Group #13116636 — subgroups

Subgroups — #13116636

Order 1664.

152 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#6090	C₂	1	1	yes	maximal, characteristic
4	#11718094	C₂	1	2	yes	maximal, complemented
5	#11718093	C₂	1	2	yes	maximal, complemented
6	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
8	C₂²×#1055	C₄	1	1	yes	characteristic
9	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
10	C₈×Dic₁₃	C₄	1	1	yes	characteristic
11	C₈×Dic₁₃	C₄	1	1	yes	characteristic
12	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×#6090	C₂²	1	2	yes	—
15	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₁₃	C₈	1	1	yes	characteristic
17	C₂²×Dic₁₃	C₈	1	1	yes	characteristic
18	C₂×C₈×C₁₃	—	2	2	no	—
19	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₄×Dic₁₃	C₈	1	1	yes	characteristic
22	C₄×Dic₁₃	C₈	1	1	yes	characteristic
23	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×#1055	—	2	2	no	—
26	C₂×#1055	C₂×C₄	1	1	yes	characteristic
27	C₂×#1055	C₂×C₄	1	1	yes	characteristic
28	C₁₃×C₁₆	—	2	2	no	—
29	#6090	—	2	2	no	—
30	#2163	—	13	1	no	maximal, Sylow
31	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₃	—	2	1	no	—
33	C₂×C₄×C₁₃	—	2	1	no	—
34	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₁₃	—	2	2	no	—
37	C₂×Dic₁₃	—	2	2	no	—
38	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
40	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
42	C₈×C₁₃	—	2	1	no	—
43	C₈×C₁₃	#41	1	2	yes	—
44	#1055	—	2	1	no	—
45	#1055	M₁₆	1	2	yes	—
46	C₂×C₄×C₈	—	13	1	no	—
47	C₄⋊C₁₆	—	13	2	no	—
48	C₂²⋊C₁₆	—	13	1	no	—
49	C₂²⋊C₁₆	D₁₃	1	1	yes	characteristic
50	#346	—	13	2	no	—
51	C₂²×C₁₃	—	2	1	no	—
52	C₂²×C₁₃	—	2	1	no	—
53	C₂²×C₁₃	M₃₂	1	2	yes	—
54	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
55	C₄×C₁₃	—	2	1	no	—
56	C₄×C₁₃	#117	1	1	yes	characteristic
57	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
58	Dic₁₃	—	2	1	no	—
59	Dic₁₃	—	2	1	no	—
60	Dic₁₃	—	2	1	no	—
61	Dic₁₃	M₃₂	1	2	yes	—
62	C₂²×C₈	—	13	1	no	—
63	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
64	C₂×C₄²	—	13	1	no	—
65	C₂×C₁₆	—	13	2	no	—
66	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
67	C₄×C₈	—	13	1	no	—
68	C₄×C₈	—	13	1	no	—
69	C₄×C₈	—	13	1	no	—
70	C₄×C₈	—	13	1	no	—
71	C₂×C₁₃	—	2	2	no	—
72	C₂×C₁₃	#431	1	1	yes	characteristic
73	C₂×C₁₃	C₂×M₃₂	1	1	yes	characteristic
74	C₂×C₁₃	C₂×M₃₂	1	1	yes	characteristic
75	C₂²×C₄	—	13	1	no	—
76	C₂²×C₄	—	13	1	no	—
77	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	13	1	no	—
80	C₂×C₈	—	13	1	no	—
81	C₂×C₈	—	26	2	no	—
82	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
83	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
84	C₄²	—	13	1	no	—
85	C₄²	—	13	1	no	—
86	C₄²	—	13	1	no	—
87	C₄²	—	13	1	no	—
88	C₁₆	—	2	2	no	—
89	C₁₆	—	26	2	no	—
90	C₁₃	#2163	1	1	yes	characteristic, complemented, Sylow
91	C₂³	C₈×D₁₃	1	1	yes	characteristic
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	13	1	no	—
95	C₂×C₄	—	13	1	no	—
96	C₂×C₄	—	13	1	no	—
97	C₂×C₄	—	13	1	no	—
98	C₂×C₄	—	26	2	no	—
99	C₂×C₄	—	26	2	no	—
100	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	13	2	no	—
104	C₈	—	26	1	no	—
105	C₈	#6129	1	2	yes	—
106	C₂²	—	2	1	no	—
107	C₂²	—	2	1	no	—
108	C₂²	#88038	1	2	yes	—
109	C₂²	C₂×C₈×D₁₃	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	13	2	no	—
112	C₄	—	26	1	no	—
113	C₄	—	26	1	no	—
114	C₄	—	26	1	no	—
115	C₄	#88131	1	1	yes	characteristic
116	C₄	M₁₆×D₁₃	1	1	yes	characteristic
117	C₂	—	2	2	no	—
118	C₂	#11718379	1	1	yes	characteristic
119	C₂	C₂×#88038	1	1	yes	characteristic
120	C₂	D₁₃×M₃₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₃

