Group #13125492 — subgroups

Subgroups — #13125492

Order 1664.

338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11719436	C₂	1	2	yes	maximal
2	C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718850	C₂	1	2	yes	maximal
4	#11718849	C₂	1	2	yes	maximal
5	#11718845	C₂	1	2	yes	maximal, complemented
6	Q₁₆×Dic₁₃	C₂	1	2	yes	maximal, complemented
7	#11718743	C₂	1	2	yes	maximal, complemented
8	#11718350	C₂	1	1	yes	maximal, characteristic
9	#11718344	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×Q₁₆	C₂²	1	2	yes	—
11	C₂×C₁₃×Q₁₆	C₂²	1	2	yes	—
12	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
13	#88200	C₂²	1	4	yes	—
14	Q₈×Dic₁₃	C₂²	1	4	yes	—
15	C₂×#6094	C₂²	1	1	yes	characteristic
16	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
17	#88152	—	2	4	no	—
18	#88143	—	2	4	no	—
19	#88126	C₂²	1	1	yes	characteristic
20	#88124	C₂²	1	2	yes	—
21	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	#88075	C₂²	1	4	yes	—
23	#88075	C₂²	1	4	yes	—
24	#88058	C₂²	1	2	yes	—
25	#88057	C₂²	1	2	yes	—
26	#88055	C₂²	1	1	yes	characteristic
27	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	#88043	C₂²	1	1	yes	characteristic
29	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
30	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
31	C₁₃×Q₁₆	—	2	4	no	—
32	C₁₃×Q₁₆	—	2	4	no	—
33	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
35	C₁₃×C₄⋊C₄	—	2	4	no	—
36	C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	#6103	—	2	4	no	—
38	#6103	D₄	1	2	yes	—
39	C₄⋊Dic₁₃	—	2	4	no	—
40	C₄⋊Dic₁₃	C₂³	1	4	yes	—
41	#6101	—	2	4	no	—
42	#6101	—	2	4	no	—
43	#6101	D₄	1	2	yes	—
44	C₄×Dic₁₃	—	2	4	no	—
45	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
46	C₂×#1055	C₂³	1	1	yes	characteristic
47	C₂×#1055	C₂³	1	1	yes	characteristic
48	#6094	—	2	2	no	—
49	C₈×D₁₃	—	2	2	no	—
50	#3177	—	13	1	no	maximal, Sylow
51	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
52	Q₈×C₁₃	—	2	4	no	—
53	Q₈×C₁₃	—	2	4	no	—
54	C₂×C₄×C₁₃	—	2	4	no	—
55	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
57	C₂×Dic₁₃	—	2	4	no	—
58	C₂×Dic₁₃	C₂×D₄	1	2	yes	—
59	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
60	C₄×D₁₃	—	2	1	no	—
61	C₄×D₁₃	—	2	1	no	—
62	C₈×C₁₃	#41	1	2	yes	—
63	C₈×C₁₃	#41	1	2	yes	—
64	#1055	—	2	1	no	—
65	#1055	—	2	1	no	—
66	#541	—	13	2	no	—
67	#499	—	13	1	no	—
68	#494	D₁₃	1	1	yes	characteristic, complemented
69	#491	—	13	2	no	—
