Group #11931353 — subgroups

Subgroups — C₅×#8633 #11931353

Order 1280.

320 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 130 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	C₅×#2960	C₂	1	1	yes	maximal, characteristic
2	C₅×#1568	C₂	1	2	yes	maximal
3	C₅×#1537	C₂	1	2	yes	maximal
4	C₅×#1307	C₂	1	2	yes	maximal
5	C₅×#533	C₂²	1	1	yes	characteristic
6	C₅×#446	—	2	2	no	—
7	C₅×C₈×Q₈	—	2	2	no	—
8	C₅×#432	C₂²	1	4	yes	—
9	C₅×#424	C₄	1	2	yes	—
10	C₅×#423	C₂²	1	1	yes	characteristic
11	C₅×#405	C₄	1	2	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#335	—	2	2	no	—
14	C₅×#334	—	2	2	no	—
15	C₅×#330	—	2	4	no	—
16	#8633	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
18	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
20	C₅×C₄⋊Q₈	Q₈	1	2	yes	—
21	C₅×#125	D₄	1	2	yes	—
22	C₅×C₂²⋊Q₈	—	2	2	no	—
23	C₄×C₅×Q₈	—	2	2	no	—
24	C₅×#117	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
26	C₅×C₄⋊C₈	—	2	4	no	—
27	C₅×C₄⋊C₈	—	2	2	no	—
28	C₅×C₄⋊C₈	—	2	4	no	—
29	C₅×C₂²⋊C₈	—	2	4	no	—
30	C₅×#97	—	2	2	no	—
31	C₅×#97	—	2	4	no	—
32	C₄×C₅×C₈	—	2	2	no	—
33	C₄×C₅×C₈	D₄	1	2	yes	—
34	C₄×C₅×C₈	D₄	1	2	yes	—
35	#2960	C₂×C₅	1	1	yes	characteristic
36	#1568	C₂×C₅	1	2	yes	—
37	#1537	C₂×C₅	1	2	yes	—
38	#1307	C₂×C₅	1	2	yes	—
39	C₂×C₅×Q₈	—	2	2	no	—
40	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₅	#41	1	2	yes	—
42	C₅×M₁₆	—	4	2	no	—
43	C₂×C₅×C₈	—	2	2	no	—
44	C₂×C₅×C₈	—	2	2	no	—
45	C₂×C₅×C₈	—	4	1	no	—
46	C₂×C₅×C₈	—	4	4	no	—
47	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
49	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
50	C₅×C₄⋊C₄	—	2	4	no	—
51	C₅×C₄⋊C₄	—	2	2	no	—
52	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
53	C₅×C₂²⋊C₄	—	2	2	no	—
54	C₄²×C₅	—	2	2	no	—
55	C₄²×C₅	C₂×D₄	1	2	yes	—
56	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
58	#533	C₂²×C₅	1	1	yes	characteristic
59	#446	—	2	2	no	—
60	C₈×Q₈	—	2	2	no	—
61	#432	C₂²×C₅	1	4	yes	—
62	#424	C₄×C₅	1	2	yes	—
63	#423	C₂²×C₅	1	1	yes	characteristic
64	#405	C₄×C₅	1	2	yes	—
65	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
66	#335	—	2	2	no	—
67	#334	—	2	2	no	—
68	#330	—	2	4	no	—
69	C₂³×C₅	#117	1	1	yes	characteristic
70	C₅×Q₈	—	4	4	no	—
71	C₂×C₄×C₅	—	2	1	no	—
72	C₂×C₄×C₅	—	2	1	no	—
73	C₂×C₄×C₅	—	2	4	no	—
74	C₂×C₄×C₅	—	4	2	no	—
75	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₅	#121	1	2	yes	—
78	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
79	C₅×C₈	—	2	1	no	—
80	C₅×C₈	—	2	2	no	—
81	C₅×C₈	—	4	2	no	—
82	C₅×C₈	—	8	4	no	—
83	C₅×C₈	#101	1	2	yes	—
84	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
85	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
86	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
87	C₄⋊Q₈	C₅×Q₈	1	2	yes	—
88	#125	C₅×D₄	1	2	yes	—
89	C₂²⋊Q₈	—	2	2	no	—
90	C₄×Q₈	—	2	2	no	—
91	#117	C₂×C₄×C₅	1	2	yes	—
92	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
93	C₄⋊C₈	—	2	4	no	—
94	C₄⋊C₈	—	2	2	no	—
95	C₄⋊C₈	—	2	4	no	—
96	C₂²⋊C₈	—	2	4	no	—
97	#97	—	2	2	no	—
98	#97	—	2	4	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	2	no	—
104	C₂²×C₅	#380	1	1	yes	characteristic
105	C₄×C₅	—	2	1	no	—
106	C₄×C₅	—	2	2	no	—
107	C₄×C₅	—	2	2	no	—
108	C₄×C₅	—	4	4	no	—
109	C₄×C₅	C₂×#101	1	1	yes	characteristic
110	C₄×C₅	#413	1	1	yes	characteristic
111	C₂×Q₈	—	2	2	no	—
112	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
113	C₂²×C₄	C₅×#41	1	2	yes	—
114	M₁₆	—	4	2	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	4	1	no	—
118	C₂×C₈	—	4	4	no	—
119	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
121	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
122	C₄⋊C₄	—	2	4	no	—
123	C₄⋊C₄	—	2	2	no	—
124	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
125	C₂²⋊C₄	—	2	2	no	—
126	C₄²	—	2	2	no	—
127	C₄²	C₂×C₅×D₄	1	2	yes	—
128	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
129	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
130	C₂×C₅	—	4	1	no	—
131	C₂×C₅	#1801	1	1	yes	characteristic
132	C₂×C₅	#1814	1	2	yes	—
133	C₂³	C₅×#117	1	1	yes	characteristic
134	Q₈	—	4	4	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	4	2	no	—
139	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄	C₅×#121	1	2	yes	—
142	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
143	C₈	—	2	1	no	—
144	C₈	—	2	2	no	—
145	C₈	—	4	2	no	—
146	C₈	—	8	4	no	—
147	C₈	C₅×#101	1	2	yes	—
148	C₅	#8633	1	1	yes	characteristic, direct product factor, Sylow
149	C₂²	—	2	1	no	—
150	C₂²	—	2	2	no	—
151	C₂²	C₅×#380	1	1	yes	characteristic
152	C₄	—	2	1	no	—
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	4	no	—
156	C₄	C₂×C₅×#101	1	1	yes	characteristic
157	C₄	C₅×#413	1	1	yes	characteristic
158	C₂	—	4	1	no	—
159	C₂	C₅×#1801	1	1	yes	characteristic
160	C₂	C₅×#1814	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2960

