

C₃×#97

yes

—

121

Dic₅

C₃×#131

yes

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

C₂×C₃×AGL(1,𝔽₅)

yes

—

128

C₄²

—

129

C₄²

—

130

C₄²

C₂×C₃×AGL(1,𝔽₅)

yes

characteristic

131

C₃×C₅

#1452

yes

characteristic, complemented, Hall

132

C₂²×C₃

—

133

C₂²×C₃

—

134

C₂²×C₃

C₂×C₄×AGL(1,𝔽₅)

yes

characteristic

135

C₃×C₄

—

136

C₃×C₄

—

137

C₃×C₄

—

138

C₃×C₄

D₅⋊M₁₆

yes

—

139

C₂×C₅

C₂×C₃×#97

yes

characteristic

140

C₂×C₅

C₃×#405

yes

—

141

D₅

—

142

C₂³

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

C₃×C₄×AGL(1,𝔽₅)

yes

—

148

C₂×C₄

C₂²×C₃×AGL(1,𝔽₅)

yes

characteristic

149

C₈

—

150

C₈

—

151

C₈

—

152

C₂×C₃

—

153

C₂×C₃

#65676

yes

characteristic

154

C₂×C₃

#65718

yes

—

155

C₅

C₃×#1452

yes

characteristic, complemented, Sylow

156

C₂²

—

157

C₂²

—

158

C₂²

C₂×C₃×C₄×AGL(1,𝔽₅)

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

C₃×D₅⋊M₁₆

yes

—

163

C₃

#10603811

yes

characteristic, direct product factor, Sylow

164

C₂

—

165

C₂

C₃×#65676

yes

characteristic

166

C₂

C₃×#65718

yes

—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₄×C₅×C₈	C₄
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂²×C₃×D₅	C₄²
cosocle	C₄×Dic₅	C₂³×C₃
hypercenter	C₃×C₄×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1452
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×C₈

subgroup

G/H

center

C₂×C₃×C₄

C₂²×AGL(1,𝔽₅)

commutator

C₂²×C₅

C₂×C₃×C₄²

Frattini

C₂×C₄

C₂²×C₃×AGL(1,𝔽₅)

Fitting

C₃×C₄×C₅×C₈

C₄

socle

C₂²×C₃×C₅

C₂×C₄²

prime radical

C₂²×C₃×D₅

C₄²

cosocle

C₄×Dic₅

C₂³×C₃

C₃×C₄×C₈

C₅

G ▷ C₂²×C₅ ▷ C₅

C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×C₈

N	H ≅ G/N	type
3. C₃×#170⋊C₈	C₂	semidirect
4. #10603811	C₃	direct (N × H)
16. #170⋊C₈	C₂×C₃	semidirect
131. C₃×C₅	#1452	semidirect
155. C₅	C₃×#1452	semidirect
163. C₃	#10603811	direct (N × H)

H ≅ G/N

type

3. C₃×#170⋊C₈

C₂

semidirect

4. #10603811

C₃

direct (N × H)

16. #170⋊C₈

C₂×C₃

semidirect

131. C₃×C₅

#1452

semidirect

155. C₅

C₃×#1452

semidirect

163. C₃

#10603811

direct (N × H)

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

subgroup	index
C₃×#65678	2
C₃×C₄×C₈×D₅	2
C₃×#170⋊C₈	2
#10603811	3
C₃×#1452	5

subgroup

index

C₃×#65678

C₃×C₄×C₈×D₅

C₃×#170⋊C₈

#10603811

C₃×#1452

Subgroups — C₃×#10603811 #14280567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10603811 #14280567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10603811 #14280567