Group #11936239 — subgroups

Subgroups — C₅×#13519 #11936239

Order 1280.

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

normal subgroups only

This group has 252 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×#2150	C₂	1	1	yes	maximal, characteristic
3	C₅×#1945	C₂	1	2	yes	maximal
4	C₅×#1389	C₂	1	2	yes	maximal
5	C₅×#1384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
8	C₂×C₅×#108	C₂²	1	2	yes	—
9	C₅×#427	C₂²	1	2	yes	—
10	C₅×#424	—	2	2	no	—
11	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×#368	—	2	2	no	—
13	C₅×C₄⋊C₁₆	—	2	2	no	—
14	C₅×#339	—	2	2	no	—
15	#13519	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×C₅×M₁₆	—	2	2	no	—
17	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
18	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
19	C₅×#117	—	2	2	no	—
20	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
21	C₅×M₃₂	—	2	2	no	—
22	C₅×M₃₂	—	2	2	no	—
23	C₂×C₅×C₁₆	—	2	1	no	—
24	C₂×C₅×C₁₆	D₄	1	2	yes	—
25	C₅×#108	—	2	2	no	—
26	C₅×#108	—	2	2	no	—
27	C₅×#107	—	2	2	no	—
28	C₅×#106	Q₈	1	4	yes	—
29	C₅×C₄⋊C₈	—	4	4	no	—
30	C₄×C₅×C₈	—	2	1	no	—
31	C₄×C₅×C₈	—	2	1	no	—
32	#2161	C₂×C₅	1	1	yes	characteristic
33	#2150	C₂×C₅	1	1	yes	characteristic
34	#1945	C₂×C₅	1	2	yes	—
35	#1389	C₂×C₅	1	2	yes	—
36	#1384	C₂×C₅	1	1	yes	characteristic
37	C₂²×C₄×C₅	—	2	1	no	—
38	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
39	C₅×M₁₆	—	4	2	no	—
40	C₅×M₁₆	—	4	2	no	—
41	C₂×C₅×C₈	—	2	1	no	—
42	C₂×C₅×C₈	—	2	2	no	—
43	C₂×C₅×C₈	—	4	2	no	—
44	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
45	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
46	C₂×C₅×C₈	#41	1	2	yes	—
47	C₂×C₅×C₈	#41	1	1	yes	characteristic
48	C₅×C₄⋊C₄	—	2	4	no	—
49	C₅×C₂²⋊C₄	—	4	2	no	—
50	C₄²×C₅	—	2	1	no	—
51	C₄²×C₅	—	4	2	no	—
52	C₄²×C₅	Q₁₆	1	1	yes	characteristic
53	C₄²×C₅	Q₁₆	1	1	yes	characteristic
54	C₅×C₁₆	—	2	2	no	—
55	C₅×C₁₆	—	4	1	no	—
56	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
57	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
58	C₂×#108	C₂²×C₅	1	2	yes	—
59	#427	C₂²×C₅	1	2	yes	—
60	#424	—	2	2	no	—
61	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
62	#368	—	2	2	no	—
63	C₄⋊C₁₆	—	2	2	no	—
64	#339	—	2	2	no	—
65	C₂³×C₅	#135	1	1	yes	characteristic
66	C₂×C₄×C₅	—	2	1	no	—
67	C₂×C₄×C₅	—	2	1	no	—
68	C₂×C₄×C₅	—	4	2	no	—
69	C₂×C₄×C₅	—	4	4	no	—
70	C₂×C₄×C₅	#121	1	1	yes	characteristic
71	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
72	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