C₂

yes

maximal, characteristic

C₅×#1568

C₂

yes

maximal

C₅×#1537

C₂

yes

maximal

C₅×#1307

C₂

yes

maximal

C₅×#533

C₂²

yes

characteristic

C₅×#446

—

C₅×C₈×Q₈

—

C₅×#432

C₂²

yes

—

C₅×#424

C₄

yes

—

C₅×#423

C₂²

yes

characteristic

C₅×#405

C₄

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

—

—

—

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×M₁₆

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₅×C₄⋊Q₈

Q₈

yes

—

C₅×#125

D₄

yes

—

C₅×C₂²⋊Q₈

—

C₄×C₅×Q₈

—

C₅×#117

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×#97

—

C₅×#97

—

C₄×C₅×C₈

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

D₄

yes

—

#2960

C₂×C₅

yes

characteristic

#1568

C₂×C₅

yes

—

#1537

C₂×C₅

yes

—

#1307

C₂×C₅

yes

—

C₂×C₅×Q₈

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

#41

yes

—

C₅×M₁₆

—

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

—

C₂×C₅×C₈

C₂²⋊C₄

yes

characteristic

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

C₄⋊C₄

yes

—

C₅×C₂²⋊C₄

—

C₄²×C₅

—

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

C₂×D₄

yes

characteristic

C₄²×C₅

C₂×Q₈

yes

characteristic

#533

C₂²×C₅

yes

characteristic

#446

—

C₈×Q₈

—

#432

C₂²×C₅

yes

—

#424

C₄×C₅

yes

—

#423

C₂²×C₅

yes

characteristic

#405

C₄×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

—

—

—

C₂³×C₅

#117

yes

characteristic

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅

#121

yes

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

#101

yes

—

C₂×M₁₆

C₂×C₄×C₅

yes

—

C₂²×C₈

C₂×C₄×C₅

yes

characteristic

C₂²×C₈

C₂×C₄×C₅

yes

characteristic

C₄⋊Q₈

C₅×Q₈

yes

—

#125

C₅×D₄

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×C₄×C₅

yes

—

C₂×C₄²

C₂³×C₅

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

100

C₄×C₈

C₅×D₄

yes

—

101

C₄×C₈

C₅×D₄

yes

—

102

C₂²×C₅

—

103

C₂²×C₅

—

104

C₂²×C₅

#380

yes

characteristic

105

C₄×C₅

—

106

C₄×C₅

—

107

C₄×C₅

—

108

C₄×C₅

—

109

C₄×C₅

C₂×#101

yes

characteristic

110

C₄×C₅

#413

yes

characteristic

111

C₂×Q₈

—

112

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

113

C₂²×C₄

C₅×#41

yes

—

114

M₁₆

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

C₅×C₂²⋊C₄

yes

characteristic

120

C₂×C₈

C₅×C₂²⋊C₄

yes

—

121

C₂×C₈

C₅×C₂²⋊C₄

yes

characteristic

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

C₅×C₄⋊C₄

yes

—

125

C₂²⋊C₄

—

126

C₄²

—

127

C₄²

C₂×C₅×D₄

yes

—

128

C₄²

C₂×C₅×D₄

yes

characteristic

129

C₄²

C₂×C₅×Q₈

yes

characteristic

130

C₂×C₅

—

131

C₂×C₅

#1801

yes

characteristic

132

C₂×C₅

#1814

yes

—

133

C₂³

C₅×#117

yes

characteristic

134

Q₈

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

C₂×C₅×C₂²⋊C₄

yes

characteristic

140

C₂×C₄

C₂×C₅×C₄⋊C₄

yes

characteristic

141

C₂×C₄

C₅×#121

yes

—

142

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

C₅×#101

yes

—

148

C₅

#8633

yes

characteristic, direct product factor, Sylow

149

C₂²

—

150

C₂²

—

151

C₂²

C₅×#380

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

C₂×C₅×#101

yes

characteristic

157

C₄

C₅×#413

yes

characteristic

158

C₂

—

159

C₂

C₅×#1801

yes

characteristic

160

C₂

C₅×#1814

yes

—

	subgroup	G/H
center, socle	C₂²×C₅	#380
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂³×C₅	#117
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#380

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂³×C₅

#117

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
16. #8633	C₅	direct (N × H)
148. C₅	#8633	direct (N × H)

H ≅ G/N

type

16. #8633

C₅

direct (N × H)

148. C₅

#8633

direct (N × H)

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

subgroup	index
C₅×#2960	2
C₅×#1568	2
C₅×#1537	2
C₅×#1307	2
#8633	5

subgroup

index

Subgroups — C₅×#8633 #11931353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8633 #11931353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8633 #11931353