70	#470	—	13	2	no	—
71	#467	—	13	2	no	—
72	#441	—	13	2	no	—
73	C₄×Q₁₆	—	13	2	no	—
74	#405	—	13	1	no	—
75	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
76	C₂×D₁₃	—	2	1	no	—
77	C₂×D₁₃	—	2	2	no	—
78	C₄×C₁₃	—	2	2	no	—
79	C₄×C₁₃	—	4	4	no	—
80	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
81	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
82	Dic₁₃	—	2	1	no	—
83	Dic₁₃	—	2	2	no	—
84	Dic₁₃	—	4	4	no	—
85	C₂×Q₁₆	C₂×D₁₃	1	2	yes	—
86	C₂×Q₁₆	C₂×D₁₃	1	2	yes	—
87	C₂×M₁₆	—	13	1	no	—
88	C₂²×C₈	—	13	1	no	—
89	C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
90	#126	—	26	4	no	—
91	#125	—	13	2	no	—
92	#125	—	26	4	no	—
93	C₂²⋊Q₈	—	13	4	no	—
94	C₄×Q₈	—	13	4	no	—
95	#117	—	13	1	no	—
96	#107	—	13	2	no	—
97	#106	—	13	2	no	—
98	#103	—	13	4	no	—
99	#103	—	13	4	no	—
100	#97	—	13	1	no	—
101	#97	—	13	1	no	—
102	C₄×C₈	—	13	1	no	—
103	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
104	C₂×C₁₃	#532	1	1	yes	characteristic
105	C₂×C₁₃	#578	1	2	yes	—
106	D₁₃	—	4	1	no	—
107	C₂×Q₈	C₂²×D₁₃	1	4	yes	—
108	C₂²×C₄	—	13	1	no	—
109	Q₁₆	—	2	4	no	—
110	Q₁₆	—	2	4	no	—
111	M₁₆	—	26	2	no	—
112	C₂×C₈	—	13	1	no	—
113	C₂×C₈	—	13	1	no	—
114	C₂×C₈	—	26	2	no	—
115	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
116	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
117	C₄⋊C₄	—	2	4	no	—
118	C₄⋊C₄	—	13	2	no	—
119	C₄⋊C₄	—	13	4	no	—
120	C₄⋊C₄	—	26	4	no	—
121	C₄⋊C₄	—	26	4	no	—
122	C₄⋊C₄	—	26	4	no	—
123	C₂²⋊C₄	—	13	2	no	—
124	C₂²⋊C₄	—	26	4	no	—
125	C₄²	—	13	1	no	—
126	C₄²	—	26	4	no	—
127	C₄²	C₂²×D₁₃	1	1	yes	characteristic
128	C₁₃	#3177	1	1	yes	characteristic, complemented, Sylow
129	C₂³	—	13	1	no	—
130	Q₈	—	2	4	no	—
131	Q₈	—	2	4	no	—
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	—	13	2	no	—
134	C₂×C₄	—	13	1	no	—
135	C₂×C₄	—	26	1	no	—
136	C₂×C₄	—	26	1	no	—
137	C₂×C₄	—	26	4	no	—
138	C₂×C₄	D₄×D₁₃	1	2	yes	—
139	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
140	C₈	—	26	1	no	—
141	C₈	—	26	1	no	—
142	C₈	#6129	1	2	yes	—
143	C₈	#6129	1	2	yes	—
144	C₂²	—	26	2	no	—
145	C₂²	—	26	1	no	—
146	C₂²	C₂×D₄×D₁₃	1	1	yes	characteristic
147	C₄	—	2	2	no	—
148	C₄	—	4	4	no	—
149	C₄	—	26	2	no	—
150	C₄	—	26	1	no	—
151	C₄	—	52	4	no	—
152	C₄	C₂×#6129	1	1	yes	characteristic
153	C₄	C₂×#6129	1	1	yes	characteristic
154	C₂	—	52	1	no	—
155	C₂	#11719421	1	1	yes	characteristic
156	C₂	#11719471	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11719436

