Group #11936240 — subgroups

Subgroups — C₅×#13520 #11936240

Order 1280.

238 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2161	C₂	1	1	yes	maximal, characteristic
2	C₅×#2151	C₂	1	1	yes	maximal, characteristic
3	C₅×#1953	C₂	1	2	yes	maximal
4	C₅×#1385	C₂	1	1	yes	maximal, characteristic
5	C₅×#1381	C₂	1	2	yes	maximal
6	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
7	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	C₅×#430	—	2	2	no	—
9	C₂×C₅×#108	C₂²	1	2	yes	—
10	C₂×C₅×#108	C₂²	1	2	yes	—
11	C₅×#405	C₂²	1	1	yes	characteristic
12	C₅×#368	—	2	2	no	—
13	C₅×C₄⋊C₁₆	—	2	2	no	—
14	C₅×#344	—	2	2	no	—
15	#13520	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×C₅×M₁₆	—	2	2	no	—
17	C₂×C₅×M₁₆	—	2	2	no	—
18	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
19	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
20	C₅×#117	D₄	1	1	yes	characteristic
21	C₅×M₃₂	—	2	2	no	—
22	C₂×C₅×C₁₆	—	2	1	no	—
23	C₂×C₅×C₁₆	—	2	2	no	—
24	C₂×C₅×C₁₆	D₄	1	2	yes	—
25	C₅×#108	—	2	2	no	—
26	C₅×#108	—	2	2	no	—
27	C₅×#108	—	2	2	no	—
28	C₅×#108	—	4	4	no	—
29	C₅×#108	Q₈	1	4	yes	—
30	C₅×#97	—	2	1	no	—
31	C₄×C₅×C₈	—	2	1	no	—
32	#2161	C₂×C₅	1	1	yes	characteristic
33	#2151	C₂×C₅	1	1	yes	characteristic
34	#1953	C₂×C₅	1	2	yes	—
35	#1385	C₂×C₅	1	1	yes	characteristic
36	#1381	C₂×C₅	1	2	yes	—
37	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
38	C₅×M₁₆	—	2	4	no	—
39	C₅×M₁₆	—	2	2	no	—
40	C₅×M₁₆	—	4	2	no	—
41	C₅×M₁₆	—	4	2	no	—
42	C₅×M₁₆	—	4	2	no	—
43	C₂×C₅×C₈	—	2	1	no	—
44	C₂×C₅×C₈	—	4	2	no	—
45	C₂×C₅×C₈	—	4	2	no	—
46	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
47	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
48	C₂×C₅×C₈	#41	1	2	yes	—
49	C₂×C₅×C₈	#41	1	1	yes	characteristic
50	C₅×C₄⋊C₄	—	2	1	no	—
51	C₅×C₂²⋊C₄	Q₁₆	1	2	yes	—
52	C₄²×C₅	—	2	1	no	—
53	C₅×C₁₆	—	2	2	no	—
54	C₅×C₁₆	—	4	1	no	—
55	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
56	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
57	#430	—	2	2	no	—
58	C₂×#108	C₂²×C₅	1	2	yes	—
59	C₂×#108	C₂²×C₅	1	2	yes	—
60	#405	C₂²×C₅	1	1	yes	characteristic
61	#368	—	2	2	no	—
62	C₄⋊C₁₆	—	2	2	no	—
63	#344	—	2	2	no	—
64	C₂³×C₅	C₂×Q₁₆	1	1	yes	characteristic
65	C₂×C₄×C₅	—	2	2	no	—
66	C₂×C₄×C₅	#121	1	1	yes	characteristic
67	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
68	C₂×C₄×C₅	#135	1	1	yes	characteristic
