Group #11934214 — subgroups

Subgroups — C₅×#11494 #11934214

Order 1280.

330 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 142 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×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#2163	C₂	1	2	yes	maximal
3	C₅×#1322	C₂	1	4	yes	maximal
4	C₂×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
5	C₅×C₈×Q₈	—	2	2	no	—
6	C₅×C₈×Q₈	—	2	2	no	—
7	C₂×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₅×C₄⋊C₁₆	—	2	2	no	—
12	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	—
13	C₅×#346	—	2	2	no	—
14	#11494	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₅×Q₈	C₈	1	1	yes	characteristic
16	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
18	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
19	C₄×C₅×Q₈	—	2	2	no	—
20	C₄×C₅×Q₈	—	2	2	no	—
21	C₂×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₄	C₈	1	2	yes	—
23	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
25	C₂×C₅×C₁₆	—	2	4	no	—
26	C₅×C₄⋊C₈	—	2	4	no	—
27	C₅×C₄⋊C₈	—	2	2	no	—
28	C₄×C₅×C₈	—	2	2	no	—
29	C₄×C₅×C₈	—	2	2	no	—
30	C₄×C₅×C₈	D₄	1	2	yes	—
31	C₄×C₅×C₈	D₄	1	2	yes	—
32	C₂×C₈×Q₈	C₂×C₅	1	1	yes	characteristic
33	#2163	C₂×C₅	1	2	yes	—
34	#1322	C₂×C₅	1	4	yes	—
35	C₂×C₅×Q₈	—	2	2	no	—
36	C₂×C₅×Q₈	—	2	4	no	—
37	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
38	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
39	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
40	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₅×C₈	—	2	2	no	—
43	C₂×C₅×C₈	—	2	2	no	—
44	C₂×C₅×C₈	—	4	1	no	—
45	C₂×C₅×C₈	—	4	2	no	—
46	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
49	C₅×C₄⋊C₄	—	2	4	no	—
50	C₅×C₄⋊C₄	—	2	2	no	—
51	C₄²×C₅	—	2	2	no	—
52	C₄²×C₅	—	2	2	no	—
53	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
54	C₄²×C₅	M₁₆	1	2	yes	—
55	C₅×C₁₆	—	4	4	no	—
56	C₂×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
57	C₈×Q₈	—	2	2	no	—
58	C₈×Q₈	—	2	2	no	—
59	C₂×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
60	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
61	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
62	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
63	C₄⋊C₁₆	—	2	2	no	—
64	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	—
65	#346	—	2	2	no	—
66	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
67	C₅×Q₈	—	2	8	no	—
68	C₂×C₄×C₅	—	2	2	no	—
69	C₂×C₄×C₅	—	2	2	no	—
70	C₂×C₄×C₅	—	2	2	no	—
71	C₂×C₄×C₅	—	2	1	no	—
72	C₂×C₄×C₅	—	2	1	no	—
73	C₂×C₄×C₅	—	2	2	no	—
74	C₂×C₄×C₅	—	4	1	no	—
75	C₂×C₄×C₅	—	4	2	no	—
76	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
77	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
78	C₂×C₄×C₅	M₃₂	1	4	yes	—
79	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
