Group #15756263 — subgroups

Subgroups — #15756263

Order 3328.

486 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 131 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	#13114904	C₂	1	2	yes	maximal
2	#13112679	C₂	1	4	yes	maximal
3	C₂×C₁₃×#383	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
5	C₁₃×#383	—	2	4	no	—
6	C₂×C₁₃×#95	C₄	1	2	yes	—
7	C₂×C₁₃×#95	C₄	1	2	yes	—
8	C₂×C₁₃×#95	C₂²	1	2	yes	—
9	C₂×C₂²⋊#1055	C₂²	1	4	yes	—
10	#11718116	—	2	4	no	—
11	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
13	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	—	2	4	no	—
16	C₂×C₄²×C₁₃	D₄	1	4	yes	—
17	C₂²×#1055	—	2	4	no	—
18	C₁₃×#95	—	2	4	no	—
19	C₁₃×#95	—	2	4	no	—
20	C₁₃×#95	—	2	4	no	—
21	C₂²⋊#1055	—	2	8	no	—
22	#8705	—	13	1	no	maximal, Sylow
23	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₃	—	2	2	no	—
25	C₂²×C₄×C₁₃	—	2	2	no	—
26	C₂²×C₄×C₁₃	—	2	4	no	—
27	C₂²×C₄×C₁₃	—	2	4	no	—
28	C₂²×C₄×C₁₃	—	2	8	no	—
29	C₂²×C₄×C₁₃	—	4	2	no	—
30	C₂²×C₄×C₁₃	—	4	2	no	—
31	C₂²×C₄×C₁₃	—	4	4	no	—
32	C₂²×C₄×C₁₃	—	4	4	no	—
33	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
36	C₂²×C₄×C₁₃	#41	1	4	yes	—
37	C₄²×C₁₃	—	2	8	no	—
38	C₂×#1055	—	4	8	no	—
39	C₂×#1055	—	4	4	no	—
40	C₂×#383	D₁₃	1	1	yes	characteristic
41	#1817	—	13	2	no	—
42	#1280	—	13	4	no	—
43	C₂³×C₁₃	—	2	2	no	—
44	C₂³×C₁₃	—	2	2	no	—
45	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂³×C₁₃	#117	1	2	yes	—
47	C₂³×C₁₃	#131	1	4	yes	—
48	C₂×C₄×C₁₃	—	2	4	no	—
49	C₂×C₄×C₁₃	—	2	2	no	—
50	C₂×C₄×C₁₃	—	2	2	no	—
51	C₂×C₄×C₁₃	—	2	4	no	—
52	C₂×C₄×C₁₃	—	2	4	no	—
53	C₂×C₄×C₁₃	—	4	4	no	—
54	C₂×C₄×C₁₃	—	4	4	no	—
55	C₂×C₄×C₁₃	—	4	4	no	—
56	C₂×C₄×C₁₃	—	4	4	no	—
57	C₂×C₄×C₁₃	—	4	4	no	—
58	C₂×C₄×C₁₃	—	4	4	no	—
59	C₂×C₄×C₁₃	—	8	8	no	—
60	C₂×C₄×C₁₃	#123	1	4	yes	—
61	#1055	—	8	4	no	—
62	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
63	C₂×C₂²⋊C₈	—	13	4	no	—
64	#383	—	2	4	no	—
65	C₂×#95	Dic₁₃	1	2	yes	—
66	C₂×#95	Dic₁₃	1	2	yes	—
67	C₂×#95	C₂×D₁₃	1	2	yes	—
68	#336	—	26	4	no	—
69	C₂²×C₁₃	—	2	2	no	—
70	C₂²×C₁₃	—	2	2	no	—
71	C₂²×C₁₃	—	2	8	no	—
72	C₂²×C₁₃	#381	1	1	yes	characteristic
73	C₂²×C₁₃	#408	1	2	yes	—
74	C₂²×C₁₃	#410	1	2	yes	—
75	C₂²×C₁₃	#413	1	2	yes	—
76	C₂²×C₁₃	#433	1	4	yes	—
77	C₄×C₁₃	—	2	4	no	—
78	C₄×C₁₃	—	4	2	no	—
79	C₄×C₁₃	—	4	2	no	—
80	C₄×C₁₃	—	8	4	no	—
81	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
82	C₂³×C₄	C₂×Dic₁₃	1	4	yes	—
83	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
84	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
85	C₂²×C₈	—	26	4	no	—
86	C₂×C₄²	—	2	4	no	—
87	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
88	C₂²⋊C₈	—	26	8	no	—
89	#95	—	2	4	no	—
90	#95	—	2	4	no	—
91	#95	—	2	4	no	—
92	C₂×C₁₃	—	2	4	no	—
93	C₂×C₁₃	#1473	1	4	yes	—
94	C₂×C₁₃	#1818	1	1	yes	characteristic
95	C₂×C₁₃	#1820	1	1	yes	characteristic
96	C₂×C₁₃	#1822	1	1	yes	characteristic
97	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
98	C₂²×C₄	—	2	2	no	—
99	C₂²×C₄	—	2	2	no	—
100	C₂²×C₄	—	2	4	no	—
101	C₂²×C₄	—	2	4	no	—
102	C₂²×C₄	—	2	8	no	—
103	C₂²×C₄	—	4	2	no	—
104	C₂²×C₄	—	4	2	no	—
105	C₂²×C₄	—	4	4	no	—
106	C₂²×C₄	—	4	4	no	—
107	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
108	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
109	C₂²×C₄	#6127	1	4	yes	—
110	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
111	C₂×C₈	—	52	8	no	—
112	C₂×C₈	—	52	4	no	—
113	C₄²	—	2	8	no	—
114	C₁₃	#8705	1	1	yes	characteristic, complemented, Sylow
115	C₂³	—	2	2	no	—
116	C₂³	—	2	2	no	—
117	C₂³	#88180	1	2	yes	—
118	C₂³	#88202	1	4	yes	—
119	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	4	4	no	—
126	C₂×C₄	—	4	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	—	4	4	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	8	8	no	—
132	C₂×C₄	#88183	1	4	yes	—
133	C₈	—	104	4	no	—
134	C₂²	—	2	2	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	8	no	—
137	C₂²	#11718661	1	4	yes	—
138	C₂²	#11718872	1	1	yes	characteristic
139	C₂²	#11718895	1	2	yes	—
140	C₂²	#11718898	1	2	yes	—
141	C₂²	#11718901	1	2	yes	—
142	C₄	—	2	4	no	—
143	C₄	—	4	2	no	—
144	C₄	—	4	2	no	—
145	C₄	—	8	4	no	—
146	C₂	—	2	4	no	—
147	C₂	#13113205	1	4	yes	—
148	C₂	#13114907	1	1	yes	characteristic
149	C₂	#13114913	1	1	yes	characteristic
150	C₂	#13114919	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13114904