69	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
70	C₅×C₈	—	4	1	no	—
71	C₅×C₈	—	4	4	no	—
72	C₅×C₈	—	8	2	no	—
73	C₅×C₈	#123	1	1	yes	characteristic
74	C₅×C₈	#125	1	2	yes	—
75	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
76	C₂×M₁₆	—	2	2	no	—
77	C₂×M₁₆	—	2	2	no	—
78	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
79	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
80	#117	C₅×D₄	1	1	yes	characteristic
81	M₃₂	—	2	2	no	—
82	C₂×C₁₆	—	2	1	no	—
83	C₂×C₁₆	—	2	2	no	—
84	C₂×C₁₆	C₅×D₄	1	2	yes	—
85	#108	—	2	2	no	—
86	#108	—	2	2	no	—
87	#108	—	2	2	no	—
88	#108	—	4	4	no	—
89	#108	C₅×Q₈	1	4	yes	—
90	#97	—	2	1	no	—
91	C₄×C₈	—	2	1	no	—
92	C₂²×C₅	—	4	1	no	—
93	C₂²×C₅	#467	1	1	yes	characteristic
94	C₂²×C₅	#477	1	2	yes	—
95	C₄×C₅	—	4	2	no	—
96	C₄×C₅	#398	1	1	yes	characteristic
97	C₄×C₅	#469	1	1	yes	characteristic
98	C₄×C₅	#478	1	2	yes	—
99	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
100	M₁₆	—	2	4	no	—
101	M₁₆	—	2	2	no	—
102	M₁₆	—	4	2	no	—
103	M₁₆	—	4	2	no	—
104	M₁₆	—	4	2	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	4	2	no	—
107	C₂×C₈	—	4	2	no	—
108	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
109	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
110	C₂×C₈	C₅×#41	1	2	yes	—
111	C₂×C₈	C₅×#41	1	1	yes	characteristic
112	C₄⋊C₄	—	2	1	no	—
113	C₂²⋊C₄	C₅×Q₁₆	1	2	yes	—
114	C₄²	—	2	1	no	—
115	C₁₆	—	2	2	no	—
116	C₁₆	—	4	1	no	—
117	C₂×C₅	—	2	1	no	—
118	C₂×C₅	—	2	2	no	—
119	C₂×C₅	#2087	1	1	yes	characteristic
120	C₂³	C₂×C₅×Q₁₆	1	1	yes	characteristic
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	C₅×#121	1	1	yes	characteristic
123	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
124	C₂×C₄	C₅×#135	1	1	yes	characteristic
125	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
126	C₈	—	4	1	no	—
127	C₈	—	4	4	no	—
128	C₈	—	8	2	no	—
129	C₈	C₅×#123	1	1	yes	characteristic
130	C₈	C₅×#125	1	2	yes	—
131	C₈	C₅×C₄⋊Q₈	1	1	yes	characteristic
132	C₅	#13520	1	1	yes	characteristic, direct product factor, Sylow
133	C₂²	—	4	1	no	—
134	C₂²	C₅×#467	1	1	yes	characteristic
135	C₂²	C₅×#477	1	2	yes	—
136	C₄	—	4	2	no	—
137	C₄	C₅×#398	1	1	yes	characteristic
138	C₄	C₅×#469	1	1	yes	characteristic
139	C₄	C₅×#478	1	2	yes	—
140	C₂	—	2	1	no	—
141	C₂	—	2	2	no	—
142	C₂	C₅×#2087	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2161