C₂

yes

maximal, characteristic

C₁₃×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂²⋊#6090

C₂

yes

maximal, characteristic

#11718094

C₂

yes

maximal, complemented

#11718093

C₂

yes

maximal, complemented

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₄

yes

characteristic

C₂²×#1055

C₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂²

yes

—

C₈×Dic₁₃

C₄

yes

characteristic

C₈×Dic₁₃

C₄

yes

characteristic

C₈×Dic₁₃

C₂²

yes

characteristic

C₈×Dic₁₃

C₂²

yes

characteristic

C₂×#6090

C₂²

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₈

yes

characteristic

C₂²×Dic₁₃

C₈

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂³

yes

characteristic

C₄×Dic₁₃

C₈

yes

characteristic

C₄×Dic₁₃

C₈

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂×#1055

—

C₂×#1055

C₂×C₄

yes

characteristic

C₂×#1055

C₂×C₄

yes

characteristic

C₁₃×C₁₆

—

#6090

—

#2163

—

maximal, Sylow

C₂³×C₁₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

#41

yes

—

#1055

—

#1055

M₁₆

yes

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

D₁₃

yes

characteristic

#346

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

M₃₂

yes

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

#117

yes

characteristic

C₄×C₁₃

C₂×M₁₆

yes

characteristic

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

M₃₂

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

#431

yes

characteristic

C₂×C₁₃

C₂×M₃₂

yes

characteristic

C₂×C₁₃

C₂×M₃₂

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₃

yes

characteristic

C₂×C₈

C₂²×D₁₃

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₃

#2163

yes

characteristic, complemented, Sylow

C₂³

C₈×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₈×D₁₃

yes

characteristic

101

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

#6129

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

#88038

yes

—

109

C₂²

C₂×C₈×D₁₃

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

#88131

yes

characteristic

116

C₄

M₁₆×D₁₃

yes

characteristic

117

C₂

—

118

C₂

#11718379

yes

characteristic

119

C₂

C₂×#88038

yes

characteristic

120

C₂

D₁₃×M₃₂

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₁₃×C₂²⋊C₁₆	C₂
prime radical	C₂³×C₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₂²⋊C₁₆	D₁₃
hypocenter	C₁₃	#2163
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₃

commutator, socle

C₂²×C₁₃

C₂²×C₈

Fitting

C₁₃×C₂²⋊C₁₆

C₂

prime radical

C₂³×C₁₃

C₂×C₈

cosocle

C₂×C₈×C₁₃

C₂³

hypercenter

C₂²⋊C₁₆

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
4. #11718094	C₂	semidirect
5. #11718093	C₂	semidirect
90. C₁₃	#2163	semidirect

H ≅ G/N

type

4. #11718094

C₂

semidirect

5. #11718093

C₂

semidirect

90. C₁₃

#2163

semidirect

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

subgroup	index
C₂×C₈×Dic₁₃	2
C₁₃×C₂²⋊C₁₆	2
C₂²⋊#6090	2
#11718094	2
#11718093	2
#2163	13

subgroup

index

C₂×C₈×Dic₁₃

C₁₃×C₂²⋊C₁₆

C₂²⋊#6090

#11718094

#11718093

#2163

Subgroups — #13116636

Conjugacy classes of subgroups

Complements

Maximal subgroups