Group #15699859 — subgroups

Subgroups — C₁₃×#13520 #15699859

Order 3328.

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	C₁₃×#2161	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2151	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1953	C₂	1	2	yes	maximal
4	C₁₃×#1385	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1381	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×#430	—	2	2	no	—
9	C₂×C₁₃×#108	C₂²	1	2	yes	—
10	C₂×C₁₃×#108	C₂²	1	2	yes	—
11	C₁₃×#405	C₂²	1	1	yes	characteristic
12	C₁₃×#368	—	2	2	no	—
13	C₁₃×C₄⋊C₁₆	—	2	2	no	—
14	C₁₃×#344	—	2	2	no	—
15	C₂×C₁₃×M₁₆	—	2	2	no	—
16	C₂×C₁₃×M₁₆	—	2	2	no	—
17	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₁₃×#117	D₄	1	1	yes	characteristic
20	C₁₃×M₃₂	—	2	2	no	—
21	C₂×C₁₃×C₁₆	—	2	1	no	—
22	C₂×C₁₃×C₁₆	—	2	2	no	—
23	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
24	C₁₃×#108	—	2	2	no	—
25	C₁₃×#108	—	2	2	no	—
26	C₁₃×#108	—	2	2	no	—
27	C₁₃×#108	—	4	4	no	—
28	C₁₃×#108	Q₈	1	4	yes	—
29	C₁₃×#97	—	2	1	no	—
30	C₄×C₈×C₁₃	—	2	1	no	—
31	#13520	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₁₃×M₁₆	—	2	4	no	—
34	C₁₃×M₁₆	—	2	2	no	—
35	C₁₃×M₁₆	—	4	2	no	—
36	C₁₃×M₁₆	—	4	2	no	—
37	C₁₃×M₁₆	—	4	2	no	—
38	C₂×C₈×C₁₃	—	2	1	no	—
39	C₂×C₈×C₁₃	—	4	2	no	—
40	C₂×C₈×C₁₃	—	4	2	no	—
41	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
43	C₂×C₈×C₁₃	#41	1	2	yes	—
44	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
45	C₁₃×C₄⋊C₄	—	2	1	no	—
46	C₁₃×C₂²⋊C₄	Q₁₆	1	2	yes	—
47	C₄²×C₁₃	—	2	1	no	—
48	C₁₃×C₁₆	—	2	2	no	—
49	C₁₃×C₁₆	—	4	1	no	—
50	#2161	C₂×C₁₃	1	1	yes	characteristic
51	#2151	C₂×C₁₃	1	1	yes	characteristic
52	#1953	C₂×C₁₃	1	2	yes	—
53	#1385	C₂×C₁₃	1	1	yes	characteristic
54	#1381	C₂×C₁₃	1	2	yes	—
55	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
56	C₂×C₄×C₁₃	—	2	2	no	—
57	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
59	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
60	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
61	C₈×C₁₃	—	4	1	no	—
62	C₈×C₁₃	—	4	4	no	—
63	C₈×C₁₃	—	8	2	no	—
64	C₈×C₁₃	#123	1	1	yes	characteristic
65	C₈×C₁₃	#125	1	2	yes	—
66	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
67	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
68	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
69	#430	—	2	2	no	—
70	C₂×#108	C₂²×C₁₃	1	2	yes	—
71	C₂×#108	C₂²×C₁₃	1	2	yes	—
72	#405	C₂²×C₁₃	1	1	yes	characteristic
73	#368	—	2	2	no	—
74	C₄⋊C₁₆	—	2	2	no	—
75	#344	—	2	2	no	—
76	C₂²×C₁₃	—	4	1	no	—
77	C₂²×C₁₃	#467	1	1	yes	characteristic
78	C₂²×C₁₃	#477	1	2	yes	—
79	C₄×C₁₃	—	4	2	no	—
80	C₄×C₁₃	#398	1	1	yes	characteristic
81	C₄×C₁₃	#469	1	1	yes	characteristic
82	C₄×C₁₃	#478	1	2	yes	—
83	C₂×M₁₆	—	2	2	no	—
84	C₂×M₁₆	—	2	2	no	—
85	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
86	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
87	#117	D₄×C₁₃	1	1	yes	characteristic
88	M₃₂	—	2	2	no	—
89	C₂×C₁₆	—	2	1	no	—
90	C₂×C₁₆	—	2	2	no	—
91	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
92	#108	—	2	2	no	—
93	#108	—	2	2	no	—
94	#108	—	2	2	no	—
95	#108	—	4	4	no	—
96	#108	Q₈×C₁₃	1	4	yes	—
97	#97	—	2	1	no	—
98	C₄×C₈	—	2	1	no	—
99	C₂×C₁₃	—	2	1	no	—
100	C₂×C₁₃	—	2	2	no	—
101	C₂×C₁₃	#2087	1	1	yes	characteristic
102	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
103	M₁₆	—	2	4	no	—
104	M₁₆	—	2	2	no	—
105	M₁₆	—	4	2	no	—
106	M₁₆	—	4	2	no	—
107	M₁₆	—	4	2	no	—
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	—	4	2	no	—
110	C₂×C₈	—	4	2	no	—
111	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
112	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
113	C₂×C₈	C₁₃×#41	1	2	yes	—
114	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
115	C₄⋊C₄	—	2	1	no	—
116	C₂²⋊C₄	C₁₃×Q₁₆	1	2	yes	—
117	C₄²	—	2	1	no	—
118	C₁₆	—	2	2	no	—
119	C₁₆	—	4	1	no	—
120	C₁₃	#13520	1	1	yes	characteristic, direct product factor, Sylow
121	C₂³	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
124	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
125	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
126	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
127	C₈	—	4	1	no	—
128	C₈	—	4	4	no	—
129	C₈	—	8	2	no	—
130	C₈	C₁₃×#123	1	1	yes	characteristic
131	C₈	C₁₃×#125	1	2	yes	—
132	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
133	C₂²	—	4	1	no	—
134	C₂²	C₁₃×#467	1	1	yes	characteristic
135	C₂²	C₁₃×#477	1	2	yes	—
136	C₄	—	4	2	no	—
137	C₄	C₁₃×#398	1	1	yes	characteristic
138	C₄	C₁₃×#469	1	1	yes	characteristic
139	C₄	C₁₃×#478	1	2	yes	—
140	C₂	—	2	1	no	—
141	C₂	—	2	2	no	—
142	C₂	C₁₃×#2087	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2161