81	C₅×C₈	—	2	2	no	—
82	C₅×C₈	—	2	1	no	—
83	C₅×C₈	—	4	2	no	—
84	C₅×C₈	#101	1	2	yes	—
85	C₂²×Q₈	C₅×C₈	1	1	yes	characteristic
86	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
87	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
88	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
89	C₄×Q₈	—	2	2	no	—
90	C₄×Q₈	—	2	2	no	—
91	C₂×C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
92	C₂×C₄⋊C₄	C₅×C₈	1	2	yes	—
93	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
94	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
95	C₂×C₁₆	—	2	4	no	—
96	C₄⋊C₈	—	2	4	no	—
97	C₄⋊C₈	—	2	2	no	—
98	C₄×C₈	—	2	2	no	—
99	C₄×C₈	—	2	2	no	—
100	C₄×C₈	C₅×D₄	1	2	yes	—
101	C₄×C₈	C₅×D₄	1	2	yes	—
102	C₂²×C₅	—	2	1	no	—
103	C₂²×C₅	—	2	1	no	—
104	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
105	C₂²×C₅	C₂×M₃₂	1	2	yes	—
106	C₄×C₅	—	2	2	no	—
107	C₄×C₅	—	2	4	no	—
108	C₄×C₅	—	2	2	no	—
109	C₄×C₅	—	2	1	no	—
110	C₄×C₅	—	4	2	no	—
111	C₄×C₅	#410	1	1	yes	characteristic
112	C₄×C₅	C₂×#101	1	1	yes	characteristic
113	C₂×Q₈	—	2	2	no	—
114	C₂×Q₈	—	2	4	no	—
115	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
116	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
117	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
118	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
119	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	4	1	no	—
123	C₂×C₈	—	4	2	no	—
124	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
127	C₄⋊C₄	—	2	4	no	—
128	C₄⋊C₄	—	2	2	no	—
129	C₄²	—	2	2	no	—
130	C₄²	—	2	2	no	—
131	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
132	C₄²	C₅×M₁₆	1	2	yes	—
133	C₁₆	—	4	4	no	—
134	C₂×C₅	—	2	2	no	—
135	C₂×C₅	#1461	1	1	yes	characteristic
136	C₂×C₅	#2112	1	1	yes	characteristic
137	C₂×C₅	#2115	1	1	yes	characteristic
138	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
139	Q₈	—	2	8	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	4	1	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
149	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
150	C₂×C₄	C₅×M₃₂	1	4	yes	—
151	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
153	C₈	—	2	2	no	—
154	C₈	—	2	1	no	—
155	C₈	—	4	2	no	—
156	C₈	C₅×#101	1	2	yes	—
157	C₅	#11494	1	1	yes	characteristic, direct product factor, Sylow
158	C₂²	—	2	1	no	—
159	C₂²	—	2	1	no	—
160	C₂²	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
161	C₂²	C₂×C₅×M₃₂	1	2	yes	—
162	C₄	—	2	2	no	—
163	C₄	—	2	4	no	—
164	C₄	—	2	2	no	—
165	C₄	—	2	1	no	—
166	C₄	—	4	2	no	—
167	C₄	C₅×#410	1	1	yes	characteristic
168	C₄	C₂×C₅×#101	1	1	yes	characteristic
169	C₂	—	2	2	no	—
170	C₂	C₅×#1461	1	1	yes	characteristic
171	C₂	C₅×#2112	1	1	yes	characteristic
172	C₂	C₅×#2115	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₈×Q₈