73	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
74	C₅×C₈	—	4	1	no	—
75	C₅×C₈	—	8	2	no	—
76	C₅×C₈	#123	1	1	yes	characteristic
77	C₅×C₈	#125	1	2	yes	—
78	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
79	C₂×M₁₆	—	2	2	no	—
80	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
81	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
82	#117	—	2	2	no	—
83	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
84	M₃₂	—	2	2	no	—
85	M₃₂	—	2	2	no	—
86	C₂×C₁₆	—	2	1	no	—
87	C₂×C₁₆	C₅×D₄	1	2	yes	—
88	#108	—	2	2	no	—
89	#108	—	2	2	no	—
90	#107	—	2	2	no	—
91	#106	C₅×Q₈	1	4	yes	—
92	C₄⋊C₈	—	4	4	no	—
93	C₄×C₈	—	2	1	no	—
94	C₄×C₈	—	2	1	no	—
95	C₂²×C₅	—	4	1	no	—
96	C₂²×C₅	#467	1	1	yes	characteristic
97	C₂²×C₅	#478	1	2	yes	—
98	C₄×C₅	—	2	2	no	—
99	C₄×C₅	—	4	1	no	—
100	C₄×C₅	—	8	4	no	—
101	C₄×C₅	#398	1	1	yes	characteristic
102	C₄×C₅	#469	1	1	yes	characteristic
103	C₄×C₅	#477	1	2	yes	—
104	C₂²×C₄	—	2	1	no	—
105	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
106	M₁₆	—	4	2	no	—
107	M₁₆	—	4	2	no	—
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	4	2	no	—
111	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
112	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
113	C₂×C₈	C₅×#41	1	2	yes	—
114	C₂×C₈	C₅×#41	1	1	yes	characteristic
115	C₄⋊C₄	—	2	4	no	—
116	C₂²⋊C₄	—	4	2	no	—
117	C₄²	—	2	1	no	—
118	C₄²	—	4	2	no	—
119	C₄²	C₅×Q₁₆	1	1	yes	characteristic
120	C₄²	C₅×Q₁₆	1	1	yes	characteristic
121	C₁₆	—	2	2	no	—
122	C₁₆	—	4	1	no	—
123	C₂×C₅	—	2	1	no	—
124	C₂×C₅	—	2	2	no	—
125	C₂×C₅	#2087	1	1	yes	characteristic
126	C₂³	C₅×#135	1	1	yes	characteristic
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	C₅×#121	1	1	yes	characteristic
132	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
133	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
134	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
135	C₈	—	4	1	no	—
136	C₈	—	8	2	no	—
137	C₈	C₅×#123	1	1	yes	characteristic
138	C₈	C₅×#125	1	2	yes	—
139	C₈	C₅×C₄⋊Q₈	1	1	yes	characteristic
140	C₅	#13519	1	1	yes	characteristic, direct product factor, Sylow
141	C₂²	—	4	1	no	—
142	C₂²	C₅×#467	1	1	yes	characteristic
143	C₂²	C₅×#478	1	2	yes	—
144	C₄	—	2	2	no	—
145	C₄	—	4	1	no	—
146	C₄	—	8	4	no	—
147	C₄	C₅×#398	1	1	yes	characteristic
148	C₄	C₅×#469	1	1	yes	characteristic
149	C₄	C₅×#477	1	2	yes	—
150	C₂	—	2	1	no	—
151	C₂	—	2	2	no	—
152	C₂	C₅×#2087	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2161

