Group #13114744 — subgroups

Subgroups — #13114744

Order 1664.

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

normal subgroups only

This group has 220 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	C₂×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
2	M₁₆×Dic₁₃	C₂	1	2	yes	maximal
3	C₂×#88059	C₂	1	1	yes	maximal, characteristic
4	C₂×#88055	C₂	1	1	yes	maximal, characteristic
5	#11718150	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×#6099	C₂²	1	2	yes	—
10	C₂²×#1055	C₂²	1	1	yes	characteristic
11	C₁₃×#108	C₄	1	4	yes	complemented
12	#88059	C₄	1	4	yes	complemented
13	#88055	—	2	2	no	—
14	#88055	C₄	1	4	yes	—
15	C₈×Dic₁₃	—	2	2	no	—
16	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₃	Q₈	1	2	yes	—
18	C₁₃×M₁₆	—	2	2	no	—
19	C₁₃×M₁₆	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
25	C₄×Dic₁₃	D₄	1	2	yes	—
26	#6099	—	2	2	no	—
27	#6099	C₂×C₄	1	4	yes	—
28	C₂×#1055	—	2	2	no	—
29	C₂×#1055	—	2	1	no	—
30	C₂×#1055	—	2	1	no	—
31	C₂×#1055	C₂×C₄	1	2	yes	—
32	#1778	—	13	1	no	maximal, Sylow
33	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
39	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
40	C₂×Dic₁₃	—	4	2	no	—
41	C₂×Dic₁₃	C₄⋊C₄	1	4	yes	—
42	C₈×C₁₃	—	2	4	no	—
43	C₈×C₁₃	C₄²	1	4	yes	—
44	#1055	—	2	2	no	—
45	#1055	—	2	4	no	—
46	C₂×#108	—	13	1	no	—
47	C₂×#108	D₁₃	1	1	yes	characteristic
48	C₄×M₁₆	—	13	2	no	—
49	C₂×#97	—	13	1	no	—
50	#341	—	13	2	no	—
51	C₂²×C₁₃	—	2	2	no	—
52	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₁₃	C₄×Q₈	1	1	yes	characteristic
54	C₂²×C₁₃	C₄×Q₈	1	1	yes	characteristic
55	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
56	C₄×C₁₃	#117	1	1	yes	characteristic
57	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
58	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
59	Dic₁₃	—	2	4	no	—
60	C₂×M₁₆	—	13	2	no	—
61	C₂×M₁₆	C₂×D₁₃	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	#108	—	13	4	no	—
66	#108	Dic₁₃	1	4	yes	complemented
67	#97	—	13	4	no	—
68	#97	—	26	2	no	—
69	C₄×C₈	—	26	2	no	—
70	C₂×C₁₃	—	2	1	no	—
71	C₂×C₁₃	—	2	1	no	—
72	C₂×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₁₃	#430	1	2	yes	—
74	C₂²×C₄	—	13	2	no	—
75	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
76	M₁₆	—	2	2	no	—
77	M₁₆	—	13	4	no	—
78	M₁₆	—	26	2	no	—
79	M₁₆	C₂×Dic₁₃	1	4	yes	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	13	2	no	—
82	C₂×C₈	—	26	2	no	—
83	C₂×C₈	—	26	1	no	—
84	C₂×C₈	—	26	1	no	—
85	C₂×C₈	C₄×D₁₃	1	2	yes	—
86	C₂×C₈	C₄×D₁₃	1	2	yes	—
87	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
88	C₄²	—	13	2	no	—
89	C₄²	—	13	2	no	—
90	C₁₃	#1778	1	1	yes	characteristic, complemented, Sylow
91	C₂³	Q₈×D₁₃	1	1	yes	characteristic
92	C₂×C₄	—	13	4	no	—
93	C₂×C₄	—	52	2	no	—
94	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
96	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
97	C₂×C₄	#6129	1	1	yes	characteristic
98	C₂×C₄	#6131	1	1	yes	characteristic
99	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
100	C₈	—	2	4	no	—
101	C₈	—	26	2	no	—
102	C₈	—	26	4	no	—
103	C₈	C₄×Dic₁₃	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	#88141	1	1	yes	characteristic
106	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
107	C₂²	Q₈×Dic₁₃	1	1	yes	characteristic
108	C₄	—	26	4	no	—
109	C₄	#88146	1	1	yes	characteristic
110	C₄	#88147	1	1	yes	characteristic
111	C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
112	C₄	D₄×Dic₁₃	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#11718554	1	2	yes	—
116	C₂	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#108

C₂

yes

maximal, characteristic

M₁₆×Dic₁₃

C₂

yes

maximal

C₂×#88059

C₂

yes

maximal, characteristic

C₂×#88055

C₂

yes

maximal, characteristic

#11718150

C₂

yes

maximal

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

—

C₂²×#1055

C₂²

yes

characteristic

C₁₃×#108

C₄

yes

complemented

#88059

C₄

yes

complemented

#88055

—

#88055

C₄

yes

—

C₈×Dic₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

Q₈

yes

—

C₁₃×M₁₆

—

C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

D₄

yes

—

#6099

—

#6099

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

#1778

—

maximal, Sylow

C₂³×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₄²

yes

—

—

—

—

D₁₃

yes

characteristic

C₄×M₁₆

—

C₂×#97

—

#341

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

C₄×Q₈

yes

characteristic

C₂²×C₁₃

C₄×Q₈

yes

characteristic

C₄×C₁₃

C₂×C₄²

yes

characteristic

C₄×C₁₃

#117

yes

characteristic

C₄×C₁₃

C₄×D₄

yes

characteristic

C₄×C₁₃

C₄×D₄

yes

characteristic

Dic₁₃

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄²

—

#108

—

#108

Dic₁₃

yes

complemented

#97

—

#97

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₃

#430

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₃

yes

—

C₂×C₈

C₄×D₁₃

yes

—

C₂×C₈

C₂×Dic₁₃

yes

—

C₄²

—

C₄²

—

C₁₃

#1778

yes

characteristic, complemented, Sylow

C₂³

Q₈×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

D₄×D₁₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×Dic₁₃

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

C₄×Dic₁₃

yes

—

104

C₂²

—

105

C₂²

#88141

yes

characteristic

106

C₂²

C₄⋊C₄×D₁₃

yes

characteristic

107

C₂²

Q₈×Dic₁₃

yes

characteristic

108

C₄

—

109

C₄

#88146

yes

characteristic

110

C₄

#88147

yes

characteristic

111

C₄

C₂×C₄×Dic₁₃

yes

characteristic

112

C₄

D₄×Dic₁₃

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#11718554

yes

—

116

C₂

C₄⋊C₄×Dic₁₃

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃
commutator	C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#108	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×#108	D₁₃
hypocenter	C₁₃	#1778
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₃

commutator

C₄×C₁₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂×C₁₃×#108

C₂

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂³×C₁₃

C₂×Q₈

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
11. C₁₃×#108	C₄	semidirect
12. #88059	C₄	semidirect
66. #108	Dic₁₃	semidirect
90. C₁₃	#1778	semidirect

H ≅ G/N

type

11. C₁₃×#108

C₄

semidirect

12. #88059

C₄

semidirect

66. #108

Dic₁₃

semidirect

90. C₁₃

#1778

semidirect

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

subgroup	index
C₂×C₁₃×#108	2
M₁₆×Dic₁₃	2
C₂×#88059	2
C₂×#88055	2
#11718150	2
#1778	13

subgroup

index

C₂×C₁₃×#108

M₁₆×Dic₁₃

Subgroups — #13114744

Conjugacy classes of subgroups

Complements

Maximal subgroups