Group #13114962 — subgroups

Subgroups — #13114962

Order 1664.

248 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 109 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	C₂×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	#11718637	C₂	1	2	yes	maximal
3	C₁₃×#340	C₂	1	1	yes	maximal, characteristic
4	#11718143	C₂	1	1	yes	maximal, characteristic
5	#11718121	C₂	1	2	yes	maximal
6	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
9	C₂×#6101	—	2	2	no	—
10	C₂×#6101	—	2	2	no	—
11	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#1055	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₃	C₄	1	4	yes	complemented
14	C₂²×C₄×C₁₃	—	2	2	no	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₃	—	2	2	no	—
17	C₂²×Dic₁₃	D₄	1	1	yes	characteristic
18	C₂²×Dic₁₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	—	2	2	no	—
20	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₁₃×C₄⋊C₄	—	2	2	no	—
22	C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₄⋊Dic₁₃	—	2	2	no	—
24	C₄⋊Dic₁₃	—	2	2	no	—
25	#6101	—	4	4	no	—
26	#6101	—	4	4	no	—
27	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
28	C₄×Dic₁₃	Q₈	1	2	yes	—
29	C₂×#1055	—	2	2	no	—
30	C₂×#1055	C₂×C₄	1	2	yes	—
31	#1834	—	13	1	no	maximal, Sylow
32	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	—	4	2	no	—
34	C₂×C₄×C₁₃	—	4	2	no	—
35	C₂×C₄×C₁₃	—	4	2	no	—
36	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₁₃	#41	1	2	yes	—
39	C₂×C₄×C₁₃	#41	1	2	yes	—
40	C₂×Dic₁₃	—	4	2	no	—
41	C₂×Dic₁₃	—	4	2	no	—
42	C₂×Dic₁₃	—	4	2	no	—
43	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
44	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
45	C₂×Dic₁₃	D₈	1	2	yes	—
46	C₂×Dic₁₃	SD₁₆	1	4	yes	—
47	C₂×Dic₁₃	Q₁₆	1	2	yes	—
48	C₈×C₁₃	—	2	2	no	—
49	#1055	—	2	2	no	—
50	C₂×C₄×C₈	—	13	1	no	—
51	#384	—	13	2	no	—
52	#340	—	13	1	no	—
53	#340	—	13	2	no	—
54	#340	D₁₃	1	1	yes	characteristic
55	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₃	#124	1	2	yes	—
57	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
58	C₂²×C₁₃	C₂×SD₁₆	1	2	yes	—
59	C₂²×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
60	C₄×C₁₃	—	8	2	no	—
61	C₄×C₁₃	#117	1	1	yes	characteristic
62	C₄×C₁₃	#117	1	1	yes	characteristic
63	C₄×C₁₃	#125	1	2	yes	—
64	Dic₁₃	—	8	2	no	—
65	Dic₁₃	#106	1	4	yes	—
66	Dic₁₃	#107	1	4	yes	—
67	C₂²×C₈	—	13	1	no	—
68	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	13	2	no	—
70	C₂×C₄⋊C₄	—	26	2	no	—
71	C₂×C₄⋊C₄	—	26	2	no	—
72	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
73	C₂×C₄²	—	13	1	no	—
74	C₄×C₈	—	13	4	no	—
75	C₂×C₁₃	#382	1	1	yes	characteristic
76	C₂×C₁₃	C₂×#106	1	1	yes	characteristic
77	C₂×C₁₃	C₂×#107	1	1	yes	characteristic
78	C₂×C₁₃	#486	1	2	yes	—
79	C₂×C₁₃	#487	1	2	yes	—
80	C₂²×C₄	—	2	2	no	—
81	C₂²×C₄	—	13	1	no	—
82	C₂²×C₄	—	13	1	no	—
83	C₂²×C₄	—	26	2	no	—
84	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	13	2	no	—
87	C₂×C₈	—	26	2	no	—
88	C₂×C₈	C₄×D₁₃	1	2	yes	—
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	26	2	no	—
92	C₄⋊C₄	—	26	2	no	—
93	C₄⋊C₄	—	52	4	no	—
94	C₄⋊C₄	—	52	4	no	—
95	C₄²	—	13	2	no	—
96	C₄²	—	13	2	no	—
97	C₁₃	#1834	1	1	yes	characteristic, complemented, Sylow
98	C₂³	D₄×D₁₃	1	1	yes	characteristic
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	13	2	no	—
103	C₂×C₄	—	13	2	no	—
104	C₂×C₄	—	13	2	no	—
105	C₂×C₄	—	13	4	no	—
106	C₂×C₄	—	13	2	no	—
107	C₂×C₄	—	52	2	no	—
108	C₂×C₄	—	52	2	no	—
109	C₂×C₄	—	52	2	no	—
110	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
111	C₂×C₄	#6127	1	2	yes	—
112	C₂×C₄	#6129	1	2	yes	—
113	C₂×C₄	Q₈×D₁₃	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	26	2	no	—
116	C₂²	#88139	1	2	yes	—
117	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
118	C₂²	D₈×D₁₃	1	1	yes	characteristic
119	C₂²	SD₁₆×D₁₃	1	2	yes	—
120	C₂²	Q₁₆×D₁₃	1	1	yes	characteristic
121	C₄	—	8	2	no	—
122	C₄	—	13	4	no	—
123	C₄	—	13	4	no	—
124	C₄	—	104	2	no	—
125	C₄	#88126	1	1	yes	characteristic
126	C₄	#88131	1	1	yes	characteristic
127	C₄	#88143	1	2	yes	—
128	C₂	#11718311	1	1	yes	characteristic
129	C₂	#11718421	1	2	yes	—
130	C₂	#11718453	1	2	yes	—
131	C₂	D₁₃×#106	1	1	yes	characteristic
132	C₂	D₁₃×#107	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₃