C₂

yes

maximal, characteristic

C₅×#2150

C₂

yes

maximal, characteristic

C₅×#1945

C₂

yes

maximal

C₅×#1389

C₂

yes

maximal

C₅×#1384

C₂

yes

maximal, characteristic

C₂×C₅×M₃₂

C₂²

yes

characteristic

C₂×C₅×M₃₂

C₂²

yes

characteristic

C₂×C₅×#108

C₂²

yes

—

C₅×#427

C₂²

yes

—

C₅×#424

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₅×#368

—

C₅×C₄⋊C₁₆

—

C₅×#339

—

#13519

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₅×M₁₆

—

C₂²×C₅×C₈

D₄

yes

characteristic

C₂²×C₅×C₈

C₂³

yes

characteristic

C₅×#117

—

C₂×C₄²×C₅

D₄

yes

characteristic

C₅×M₃₂

—

C₅×M₃₂

—

C₂×C₅×C₁₆

—

C₂×C₅×C₁₆

D₄

yes

—

—

—

—

Q₈

yes

—

C₅×C₄⋊C₈

—

C₄×C₅×C₈

—

C₄×C₅×C₈

—

#2161

C₂×C₅

yes

characteristic

#2150

C₂×C₅

yes

characteristic

#1945

C₂×C₅

yes

—

#1389

C₂×C₅

yes

—

#1384

C₂×C₅

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

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

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

Q₁₆

yes

characteristic

C₄²×C₅

Q₁₆

yes

characteristic

C₅×C₁₆

—

C₅×C₁₆

—

C₂×M₃₂

C₂²×C₅

yes

characteristic

C₂×M₃₂

C₂²×C₅

yes

characteristic

C₂×#108

C₂²×C₅

yes

—

#427

C₂²×C₅

yes

—

#424

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

#368

—

C₄⋊C₁₆

—

#339

—

C₂³×C₅

#135

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#121

yes

characteristic

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₂×C₄×C₅

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

#123

yes

characteristic

C₅×C₈

#125

yes

—

C₅×C₈

C₄⋊Q₈

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₅×D₄

yes

characteristic

C₂²×C₈

C₂³×C₅

yes

characteristic

#117

—

C₂×C₄²

C₅×D₄

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₅×D₄

yes

—

—

—

—

C₅×Q₈

yes

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₅

—

C₂²×C₅

#467

yes

characteristic

C₂²×C₅

#478

yes

—

C₄×C₅

—

C₄×C₅

—

100

C₄×C₅

—

101

C₄×C₅

#398

yes

characteristic

102

C₄×C₅

#469

yes

characteristic

103

C₄×C₅

#477

yes

—

104

C₂²×C₄

—

105

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

106

M₁₆

—

107

M₁₆

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

C₂×C₅×D₄

yes

characteristic

112

C₂×C₈

C₂×C₅×Q₈

yes

—

113

C₂×C₈

C₅×#41

yes

—

114

C₂×C₈

C₅×#41

yes

characteristic

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₄²

—

119

C₄²

C₅×Q₁₆

yes

characteristic

120

C₄²

C₅×Q₁₆

yes

characteristic

121

C₁₆

—

122

C₁₆

—

123

C₂×C₅

—

124

C₂×C₅

—

125

C₂×C₅

#2087

yes

characteristic

126

C₂³

C₅×#135

yes

characteristic

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₅×#121

yes

characteristic

132

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

133

C₂×C₄

C₂×C₅×Q₁₆

yes

characteristic

134

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

135

C₈

—

136

C₈

—

137

C₈

C₅×#123

yes

characteristic

138

C₈

C₅×#125

yes

—

139

C₈

C₅×C₄⋊Q₈

yes

characteristic

140

C₅

#13519

yes

characteristic, direct product factor, Sylow

141

C₂²

—

142

C₂²

C₅×#467

yes

characteristic

143

C₂²

C₅×#478

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

C₅×#398

yes

characteristic

148

C₄

C₅×#469

yes

characteristic

149

C₄

C₅×#477

yes

—

150

C₂

—

151

C₂

—

152

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	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

subgroup

G/H

center

C₄×C₅

#469

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₅

C₂×C₅

C₂³×C₅

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

N	H ≅ G/N	type
15. #13519	C₅	direct (N × H)
140. C₅	#13519	direct (N × H)

H ≅ G/N

type

15. #13519

C₅

direct (N × H)

140. C₅

#13519

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×#2150	2
C₅×#1945	2
C₅×#1389	2
C₅×#1384	2
#13519	5

subgroup

index

Subgroups — C₅×#13519 #11936239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#13519 #11936239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13519 #11936239