C₂

yes

maximal, characteristic

C₅×#2163

C₂

yes

maximal

C₅×#1322

C₂

yes

maximal

C₂×C₄×C₅×Q₈

C₄

yes

characteristic

C₅×C₈×Q₈

—

C₅×C₈×Q₈

—

C₂×C₅×C₄⋊C₈

C₄

yes

characteristic

C₂×C₅×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₅×C₈

C₄

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₅×C₄⋊C₁₆

—

C₅×C₂²⋊C₁₆

C₂²

yes

—

C₅×#346

—

#11494

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×Q₈

C₈

yes

characteristic

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂³

yes

characteristic

C₄×C₅×Q₈

—

C₄×C₅×Q₈

—

C₂×C₅×C₄⋊C₄

C₈

yes

characteristic

C₂×C₅×C₄⋊C₄

C₈

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

characteristic

C₂×C₅×C₁₆

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₄×C₅×C₈

—

C₄×C₅×C₈

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

D₄

yes

—

C₂×C₈×Q₈

C₂×C₅

yes

characteristic

#2163

C₂×C₅

yes

—

#1322

C₂×C₅

yes

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂²×C₄×C₅

C₂×C₈

yes

characteristic

C₂²×C₄×C₅

C₂×C₈

yes

—

C₂²×C₄×C₅

C₂×C₈

yes

—

C₂²×C₄×C₅

C₂×C₈

yes

characteristic

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₂²⋊C₄

yes

characteristic

C₂×C₅×C₈

C₂²⋊C₄

yes

characteristic

C₂×C₅×C₈

C₂×D₄

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

C₂²⋊C₄

yes

—

C₄²×C₅

M₁₆

yes

—

C₅×C₁₆

—

C₂×C₄×Q₈

C₄×C₅

yes

characteristic

C₈×Q₈

—

C₈×Q₈

—

C₂×C₄⋊C₈

C₄×C₅

yes

characteristic

C₂×C₄⋊C₈

C₂²×C₅

yes

—

C₂×C₄×C₈

C₄×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

C₂²×C₅

yes

—

#346

—

C₂³×C₅

C₂²×C₈

yes

characteristic

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²⋊C₈

yes

—

C₂×C₄×C₅

C₂²⋊C₈

yes

—

C₂×C₄×C₅

M₃₂

yes

—

C₂×C₄×C₅

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅

C₂×M₁₆

yes

characteristic

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

#101

yes

—

C₂²×Q₈

C₅×C₈

yes

characteristic

C₂²×C₈

C₂×C₄×C₅

yes

characteristic

C₂²×C₈

C₂×C₄×C₅

yes

—

C₂²×C₈

C₂³×C₅

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

C₅×C₈

yes

characteristic

C₂×C₄⋊C₄

C₅×C₈

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂×C₄×C₅

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

C₅×D₄

yes

—

101

C₄×C₈

C₅×D₄

yes

—

102

C₂²×C₅

—

103

C₂²×C₅

—

104

C₂²×C₅

C₂×C₂²⋊C₈

yes

characteristic

105

C₂²×C₅

C₂×M₃₂

yes

—

106

C₄×C₅

—

107

C₄×C₅

—

108

C₄×C₅

—

109

C₄×C₅

—

110

C₄×C₅

—

111

C₄×C₅

#410

yes

characteristic

112

C₄×C₅

C₂×#101

yes

characteristic

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂²×C₄

C₂×C₅×C₈

yes

characteristic

116

C₂²×C₄

C₂×C₅×C₈

yes

—

117

C₂²×C₄

C₂×C₅×C₈

yes

—

118

C₂²×C₄

C₂×C₅×C₈

yes

characteristic

119

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

C₅×C₂²⋊C₄

yes

characteristic

125

C₂×C₈

C₅×C₂²⋊C₄

yes

characteristic

126

C₂×C₈

C₂×C₅×D₄

yes

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄²

—

130

C₄²

—

131

C₄²

C₅×C₂²⋊C₄

yes

—

132

C₄²

C₅×M₁₆

yes

—

133

C₁₆

—

134

C₂×C₅

—

135

C₂×C₅

#1461

yes

characteristic

136

C₂×C₅

#2112

yes

characteristic

137

C₂×C₅

#2115

yes

characteristic

138

C₂³

C₂²×C₅×C₈

yes

characteristic

139

Q₈

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

C₅×C₂²⋊C₈

yes

—

149

C₂×C₄

C₅×C₂²⋊C₈

yes

—

150

C₂×C₄

C₅×M₃₂

yes

—

151

C₂×C₄

C₂×C₅×C₂²⋊C₄

yes

characteristic

152

C₂×C₄

C₂×C₅×M₁₆

yes

characteristic

153

C₈

—

154

C₈

—

155

C₈

—

156

C₈

C₅×#101

yes

—

157

C₅

#11494

yes

characteristic, direct product factor, Sylow

158

C₂²

—

159

C₂²

—

160

C₂²

C₂×C₅×C₂²⋊C₈

yes

characteristic

161

C₂²

C₂×C₅×M₃₂

yes

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

C₅×#410

yes

characteristic

168

C₄

C₂×C₅×#101

yes

characteristic

169

C₂

—

170

C₂

C₅×#1461

yes

characteristic

171

C₂

C₅×#2112

yes

characteristic

172

C₂

C₅×#2115

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	C₂×C₂²⋊C₈
prime radical	C₂³×C₅	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

subgroup

G/H

center

C₂×C₄×C₅

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₅×C₈

Frattini, cosocle

C₂²×C₈

C₂³×C₅

socle

C₂²×C₅

C₂×C₂²⋊C₈

prime radical

C₂³×C₅

C₂²×C₈

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

N	H ≅ G/N	type
14. #11494	C₅	direct (N × H)
157. C₅	#11494	direct (N × H)

H ≅ G/N

type

14. #11494

C₅

direct (N × H)

157. C₅

#11494

direct (N × H)

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

subgroup	index
C₂×C₅×C₈×Q₈	2
C₅×#2163	2
C₅×#1322	2
#11494	5

subgroup

index

C₂×C₅×C₈×Q₈

C₅×#2163

C₅×#1322

#11494

Subgroups — C₅×#11494 #11934214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#11494 #11934214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11494 #11934214