C₂

yes

maximal, characteristic

C₅×#2151

C₂

yes

maximal, characteristic

C₅×#1953

C₂

yes

maximal

C₅×#1385

C₂

yes

maximal, characteristic

C₅×#1381

C₂

yes

maximal

C₂×C₅×M₃₂

C₂²

yes

characteristic

C₂²×C₅×C₁₆

C₂²

yes

characteristic

C₅×#430

—

C₂×C₅×#108

C₂²

yes

—

C₂×C₅×#108

C₂²

yes

—

C₅×#405

C₂²

yes

characteristic

C₅×#368

—

C₅×C₄⋊C₁₆

—

C₅×#344

—

#13520

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×M₁₆

—

C₂×C₅×M₁₆

—

C₂×C₅×M₁₆

D₄

yes

characteristic

C₂²×C₅×C₈

C₂³

yes

characteristic

C₅×#117

D₄

yes

characteristic

C₅×M₃₂

—

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

D₄

yes

—

—

—

—

—

Q₈

yes

—

C₅×#97

—

C₄×C₅×C₈

—

#2161

C₂×C₅

yes

characteristic

#2151

C₂×C₅

yes

characteristic

#1953

C₂×C₅

yes

—

#1385

C₂×C₅

yes

characteristic

#1381

C₂×C₅

yes

—

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₅×M₁₆

—

C₅×M₁₆

—

C₅×M₁₆

—

C₅×M₁₆

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₂×D₄

yes

characteristic

C₂×C₅×C₈

C₂×Q₈

yes

—

C₂×C₅×C₈

#41

yes

—

C₂×C₅×C₈

#41

yes

characteristic

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

Q₁₆

yes

—

C₄²×C₅

—

C₅×C₁₆

—

C₅×C₁₆

—

C₂×M₃₂

C₂²×C₅

yes

characteristic

C₂²×C₁₆

C₂²×C₅

yes

characteristic

#430

—

C₂×#108

C₂²×C₅

yes

—

C₂×#108

C₂²×C₅

yes

—

#405

C₂²×C₅

yes

characteristic

#368

—

C₄⋊C₁₆

—

#344

—

C₂³×C₅

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

#121

yes

characteristic

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₂×C₄×C₅

#135

yes

characteristic

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

#123

yes

characteristic

C₅×C₈

#125

yes

—

C₅×C₈

C₄⋊Q₈

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₅×D₄

yes

characteristic

C₂²×C₈

C₂³×C₅

yes

characteristic

#117

C₅×D₄

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₅×D₄

yes

—

—

—

—

—

C₅×Q₈

yes

—

#97

—

C₄×C₈

—

C₂²×C₅

—

C₂²×C₅

#467

yes

characteristic

C₂²×C₅

#477

yes

—

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

C₄×C₅

yes

—

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂×C₅×D₄

yes

characteristic

109

C₂×C₈

C₂×C₅×Q₈

yes

—

110

C₂×C₈

C₅×#41

yes

—

111

C₂×C₈

C₅×#41

yes

characteristic

112

C₄⋊C₄

—

113

C₂²⋊C₄

C₅×Q₁₆

yes

—

114

C₄²

—

115

C₁₆

—

116

C₁₆

—

117

C₂×C₅

—

118

C₂×C₅

—

119

C₂×C₅

#2087

yes

characteristic

120

C₂³

C₂×C₅×Q₁₆

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

C₅×#121

yes

characteristic

123

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

124

C₂×C₄

C₅×#135

yes

characteristic

125

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

C₅×#123

yes

characteristic

130

C₈

C₅×#125

yes

—

131

C₈

C₅×C₄⋊Q₈

yes

characteristic

132

C₅

#13520

yes

characteristic, direct product factor, Sylow

133

C₂²

—

134

C₂²

C₅×#467

yes

characteristic

135

C₂²

C₅×#477

yes

—

136

C₄

—

137

C₄

C₅×#398

yes

characteristic

138

C₄

C₅×#469

yes

characteristic

139

C₄

C₅×#478

yes

—

140

C₂

—

141

C₂

—

142

C₂

C₅×#2087

yes

characteristic

	subgroup	G/H
center	C₄×C₅	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂×C₅	#2087
prime radical	C₂³×C₅	C₂×Q₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#405 ◁ G

subgroup

G/H

center

C₄×C₅

#469

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₅

socle

C₂×C₅

#2087

prime radical

C₂³×C₅

C₂×Q₁₆

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#405 ◁ G

N	H ≅ G/N	type
15. #13520	C₅	direct (N × H)
132. C₅	#13520	direct (N × H)

H ≅ G/N

type

15. #13520

C₅

direct (N × H)

132. C₅

#13520

direct (N × H)

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

subgroup	index
C₅×#2161	2
C₅×#2151	2
C₅×#1953	2
C₅×#1385	2
C₅×#1381	2
#13520	5

subgroup

index

Subgroups — C₅×#13520 #11936240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#13520 #11936240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13520 #11936240