Group #13116388 — subgroups

Subgroups — #13116388

Order 1664.

210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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	C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718800	C₂	1	2	yes	maximal
3	#11718790	C₂	1	1	yes	maximal, characteristic
4	#11718780	C₂	1	2	yes	maximal, complemented
5	#11718149	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#6127	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
8	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
9	#88180	C₂²	1	2	yes	—
10	C₂²×#1055	C₂²	1	1	yes	characteristic
11	C₁₃×#108	—	2	2	no	—
12	#88065	—	2	4	no	—
13	#88060	—	2	2	no	—
14	#88054	—	2	4	no	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂×C₂²⋊D₁₃	—	2	1	no	—
17	#6127	—	2	2	no	—
18	#6127	—	2	2	no	—
19	C₂×D₅₂	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₁₃	—	2	1	no	—
21	C₂×Dic₂₆	Q₈	1	1	yes	characteristic
22	C₁₃×M₁₆	—	2	2	no	—
23	C₁₃×M₁₆	—	2	2	no	—
24	C₁₃×M₁₆	—	2	2	no	—
25	C₂×C₈×C₁₃	—	2	2	no	—
26	C₂×C₈×C₁₃	D₄	1	2	yes	—
27	C₂²⋊Dic₁₃	—	2	2	no	—
28	C₄⋊Dic₁₃	—	2	2	no	—
29	C₄×Dic₁₃	D₄	1	4	yes	—
30	C₂×#1055	—	2	2	no	—
31	C₂×#1055	—	2	1	no	—
32	#2098	—	13	1	no	maximal, Sylow
33	C₂³×C₁₃	#41	1	1	yes	characteristic
34	C₂²×D₁₃	—	2	1	no	—
35	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₁₃	#41	1	2	yes	—
39	C₂²⋊D₁₃	—	4	2	no	—
40	C₂×Dic₁₃	—	2	1	no	—
41	C₂×Dic₁₃	—	2	4	no	—
42	D₅₂	—	2	2	no	—
43	C₄×D₁₃	—	4	1	no	—
44	C₄×D₁₃	—	4	1	no	—
45	Dic₂₆	—	2	2	no	—
46	C₈×C₁₃	—	2	2	no	—
47	C₈×C₁₃	—	4	2	no	—
48	#1055	—	4	1	no	—
49	#430	D₁₃	1	1	yes	characteristic, complemented
50	#424	—	13	2	no	—
51	#421	—	13	2	no	—
52	#408	—	13	1	no	—
53	H(3,ℤ/4)	—	13	1	no	—
54	C₂²×C₁₃	—	4	1	no	—
55	C₂²×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
56	C₂²×C₁₃	#123	1	2	yes	—
57	C₂×D₁₃	—	4	2	no	—
58	C₂×D₁₃	—	4	1	no	—
59	C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
60	C₄×C₁₃	#123	1	1	yes	characteristic
61	C₄×C₁₃	#127	1	1	yes	characteristic
62	Dic₁₃	—	4	4	no	—
63	Dic₁₃	—	4	1	no	—
64	C₂×#41	—	13	1	no	—
65	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
66	C₂×M₁₆	C₂×D₁₃	1	1	yes	characteristic
67	C₂²×C₈	—	13	1	no	—
68	#117	—	13	2	no	—
69	#108	—	2	2	no	—
70	C₄⋊C₈	—	26	4	no	—
71	#104	—	26	4	no	—
72	C₂²⋊C₈	—	26	2	no	—
73	C₂×C₁₃	—	2	2	no	—
74	C₂×C₁₃	—	2	1	no	—
75	C₂×C₁₃	#399	1	1	yes	characteristic
76	D₁₃	—	8	1	no	—
77	#41	—	26	2	no	—
78	#41	—	26	2	no	—
79	C₂×Q₈	—	13	1	no	—
80	C₂×D₄	—	13	1	no	—
81	C₂×D₄	—	26	1	no	—
82	C₂²×C₄	—	26	1	no	—
83	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	—	2	2	no	—
86	M₁₆	—	2	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	26	2	no	—
89	C₂×C₈	—	26	1	no	—
90	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
91	C₄⋊C₄	—	26	2	no	—
92	C₂²⋊C₄	—	26	2	no	—
93	C₄²	—	13	4	no	—
94	C₁₃	#2098	1	1	yes	characteristic, complemented, Sylow
95	C₂³	—	26	1	no	—
96	C₂³	#6131	1	1	yes	characteristic
97	Q₈	—	26	2	no	—
98	D₄	—	26	2	no	—
99	D₄	—	52	2	no	—
100	C₂×C₄	—	26	4	no	—
101	C₂×C₄	—	26	1	no	—
102	C₂×C₄	—	52	1	no	—
103	C₂×C₄	—	52	1	no	—
104	C₂×C₄	#6127	1	2	yes	—
105	C₂×C₄	D₄×D₁₃	1	2	yes	—
106	C₂×C₄	Q₈×D₁₃	1	1	yes	characteristic
107	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	—	4	2	no	—
110	C₈	—	52	1	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	52	2	no	—
113	C₂²	—	52	1	no	—
114	C₂²	#88148	1	2	yes	—
115	C₂²	#88200	1	1	yes	characteristic
116	C₄	—	52	4	no	—
117	C₄	—	52	1	no	—
118	C₄	#88150	1	2	yes	—
119	C₄	#88183	1	1	yes	characteristic
120	C₄	#88194	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	104	1	no	—
124	C₂	#11718653	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#430