C₂

yes

maximal

#13112679

C₂

yes

maximal

C₂×C₁₃×#383

C₂

yes

maximal, characteristic

C₂²×C₄²×C₁₃

C₂²

yes

characteristic

C₁₃×#383

—

C₂×C₁₃×#95

C₄

yes

—

C₂×C₁₃×#95

C₄

yes

—

C₂×C₁₃×#95

C₂²

yes

—

C₂×C₂²⋊#1055

C₂²

yes

—

#11718116

—

C₂³×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₃

C₂×C₄

yes

—

C₂³×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂²×#1055

—

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

C₂²⋊#1055

—

#8705

—

maximal, Sylow

C₂⁴×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

#41

yes

—

C₄²×C₁₃

—

C₂×#1055

—

C₂×#1055

—

C₂×#383

D₁₃

yes

characteristic

#1817

—

#1280

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₃

#117

yes

—

C₂³×C₁₃

#131

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#123

yes

—

#1055

—

C₂²×C₄²

C₂×D₁₃

yes

characteristic

C₂×C₂²⋊C₈

—

#383

—

C₂×#95

Dic₁₃

yes

—

C₂×#95

Dic₁₃

yes

—

C₂×#95

C₂×D₁₃

yes

—

#336

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#381

yes

characteristic

C₂²×C₁₃

#408

yes

—

C₂²×C₁₃

#410

yes

—

C₂²×C₁₃

#413

yes

—

C₂²×C₁₃

#433

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₂³×C₄

C₂×Dic₁₃

yes

characteristic

C₂³×C₄

C₂×Dic₁₃

yes

—

C₂³×C₄

C₂×Dic₁₃

yes

characteristic

C₂³×C₄

C₂²×D₁₃

yes

characteristic

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

C₂²⋊D₁₃

yes

—

C₂²⋊C₈

—

#95

—

#95

—

#95

—

C₂×C₁₃

—

C₂×C₁₃

#1473

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂⁴

C₂²×Dic₁₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

108

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

109

C₂²×C₄

#6127

yes

—

110

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₄²

—

114

C₁₃

#8705

yes

characteristic, complemented, Sylow

115

C₂³

—

116

C₂³

—

117

C₂³

#88180

yes

—

118

C₂³

#88202

yes

—

119

C₂³

C₂×C₂²⋊Dic₁₃

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

#88183

yes

—

133

C₈

—

104

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

#11718661

yes

—

138

C₂²

#11718872

yes

characteristic

139

C₂²

#11718895

yes

—

140

C₂²

#11718898

yes

—

141

C₂²

#11718901

yes

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₂

—

147

C₂

#13113205

yes

—

148

C₂

#13114907

yes

characteristic

149

C₂

#13114913

yes

characteristic

150

C₂

#13114919

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₃
commutator, prime radical	C₂⁴×C₁₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#383	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#383	D₁₃
hypocenter	C₁₃	#8705
LCS	G ▷ C₂⁴×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#383

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₃

commutator, prime radical

C₂⁴×C₁₃

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₃

Fitting

C₂×C₁₃×#383

C₂

socle

C₂³×C₁₃

C₂×C₂²⋊C₄

cosocle

C₂³×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂⁴×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#383

N	H ≅ G/N	type
114. C₁₃	#8705	semidirect

H ≅ G/N

type

114. C₁₃

#8705

semidirect

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

subgroup	index
#13114904	2
#13112679	2
C₂×C₁₃×#383	2
#8705	13

subgroup

index

#13114904

#13112679

C₂×C₁₃×#383

#8705

Subgroups — #15756263

Conjugacy classes of subgroups

Complements

Maximal subgroups