Group #13114980 — subgroups

Subgroups — #13114980

Order 1664.

196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 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	#11718593	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#336	C₂	1	1	yes	maximal, characteristic
3	#11718142	C₂	1	2	yes	maximal
4	#11718142	C₂	1	2	yes	maximal
5	#11718116	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#1055	C₂²	1	2	yes	—
11	#88071	C₄	1	2	yes	—
12	#88071	C₄	1	2	yes	—
13	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₁₃	—	2	2	no	—
19	C₂×C₈×C₁₃	—	2	2	no	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₄²×C₁₃	—	2	2	no	—
22	C₄×Dic₁₃	—	2	2	no	—
23	C₄×Dic₁₃	—	2	1	no	—
24	C₄×Dic₁₃	—	2	1	no	—
25	C₂×#1055	—	2	2	no	—
26	C₂×#1055	—	2	2	no	—
27	C₂×#1055	—	2	2	no	—
28	#1840	—	13	1	no	maximal, Sylow
29	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃	—	2	2	no	—
31	C₂×C₄×C₁₃	—	2	2	no	—
32	C₂×C₄×C₁₃	—	2	2	no	—
33	C₂×C₄×C₁₃	#41	1	2	yes	—
34	C₂×C₄×C₁₃	#41	1	2	yes	—
35	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
36	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
37	C₂×Dic₁₃	—	2	1	no	—
38	C₂×Dic₁₃	—	2	1	no	—
39	C₂×Dic₁₃	—	2	2	no	—
40	C₂×Dic₁₃	—	2	2	no	—
41	C₂×Dic₁₃	—	2	2	no	—
42	C₂×Dic₁₃	—	2	2	no	—
43	C₂×Dic₁₃	—	2	2	no	—
44	C₈×C₁₃	—	4	2	no	—
45	#1055	—	4	2	no	—
46	#376	—	13	1	no	—
47	#336	—	13	2	no	—
48	#336	—	13	2	no	—
49	#336	—	13	1	no	—
50	#336	D₁₃	1	1	yes	characteristic
51	C₂²×C₁₃	#117	1	1	yes	characteristic
52	C₂²×C₁₃	#117	1	1	yes	characteristic
53	C₂²×C₁₃	#117	1	1	yes	characteristic
54	C₂²×C₁₃	#131	1	2	yes	—
55	C₂²×C₁₃	#131	1	2	yes	—
56	C₄×C₁₃	—	4	2	no	—
57	C₄×C₁₃	#126	1	2	yes	—
58	C₄×C₁₃	#126	1	2	yes	—
59	Dic₁₃	—	4	2	no	—
60	Dic₁₃	—	4	1	no	—
61	Dic₁₃	—	4	1	no	—
62	C₂²×C₈	—	13	2	no	—
63	C₂²×C₈	C₂×D₁₃	1	2	yes	—
64	C₂×C₄²	—	13	1	no	—
65	C₂×C₄²	—	13	1	no	—
66	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
67	#95	—	13	2	no	—
68	#95	—	13	2	no	—
69	C₂×C₁₃	#383	1	1	yes	characteristic
70	C₂×C₁₃	#433	1	2	yes	—
71	C₂×C₁₃	#433	1	1	yes	characteristic
72	C₂×C₁₃	#433	1	1	yes	characteristic
73	C₂×C₁₃	#433	1	2	yes	—
74	C₂²×C₄	—	13	1	no	—
75	C₂²×C₄	—	13	1	no	—
76	C₂²×C₄	—	13	2	no	—
77	C₂²×C₄	C₄×D₁₃	1	2	yes	—
78	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	26	2	no	—
83	C₂×C₈	—	26	2	no	—
84	C₂×C₈	—	26	2	no	—
85	C₄²	—	2	2	no	—
86	C₄²	—	26	2	no	—
87	C₄²	—	26	1	no	—
88	C₄²	—	26	1	no	—
89	C₁₃	#1840	1	1	yes	characteristic, complemented, Sylow
90	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	26	1	no	—
95	C₂×C₄	—	26	1	no	—
96	C₂×C₄	—	26	2	no	—
97	C₂×C₄	—	26	2	no	—
98	C₂×C₄	—	26	2	no	—
99	C₂×C₄	—	26	2	no	—
100	C₂×C₄	—	26	2	no	—
101	C₂×C₄	#6127	1	2	yes	—
102	C₂×C₄	#6129	1	1	yes	characteristic
103	C₂×C₄	#6129	1	2	yes	—
104	C₂×C₄	#6131	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	52	2	no	—
107	C₂²	#88126	1	1	yes	characteristic
108	C₂²	#88131	1	1	yes	characteristic
109	C₂²	#88146	1	1	yes	characteristic
110	C₂²	#88155	1	2	yes	—
111	C₂²	#88161	1	2	yes	—
112	C₄	—	4	2	no	—
113	C₄	—	52	2	no	—
114	C₄	—	52	1	no	—
115	C₄	—	52	1	no	—
116	C₄	#88133	1	2	yes	—
117	C₄	#88152	1	2	yes	—
118	C₂	#11718312	1	1	yes	characteristic
119	C₂	#11718351	1	1	yes	characteristic
120	C₂	#11718370	1	1	yes	characteristic
121	C₂	#11718381	1	2	yes	—
122	C₂	#11718501	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11718593

C₂

yes

maximal, characteristic

C₁₃×#336

C₂

yes

maximal, characteristic

#11718142

C₂

yes

maximal

#11718142

C₂

yes

maximal

#11718116

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₃

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂²×#1055

C₂²

yes

—

#88071

C₄

yes

—

#88071

C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

—

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

—

—

—

—

—

D₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₂²×C₁₃

#131

yes

—

C₄×C₁₃

—

C₄×C₁₃

#126

yes

—

C₄×C₁₃

#126

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

#95

—

#95

—

C₂×C₁₃

#383

yes

characteristic

C₂×C₁₃

#433

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1840

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

#6127

yes

—

102

C₂×C₄

#6129

yes

characteristic

103

C₂×C₄

#6129

yes

—

104

C₂×C₄

#6131

yes

characteristic

105

C₈

—

106

C₈

—

107

C₂²

#88126

yes

characteristic

108

C₂²

#88131

yes

characteristic

109

C₂²

#88146

yes

characteristic

110

C₂²

#88155

yes

—

111

C₂²

#88161

yes

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

#88133

yes

—

117

C₄

#88152

yes

—

118

C₂

#11718312

yes

characteristic

119

C₂

#11718351

yes

characteristic

120

C₂

#11718370

yes

characteristic

121

C₂

#11718381

yes

—

122

C₂

#11718501

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₄
Fitting	C₁₃×#336	C₂
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#336	D₁₃
hypocenter	C₁₃	#1840
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₃

commutator, socle, prime radical

C₂³×C₁₃

C₂²×C₄

Fitting

C₁₃×#336

C₂

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
89. C₁₃	#1840	semidirect

H ≅ G/N

type

89. C₁₃

#1840

semidirect

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

subgroup	index
#11718593	2
C₁₃×#336	2
#11718142	2
#11718116	2
#1840	13

subgroup

index

C₁₃×#336

Subgroups — #13114980

Conjugacy classes of subgroups

Complements

Maximal subgroups