C₂

yes

maximal, characteristic, complemented

#11718800

C₂

yes

maximal

#11718790

C₂

yes

maximal, characteristic

#11718780

C₂

yes

maximal, complemented

#11718149

C₂

yes

maximal, characteristic, complemented

C₂×#6127

C₂²

yes

characteristic

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂×C₁₃×M₁₆

C₂²

yes

characteristic

#88180

C₂²

yes

—

C₂²×#1055

C₂²

yes

characteristic

C₁₃×#108

—

#88065

—

#88060

—

#88054

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₂²⋊D₁₃

—

#6127

—

#6127

—

C₂×D₅₂

Q₈

yes

characteristic

C₂×C₄×D₁₃

—

C₂×Dic₂₆

Q₈

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

D₄

yes

—

—

—

—

C₂³×C₁₃

yes

C₂²×D₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂²⋊D₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

D₅₂

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#430

D₁₃

yes

characteristic, complemented

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₃

#123

yes

—

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

C₂²⋊Q₈

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

—

C₂×#41

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₂×M₁₆

C₂×D₁₃

yes

characteristic

C₂²×C₈

—

#117

—

#108

—

C₄⋊C₈

—

#104

—

C₂²⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#399

yes

characteristic

D₁₃

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₃

#2098

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

#6131

yes

characteristic

Q₈

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

#6127

yes

—

105

C₂×C₄

D₄×D₁₃

yes

—

106

C₂×C₄

Q₈×D₁₃

yes

characteristic

107

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

#88148

yes

—

115

C₂²

#88200

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

#88150

yes

—

119

C₄

#88183

yes

characteristic

120

C₄

#88194

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

104

—

124

C₂

#11718653

yes

characteristic

	subgroup	G/H
center	C₄	#88194
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#430	C₂
socle	C₂×C₁₃	#399
prime radical	C₂×#6127	C₂²
hypercenter	#430	D₁₃
hypocenter	C₁₃	#2098
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₄

#88194

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#430

C₂

C₂×C₁₃

C₂²

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
1. C₁₃×#430	C₂	semidirect
4. #11718780	C₂	semidirect
5. #11718149	C₂	semidirect
49. #430	D₁₃	semidirect
94. C₁₃	#2098	semidirect

H ≅ G/N

type

1. C₁₃×#430

C₂

semidirect

4. #11718780

C₂

semidirect

5. #11718149

C₂

semidirect

49. #430

D₁₃

semidirect

94. C₁₃

#2098

semidirect

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

subgroup	index
C₁₃×#430	2
#11718800	2
#11718790	2
#11718780	2
#11718149	2
#2098	13

subgroup

index

C₁₃×#430

Subgroups — #13116388

Conjugacy classes of subgroups

Complements

Maximal subgroups