Group #15696678 — subgroups

Subgroups — C₁₃×#10339 #15696678

Order 3328.

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

normal subgroups only

This group has 738 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×#2483	C₂	1	3	yes	maximal
2	C₁₃×#1819	C₂	1	3	yes	maximal
3	C₁₃×#1304	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
5	C₁₃×#397	—	2	6	no	—
6	C₁₃×#385	—	2	6	no	—
7	C₁₃×#381	—	2	6	no	—
8	C₁₃×#379	C₂²	1	1	yes	characteristic
9	C₁₃×#379	C₂²	1	3	yes	—
10	C₁₃×#342	—	2	6	no	—
11	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
12	C₂³×C₄×C₁₃	D₄	1	6	yes	—
13	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
14	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
15	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
16	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
17	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
18	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
19	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
20	C₂×C₁₃×C₂²⋊C₄	D₄	1	6	yes	—
21	C₁₃×#95	—	2	6	no	—
22	C₁₃×#95	—	2	12	no	—
23	#10339	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂⁴×C₁₃	—	4	6	no	—
25	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
26	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
27	C₂⁴×C₁₃	#41	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	—	2	6	no	—
29	C₂²×C₄×C₁₃	—	2	6	no	—
30	C₂²×C₄×C₁₃	—	2	6	no	—
31	C₂²×C₄×C₁₃	—	2	6	no	—
32	C₂²×C₄×C₁₃	—	4	12	no	—
33	C₂²×C₄×C₁₃	—	4	1	no	—
34	C₁₃×C₄⋊C₄	—	8	6	no	—
35	C₁₃×C₂²⋊C₄	—	4	12	no	—
36	C₁₃×C₂²⋊C₄	—	4	3	no	—
37	C₁₃×C₂²⋊C₄	—	4	6	no	—
38	C₁₃×C₂²⋊C₄	—	4	3	no	—
39	C₁₃×C₂²⋊C₄	—	4	6	no	—
40	C₁₃×C₂²⋊C₄	—	4	6	no	—
41	#2483	C₂×C₁₃	1	3	yes	—
42	#1819	C₂×C₁₃	1	3	yes	—
43	#1304	C₂×C₁₃	1	1	yes	characteristic
44	C₂³×C₁₃	—	2	12	no	—
45	C₂³×C₁₃	—	2	6	no	—
46	C₂³×C₁₃	—	4	3	no	—
47	C₂³×C₁₃	—	4	6	no	—
48	C₂³×C₁₃	—	4	3	no	—
49	C₂³×C₁₃	—	8	8	no	—
50	C₂³×C₁₃	#120	1	3	yes	—
51	C₂³×C₁₃	#121	1	3	yes	—
52	C₂³×C₁₃	#127	1	1	yes	characteristic
53	C₂×C₄×C₁₃	—	4	12	no	—
54	C₂×C₄×C₁₃	—	4	12	no	—
55	C₂×C₄×C₁₃	—	4	6	no	—
56	C₂×C₄×C₁₃	—	4	6	no	—
57	C₂×C₄×C₁₃	—	4	12	no	—
58	C₂×C₄×C₁₃	—	8	6	no	—
59	C₂×C₄×C₁₃	—	8	3	no	—
60	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
61	#397	—	2	6	no	—
62	#385	—	2	6	no	—
63	#381	—	2	6	no	—
64	#379	C₂²×C₁₃	1	1	yes	characteristic
65	#379	C₂²×C₁₃	1	3	yes	—
66	#342	—	2	6	no	—
67	C₂²×C₁₃	—	2	6	no	—
68	C₂²×C₁₃	—	2	6	no	—
69	C₂²×C₁₃	—	2	3	no	—
70	C₂²×C₁₃	—	2	3	no	—
71	C₂²×C₁₃	—	4	12	no	—
72	C₂²×C₁₃	—	8	6	no	—
73	C₂²×C₁₃	—	8	2	no	—
74	C₂²×C₁₃	#392	1	1	yes	characteristic
75	C₂²×C₁₃	#458	1	6	yes	—
76	C₄×C₁₃	—	8	6	no	—
77	C₄×C₁₃	—	8	6	no	—
78	C₄×C₁₃	—	16	1	no	—
79	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
80	C₂³×C₄	D₄×C₁₃	1	6	yes	—
81	C₂×C₄⋊C₄	—	2	6	no	—
82	C₂×C₂²⋊C₄	—	2	3	no	—
83	C₂×C₂²⋊C₄	—	2	6	no	—
84	C₂×C₂²⋊C₄	—	2	6	no	—
85	C₂×C₂²⋊C₄	—	2	6	no	—
86	C₂×C₂²⋊C₄	—	2	3	no	—
87	C₂×C₂²⋊C₄	—	2	3	no	—
88	C₂×C₂²⋊C₄	D₄×C₁₃	1	6	yes	—
89	#95	—	2	6	no	—
90	#95	—	2	12	no	—
91	C₂×C₁₃	—	2	6	no	—
92	C₂×C₁₃	—	4	1	no	—
93	C₂×C₁₃	—	4	3	no	—
94	C₂×C₁₃	#2022	1	3	yes	—
95	C₂⁴	—	4	6	no	—
96	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
97	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
98	C₂⁴	C₁₃×#41	1	1	yes	characteristic
99	C₂²×C₄	—	2	6	no	—
100	C₂²×C₄	—	2	6	no	—
101	C₂²×C₄	—	2	6	no	—
102	C₂²×C₄	—	2	6	no	—
103	C₂²×C₄	—	4	12	no	—
104	C₂²×C₄	—	4	1	no	—
105	C₄⋊C₄	—	8	6	no	—
106	C₂²⋊C₄	—	4	12	no	—
107	C₂²⋊C₄	—	4	3	no	—
108	C₂²⋊C₄	—	4	6	no	—
109	C₂²⋊C₄	—	4	3	no	—
110	C₂²⋊C₄	—	4	6	no	—
111	C₂²⋊C₄	—	4	6	no	—
112	C₁₃	#10339	1	1	yes	characteristic, direct product factor, Sylow
113	C₂³	—	2	12	no	—
114	C₂³	—	2	6	no	—
115	C₂³	—	4	3	no	—
116	C₂³	—	4	6	no	—
117	C₂³	—	4	3	no	—
118	C₂³	—	8	8	no	—
119	C₂³	C₁₃×#120	1	3	yes	—
120	C₂³	C₁₃×#121	1	3	yes	—
121	C₂³	C₁₃×#127	1	1	yes	characteristic
122	C₂×C₄	—	4	12	no	—
123	C₂×C₄	—	4	12	no	—
124	C₂×C₄	—	4	6	no	—
125	C₂×C₄	—	4	6	no	—
126	C₂×C₄	—	4	12	no	—
127	C₂×C₄	—	8	6	no	—
128	C₂×C₄	—	8	3	no	—
129	C₂²	—	2	6	no	—
130	C₂²	—	2	6	no	—
131	C₂²	—	2	3	no	—
132	C₂²	—	2	3	no	—
133	C₂²	—	4	12	no	—
134	C₂²	—	8	6	no	—
135	C₂²	—	8	2	no	—
136	C₂²	C₁₃×#392	1	1	yes	characteristic
137	C₂²	C₁₃×#458	1	6	yes	—
138	C₄	—	8	6	no	—
139	C₄	—	8	6	no	—
140	C₄	—	16	1	no	—
141	C₂	—	2	6	no	—
142	C₂	—	4	1	no	—
143	C₂	—	4	3	no	—
144	C₂	C₁₃×#2022	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2483

