Group #15699858 — subgroups

Subgroups — C₁₃×#13519 #15699858

Order 3328.

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	C₁₃×#2161	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1945	C₂	1	2	yes	maximal
4	C₁₃×#1389	C₂	1	2	yes	maximal
5	C₁₃×#1384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#108	C₂²	1	2	yes	—
9	C₁₃×#427	C₂²	1	2	yes	—
10	C₁₃×#424	—	2	2	no	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#368	—	2	2	no	—
13	C₁₃×C₄⋊C₁₆	—	2	2	no	—
14	C₁₃×#339	—	2	2	no	—
15	C₂×C₁₃×M₁₆	—	2	2	no	—
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₁₃×#117	—	2	2	no	—
19	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₁₃×M₃₂	—	2	2	no	—
21	C₁₃×M₃₂	—	2	2	no	—
22	C₂×C₁₃×C₁₆	—	2	1	no	—
23	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
24	C₁₃×#108	—	2	2	no	—
25	C₁₃×#108	—	2	2	no	—
26	C₁₃×#107	—	2	2	no	—
27	C₁₃×#106	Q₈	1	4	yes	—
28	C₁₃×C₄⋊C₈	—	4	4	no	—
29	C₄×C₈×C₁₃	—	2	1	no	—
30	C₄×C₈×C₁₃	—	2	1	no	—
31	#13519	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₄×C₁₃	—	2	1	no	—
33	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₁₃×M₁₆	—	4	2	no	—
35	C₁₃×M₁₆	—	4	2	no	—
36	C₂×C₈×C₁₃	—	2	1	no	—
37	C₂×C₈×C₁₃	—	2	2	no	—
38	C₂×C₈×C₁₃	—	4	2	no	—
39	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
41	C₂×C₈×C₁₃	#41	1	2	yes	—
42	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
43	C₁₃×C₄⋊C₄	—	2	4	no	—
44	C₁₃×C₂²⋊C₄	—	4	2	no	—
45	C₄²×C₁₃	—	2	1	no	—
46	C₄²×C₁₃	—	4	2	no	—
47	C₄²×C₁₃	Q₁₆	1	1	yes	characteristic
48	C₄²×C₁₃	Q₁₆	1	1	yes	characteristic
49	C₁₃×C₁₆	—	2	2	no	—
50	C₁₃×C₁₆	—	4	1	no	—
51	#2161	C₂×C₁₃	1	1	yes	characteristic
52	#2150	C₂×C₁₃	1	1	yes	characteristic
53	#1945	C₂×C₁₃	1	2	yes	—
54	#1389	C₂×C₁₃	1	2	yes	—
55	#1384	C₂×C₁₃	1	1	yes	characteristic
56	C₂³×C₁₃	#135	1	1	yes	characteristic
57	C₂×C₄×C₁₃	—	2	1	no	—
58	C₂×C₄×C₁₃	—	2	1	no	—
59	C₂×C₄×C₁₃	—	4	2	no	—
60	C₂×C₄×C₁₃	—	4	4	no	—
61	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
63	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
64	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
65	C₈×C₁₃	—	4	1	no	—
66	C₈×C₁₃	—	8	2	no	—
67	C₈×C₁₃	#123	1	1	yes	characteristic
68	C₈×C₁₃	#125	1	2	yes	—
69	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
71	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
72	C₂×#108	C₂²×C₁₃	1	2	yes	—
73	#427	C₂²×C₁₃	1	2	yes	—
74	#424	—	2	2	no	—
75	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
76	#368	—	2	2	no	—
77	C₄⋊C₁₆	—	2	2	no	—
78	#339	—	2	2	no	—
79	C₂²×C₁₃	—	4	1	no	—
80	C₂²×C₁₃	#467	1	1	yes	characteristic
81	C₂²×C₁₃	#478	1	2	yes	—
82	C₄×C₁₃	—	2	2	no	—
83	C₄×C₁₃	—	4	1	no	—
84	C₄×C₁₃	—	8	4	no	—
85	C₄×C₁₃	#398	1	1	yes	characteristic
86	C₄×C₁₃	#469	1	1	yes	characteristic
87	C₄×C₁₃	#477	1	2	yes	—
88	C₂×M₁₆	—	2	2	no	—
89	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
90	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
91	#117	—	2	2	no	—
92	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
93	M₃₂	—	2	2	no	—
94	M₃₂	—	2	2	no	—
95	C₂×C₁₆	—	2	1	no	—
96	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
97	#108	—	2	2	no	—
98	#108	—	2	2	no	—
99	#107	—	2	2	no	—
100	#106	Q₈×C₁₃	1	4	yes	—
101	C₄⋊C₈	—	4	4	no	—
102	C₄×C₈	—	2	1	no	—
103	C₄×C₈	—	2	1	no	—
104	C₂×C₁₃	—	2	1	no	—
105	C₂×C₁₃	—	2	2	no	—
106	C₂×C₁₃	#2087	1	1	yes	characteristic
107	C₂²×C₄	—	2	1	no	—
108	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
109	M₁₆	—	4	2	no	—
110	M₁₆	—	4	2	no	—
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	2	2	no	—
113	C₂×C₈	—	4	2	no	—
114	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
115	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
116	C₂×C₈	C₁₃×#41	1	2	yes	—
117	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
118	C₄⋊C₄	—	2	4	no	—
119	C₂²⋊C₄	—	4	2	no	—
120	C₄²	—	2	1	no	—
121	C₄²	—	4	2	no	—
122	C₄²	C₁₃×Q₁₆	1	1	yes	characteristic
123	C₄²	C₁₃×Q₁₆	1	1	yes	characteristic
124	C₁₆	—	2	2	no	—
125	C₁₆	—	4	1	no	—
126	C₁₃	#13519	1	1	yes	characteristic, direct product factor, Sylow
127	C₂³	C₁₃×#135	1	1	yes	characteristic
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	4	4	no	—
132	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
133	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
134	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
135	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
136	C₈	—	4	1	no	—
137	C₈	—	8	2	no	—
138	C₈	C₁₃×#123	1	1	yes	characteristic
139	C₈	C₁₃×#125	1	2	yes	—
140	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
141	C₂²	—	4	1	no	—
142	C₂²	C₁₃×#467	1	1	yes	characteristic
143	C₂²	C₁₃×#478	1	2	yes	—
144	C₄	—	2	2	no	—
145	C₄	—	4	1	no	—
146	C₄	—	8	4	no	—
147	C₄	C₁₃×#398	1	1	yes	characteristic
148	C₄	C₁₃×#469	1	1	yes	characteristic
149	C₄	C₁₃×#477	1	2	yes	—
150	C₂	—	2	1	no	—
151	C₂	—	2	2	no	—
152	C₂	C₁₃×#2087	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2161