C₂

yes

maximal

C₁₃×#494

C₂

yes

maximal, characteristic, complemented

#11718850

C₂

yes

maximal

#11718849

C₂

yes

maximal

#11718845

C₂

yes

maximal, complemented

Q₁₆×Dic₁₃

C₂

yes

maximal, complemented

#11718743

C₂

yes

maximal, complemented

#11718350

C₂

yes

maximal, characteristic

#11718344

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×Q₁₆

C₂²

yes

—

C₂×C₁₃×Q₁₆

C₂²

yes

—

C₁₃×C₄⋊Q₈

C₂²

yes

—

#88200

C₂²

yes

—

Q₈×Dic₁₃

C₂²

yes

—

C₂×#6094

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

—

—

C₂²

yes

characteristic

#88124

C₂²

yes

—

C₄×C₈×C₁₃

C₂²

yes

characteristic

#88075

C₂²

yes

—

#88075

C₂²

yes

—

#88058

C₂²

yes

—

#88057

C₂²

yes

—

#88055

C₂²

yes

characteristic

C₈×Dic₁₃

C₂²

yes

characteristic

#88043

C₂²

yes

characteristic

C₂×Q₈×C₁₃

C₂³

yes

—

C₂×C₄×D₁₃

C₂³

yes

characteristic

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂³

yes

characteristic

#6103

—

#6103

D₄

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

C₂³

yes

—

#6101

—

#6101

—

#6101

D₄

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₂³

yes

characteristic

C₂×#1055

C₂³

yes

characteristic

C₂×#1055

C₂³

yes

characteristic

#6094

—

C₈×D₁₃

—

#3177

—

maximal, Sylow

C₂²×D₁₃

C₂×D₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂⁴

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×D₄

yes

—

C₂×Dic₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₈×C₁₃

#41

yes

—

C₈×C₁₃

#41

yes

—

—

—

—

—

D₁₃

yes

characteristic, complemented

—

—

—

—

C₄×Q₁₆

—

#405

—

C₂²×C₁₃

C₂²×D₄

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂×#41

yes

characteristic

C₄×C₁₃

C₂×#41

yes

characteristic

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂×Q₁₆

C₂×D₁₃

yes

—

C₂×Q₁₆

C₂×D₁₃

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₄⋊Q₈

C₂×D₁₃

yes

—

#126

—

#125

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

—

—

—

—

—

100

#97

—

101

#97

—

102

C₄×C₈

—

103

C₄×C₈

C₂×D₁₃

yes

characteristic

104

C₂×C₁₃

#532

yes

characteristic

105

C₂×C₁₃

#578

yes

—

106

D₁₃

—

107

C₂×Q₈

C₂²×D₁₃

yes

—

108

C₂²×C₄

—

109

Q₁₆

—

110

Q₁₆

—

111

M₁₆

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₂²×D₁₃

yes

characteristic

116

C₂×C₈

C₂²×D₁₃

yes

characteristic

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

—

126

C₄²

—

127

C₄²

C₂²×D₁₃

yes

characteristic

128

C₁₃

#3177

yes

characteristic, complemented, Sylow

129

C₂³

—

130

Q₈

—

131

Q₈

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

D₄×D₁₃

yes

—

139

C₂×C₄

C₂³×D₁₃

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

#6129

yes

—

143

C₈

#6129

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₂×D₄×D₁₃

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

C₂×#6129

yes

characteristic

153

C₄

C₂×#6129

yes

characteristic

154

C₂

—

155

C₂

#11719421

yes

characteristic

156

C₂

#11719471

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃
Fitting	C₁₃×#494	C₂
socle	C₂²×C₁₃	C₂²×D₄
prime radical	C₂²×D₁₃	C₂×D₄
hypercenter	#494	D₁₃
hypocenter	C₁₃	#3177
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₁₃

commutator, cosocle

C₂×C₄×C₁₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₃

Fitting

C₁₃×#494

C₂

socle

C₂²×C₁₃

C₂²×D₄

prime radical

C₂²×D₁₃

C₂×D₄

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
2. C₁₃×#494	C₂	semidirect
5. #11718845	C₂	semidirect
6. Q₁₆×Dic₁₃	C₂	semidirect
7. #11718743	C₂	semidirect
9. #11718344	C₂	semidirect
68. #494	D₁₃	semidirect
128. C₁₃	#3177	semidirect

H ≅ G/N

type

2. C₁₃×#494

C₂

semidirect

5. #11718845

C₂

semidirect

6. Q₁₆×Dic₁₃

C₂

semidirect

7. #11718743

C₂

semidirect

9. #11718344

C₂

semidirect

68. #494

D₁₃

semidirect

128. C₁₃

#3177

semidirect

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

subgroup	index
#11719436	2
C₁₃×#494	2
#11718850	2
#11718849	2
#11718845	2
Q₁₆×Dic₁₃	2
#11718743	2
#11718350	2
#11718344	2
#3177	13

subgroup

index

C₁₃×#494

Q₁₆×Dic₁₃

Subgroups — #13125492

Conjugacy classes of subgroups

Complements

Maximal subgroups