C₂

yes

maximal, characteristic

C₁₃×#2151

C₂

yes

maximal, characteristic

C₁₃×#1953

C₂

yes

maximal

C₁₃×#1385

C₂

yes

maximal, characteristic

C₁₃×#1381

C₂

yes

maximal

C₂×C₁₃×M₃₂

C₂²

yes

characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₁₃×#430

—

C₂×C₁₃×#108

C₂²

yes

—

C₂×C₁₃×#108

C₂²

yes

—

C₁₃×#405

C₂²

yes

characteristic

C₁₃×#368

—

C₁₃×C₄⋊C₁₆

—

C₁₃×#344

—

C₂×C₁₃×M₁₆

—

C₂×C₁₃×M₁₆

—

C₂×C₁₃×M₁₆

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×#117

D₄

yes

characteristic

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

D₄

yes

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×#108

Q₈

yes

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

#13520

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

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

Q₁₆

yes

—

C₄²×C₁₃

—

C₁₃×C₁₆

—

C₁₃×C₁₆

—

#2161

C₂×C₁₃

yes

characteristic

#2151

C₂×C₁₃

yes

characteristic

#1953

C₂×C₁₃

yes

—

#1385

C₂×C₁₃

yes

characteristic

#1381

C₂×C₁₃

yes

—

C₂³×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#121

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

#135

yes

characteristic

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₈×C₁₃

—

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

C₂²×C₁₆

C₂²×C₁₃

yes

characteristic

#430

—

C₂×#108

C₂²×C₁₃

yes

—

C₂×#108

C₂²×C₁₃

yes

—

#405

C₂²×C₁₃

yes

characteristic

#368

—

C₄⋊C₁₆

—

#344

—

C₂²×C₁₃

—

C₂²×C₁₃

#467

yes

characteristic

C₂²×C₁₃

#477

yes

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

D₄×C₁₃

yes

characteristic

C₂²×C₈

C₂³×C₁₃

yes

characteristic

#117

D₄×C₁₃

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

D₄×C₁₃

yes

—

—

—

—

—

Q₈×C₁₃

yes

—

#97

—

C₄×C₈

—

C₂×C₁₃

—

100

C₂×C₁₃

—

101

C₂×C₁₃

#2087

yes

characteristic

102

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

107

M₁₆

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

C₂×D₄×C₁₃

yes

characteristic

112

C₂×C₈

C₂×Q₈×C₁₃

yes

—

113

C₂×C₈

C₁₃×#41

yes

—

114

C₂×C₈

C₁₃×#41

yes

characteristic

115

C₄⋊C₄

—

116

C₂²⋊C₄

C₁₃×Q₁₆

yes

—

117

C₄²

—

118

C₁₆

—

119

C₁₆

—

120

C₁₃

#13520

yes

characteristic, direct product factor, Sylow

121

C₂³

C₂×C₁₃×Q₁₆

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

C₁₃×#121

yes

characteristic

124

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

125

C₂×C₄

C₁₃×#135

yes

characteristic

126

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

C₁₃×#123

yes

characteristic

131

C₈

C₁₃×#125

yes

—

132

C₈

C₁₃×C₄⋊Q₈

yes

characteristic

133

C₂²

—

134

C₂²

C₁₃×#467

yes

characteristic

135

C₂²

C₁₃×#477

yes

—

136

C₄

—

137

C₄

C₁₃×#398

yes

characteristic

138

C₄

C₁₃×#469

yes

characteristic

139

C₄

C₁₃×#478

yes

—

140

C₂

—

141

C₂

—

142

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	C₂×Q₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

subgroup

G/H

center

C₄×C₁₃

#469

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

socle

C₂×C₁₃

#2087

prime radical

C₂³×C₁₃

C₂×Q₁₆

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

N	H ≅ G/N	type
31. #13520	C₁₃	direct (N × H)
120. C₁₃	#13520	direct (N × H)

H ≅ G/N

type

31. #13520

C₁₃

direct (N × H)

120. C₁₃

#13520

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×#2151	2
C₁₃×#1953	2
C₁₃×#1385	2
C₁₃×#1381	2
#13520	13

subgroup

index

C₁₃×#2161

C₁₃×#2151

C₁₃×#1953

C₁₃×#1385

C₁₃×#1381

#13520

Subgroups — C₁₃×#13520 #15699859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#13520 #15699859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13520 #15699859