C₂

yes

maximal, characteristic

C₁₃×#2150

C₂

yes

maximal, characteristic

C₁₃×#1945

C₂

yes

maximal

C₁₃×#1389

C₂

yes

maximal

C₁₃×#1384

C₂

yes

maximal, characteristic

C₂×C₁₃×M₃₂

C₂²

yes

characteristic

C₂×C₁₃×M₃₂

C₂²

yes

characteristic

C₂×C₁₃×#108

C₂²

yes

—

C₁₃×#427

C₂²

yes

—

C₁₃×#424

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#368

—

C₁₃×C₄⋊C₁₆

—

C₁₃×#339

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×#117

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₁₃×M₃₂

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

D₄

yes

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×#107

—

C₁₃×#106

Q₈

yes

—

C₁₃×C₄⋊C₈

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

—

#13519

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

—

C₂×C₈×C₁₃

#41

yes

—

C₂×C₈×C₁₃

#41

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

Q₁₆

yes

characteristic

C₄²×C₁₃

Q₁₆

yes

characteristic

C₁₃×C₁₆

—

C₁₃×C₁₆

—

#2161

C₂×C₁₃

yes

characteristic

#2150

C₂×C₁₃

yes

characteristic

#1945

C₂×C₁₃

yes

—

#1389

C₂×C₁₃

yes

—

#1384

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

#135

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#121

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#123

yes

characteristic

C₈×C₁₃

#125

yes

—

C₈×C₁₃

C₄⋊Q₈

yes

characteristic

C₂×M₃₂

C₂²×C₁₃

yes

characteristic

C₂×M₃₂

C₂²×C₁₃

yes

characteristic

C₂×#108

C₂²×C₁₃

yes

—

#427

C₂²×C₁₃

yes

—

#424

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

#368

—

C₄⋊C₁₆

—

#339

—

C₂²×C₁₃

—

C₂²×C₁₃

#467

yes

characteristic

C₂²×C₁₃

#478

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂×M₁₆

—

C₂²×C₈

D₄×C₁₃

yes

characteristic

C₂²×C₈

C₂³×C₁₃

yes

characteristic

#117

—

C₂×C₄²

D₄×C₁₃

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

D₄×C₁₃

yes

—

#108

—

#108

—

#107

—

100

#106

Q₈×C₁₃

yes

—

101

C₄⋊C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₂×C₁₃

—

105

C₂×C₁₃

—

106

C₂×C₁₃

#2087

yes

characteristic

107

C₂²×C₄

—

108

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

C₂×D₄×C₁₃

yes

characteristic

115

C₂×C₈

C₂×Q₈×C₁₃

yes

—

116

C₂×C₈

C₁₃×#41

yes

—

117

C₂×C₈

C₁₃×#41

yes

characteristic

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

—

121

C₄²

—

122

C₄²

C₁₃×Q₁₆

yes

characteristic

123

C₄²

C₁₃×Q₁₆

yes

characteristic

124

C₁₆

—

125

C₁₆

—

126

C₁₃

#13519

yes

characteristic, direct product factor, Sylow

127

C₂³

C₁₃×#135

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

C₁₃×#121

yes

characteristic

133

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

134

C₂×C₄

C₂×C₁₃×Q₁₆

yes

characteristic

135

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

136

C₈

—

137

C₈

—

138

C₈

C₁₃×#123

yes

characteristic

139

C₈

C₁₃×#125

yes

—

140

C₈

C₁₃×C₄⋊Q₈

yes

characteristic

141

C₂²

—

142

C₂²

C₁₃×#467

yes

characteristic

143

C₂²

C₁₃×#478

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

C₁₃×#398

yes

characteristic

148

C₄

C₁₃×#469

yes

characteristic

149

C₄

C₁₃×#477

yes

—

150

C₂

—

151

C₂

—

152

C₂

C₁₃×#2087

yes

characteristic

	subgroup	G/H
center	C₄×C₁₃	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2087
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

subgroup

G/H

center

C₄×C₁₃

#469

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

C₂×C₁₃

C₂³×C₁₃

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
31. #13519	C₁₃	direct (N × H)
126. C₁₃	#13519	direct (N × H)

H ≅ G/N

type

31. #13519

C₁₃

direct (N × H)

126. C₁₃

#13519

direct (N × H)

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

subgroup	index
C₁₃×#2161	2
C₁₃×#2150	2
C₁₃×#1945	2
C₁₃×#1389	2
C₁₃×#1384	2
#13519	13

subgroup

index

C₁₃×#2161

C₁₃×#2150

C₁₃×#1945

C₁₃×#1389

C₁₃×#1384

#13519

Subgroups — C₁₃×#13519 #15699858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#13519 #15699858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13519 #15699858