C₂

yes

maximal

C₁₃×#1819

C₂

yes

maximal

C₁₃×#1304

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₂²⋊C₄

C₂²

yes

—

C₁₃×#397

—

C₁₃×#385

—

C₁₃×#381

—

C₁₃×#379

C₂²

yes

characteristic

C₁₃×#379

C₂²

yes

—

C₁₃×#342

—

C₂⁵×C₁₃

C₂³

yes

characteristic

C₂³×C₄×C₁₃

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

D₄

yes

—

C₁₃×#95

—

C₁₃×#95

—

#10339

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

—

C₂⁴×C₁₃

C₂×D₄

yes

—

C₂⁴×C₁₃

C₂×D₄

yes

—

C₂⁴×C₁₃

#41

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

#2483

C₂×C₁₃

yes

—

#1819

C₂×C₁₃

yes

—

#1304

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#120

yes

—

C₂³×C₁₃

#121

yes

—

C₂³×C₁₃

#127

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂²×C₂²⋊C₄

C₂²×C₁₃

yes

—

—

—

—

C₂²×C₁₃

yes

characteristic

#379

C₂²×C₁₃

yes

—

#342

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#392

yes

characteristic

C₂²×C₁₃

#458

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₂⁵

C₂³×C₁₃

yes

characteristic

C₂³×C₄

D₄×C₁₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

D₄×C₁₃

yes

—

#95

—

#95

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#2022

yes

—

C₂⁴

—

C₂⁴

C₂×D₄×C₁₃

yes

—

C₂⁴

C₂×D₄×C₁₃

yes

—

C₂⁴

C₁₃×#41

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

—

112

C₁₃

#10339

yes

characteristic, direct product factor, Sylow

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₁₃×#120

yes

—

120

C₂³

C₁₃×#121

yes

—

121

C₂³

C₁₃×#127

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

C₁₃×#392

yes

characteristic

137

C₂²

C₁₃×#458

yes

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₂

—

142

C₂

—

143

C₂

—

144

C₂

C₁₃×#2022

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#392

commutator, Frattini, cosocle

C₂⁵

C₂³×C₁₃

prime radical

C₂⁵×C₁₃

C₂³

LCS

G ▷ C₂⁵ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

N	H ≅ G/N	type
23. #10339	C₁₃	direct (N × H)
112. C₁₃	#10339	direct (N × H)

H ≅ G/N

type

23. #10339

C₁₃

direct (N × H)

112. C₁₃

#10339

direct (N × H)

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

subgroup	index
C₁₃×#2483	2
C₁₃×#1819	2
C₁₃×#1304	2
#10339	13

subgroup

index

C₁₃×#2483

C₁₃×#1819

C₁₃×#1304

#10339

Subgroups — C₁₃×#10339 #15696678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10339 #15696678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10339 #15696678