C₂

yes

maximal, characteristic

#11718637

C₂

yes

maximal

C₁₃×#340

C₂

yes

maximal, characteristic

#11718143

C₂

yes

maximal, characteristic

#11718121

C₂

yes

maximal

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

—

C₂×#6101

—

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂²×#1055

C₂²

yes

characteristic

C₈×Dic₁₃

C₄

yes

complemented

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

D₄

yes

characteristic

C₂²×Dic₁₃

D₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

#6101

—

C₄×Dic₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

Q₈

yes

—

C₂×#1055

—

C₂×#1055

C₂×C₄

yes

—

#1834

—

maximal, Sylow

C₂³×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

D₈

yes

—

C₂×Dic₁₃

SD₁₆

yes

—

C₂×Dic₁₃

Q₁₆

yes

—

C₈×C₁₃

—

#1055

—

C₂×C₄×C₈

—

—

—

—

D₁₃

yes

characteristic

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#124

yes

—

C₂²×C₁₃

C₂×D₈

yes

characteristic

C₂²×C₁₃

C₂×SD₁₆

yes

—

C₂²×C₁₃

C₂×Q₁₆

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

Dic₁₃

#106

yes

—

Dic₁₃

#107

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄²

—

C₄×C₈

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×C₁₃

#487

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₁₃

#1834

yes

characteristic, complemented, Sylow

C₂³

D₄×D₁₃

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

111

C₂×C₄

#6127

yes

—

112

C₂×C₄

#6129

yes

—

113

C₂×C₄

Q₈×D₁₃

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#88139

yes

—

117

C₂²

C₄⋊C₄×D₁₃

yes

characteristic

118

C₂²

D₈×D₁₃

yes

characteristic

119

C₂²

SD₁₆×D₁₃

yes

—

120

C₂²

Q₁₆×D₁₃

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

104

—

125

C₄

#88126

yes

characteristic

126

C₄

#88131

yes

characteristic

127

C₄

#88143

yes

—

128

C₂

#11718311

yes

characteristic

129

C₂

#11718421

yes

—

130

C₂

#11718453

yes

—

131

C₂

D₁₃×#106

yes

characteristic

132

C₂

D₁₃×#107

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#340	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#340	D₁₃
hypocenter	C₁₃	#1834
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#340

C₂

socle, prime radical

C₂³×C₁₃

C₂×D₄

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
13. C₈×Dic₁₃	C₄	semidirect
97. C₁₃	#1834	semidirect

H ≅ G/N

type

13. C₈×Dic₁₃

C₄

semidirect

97. C₁₃

#1834

semidirect

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

subgroup	index
C₂×C₈×Dic₁₃	2
#11718637	2
C₁₃×#340	2
#11718143	2
#11718121	2
#1834	13

subgroup

index

C₂×C₈×Dic₁₃

C₁₃×#340

Subgroups — #13114962

Conjugacy classes of subgroups

Complements

Maximal subgroups