Group #13114972 — subgroups

Subgroups — #13114972

Order 1664.

188 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 81 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	#11718779	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#341	C₂	1	1	yes	maximal, characteristic
4	#11718150	C₂	1	2	yes	maximal
5	#11718144	C₂	1	1	yes	maximal, characteristic
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	#88054	—	2	4	no	—
12	C₈×Dic₁₃	C₄	1	2	yes	—
13	C₈×Dic₁₃	C₄	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂²×Dic₁₃	Q₈	1	2	yes	—
16	C₁₃×M₁₆	—	2	2	no	—
17	C₁₃×M₁₆	—	2	2	no	—
18	C₂×C₈×C₁₃	—	2	2	no	—
19	C₂×C₈×C₁₃	—	2	2	no	—
20	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₁₃	D₄	1	2	yes	—
24	#6099	—	2	2	no	—
25	#6099	—	2	2	no	—
26	C₂×#1055	—	2	2	no	—
27	C₂×#1055	—	2	2	no	—
28	C₂×#1055	C₂×C₄	1	2	yes	—
29	#1837	—	13	1	no	maximal, Sylow
30	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	#41	1	2	yes	—
34	C₂×C₄×C₁₃	#41	1	2	yes	—
35	C₂×Dic₁₃	—	2	4	no	—
36	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
37	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
38	C₈×C₁₃	—	2	2	no	—
39	C₈×C₁₃	—	4	2	no	—
40	#1055	—	2	2	no	—
41	#1055	—	4	2	no	—
42	#423	—	13	2	no	—
43	C₂×C₄×C₈	—	13	1	no	—
44	#341	—	13	2	no	—
45	#341	—	13	1	no	—
46	#341	D₁₃	1	1	yes	characteristic
47	C₂²×C₁₃	—	2	2	no	—
48	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₁₃	#125	1	2	yes	—
50	C₄×C₁₃	#117	1	1	yes	characteristic
51	C₄×C₁₃	#117	1	1	yes	characteristic
52	C₄×C₁₃	#124	1	2	yes	—
53	Dic₁₃	—	2	2	no	—
54	Dic₁₃	#108	1	4	yes	—
55	C₂×M₁₆	—	13	2	no	—
56	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
57	C₂²×C₈	—	13	1	no	—
58	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
59	C₂×C₄²	—	13	1	no	—
60	C₄⋊C₈	—	26	4	no	—
61	C₄×C₈	—	13	2	no	—
62	C₄×C₈	—	13	2	no	—
63	C₂×C₁₃	—	2	2	no	—
64	C₂×C₁₃	#382	1	1	yes	characteristic
65	C₂×C₁₃	C₂×#108	1	2	yes	—
66	C₂²×C₄	—	13	2	no	—
67	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	26	2	no	—
71	M₁₆	—	26	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	13	2	no	—
75	C₂×C₈	—	26	2	no	—
76	C₂×C₈	—	26	2	no	—
77	C₂×C₈	C₄×D₁₃	1	2	yes	—
78	C₄²	—	13	1	no	—
79	C₄²	—	13	1	no	—
80	C₄²	—	13	2	no	—
81	C₁₃	#1837	1	1	yes	characteristic, complemented, Sylow
82	C₂³	Q₈×D₁₃	1	1	yes	characteristic
83	C₂×C₄	—	13	2	no	—
84	C₂×C₄	—	13	2	no	—
85	C₂×C₄	—	26	4	no	—
86	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
87	C₂×C₄	#6127	1	2	yes	—
88	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
89	C₂×C₄	#6129	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	4	2	no	—
92	C₈	—	26	2	no	—
93	C₈	—	52	2	no	—
94	C₂²	—	2	2	no	—
95	C₂²	#88143	1	2	yes	—
96	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
97	C₄	—	13	4	no	—
98	C₄	—	26	2	no	—
99	C₄	#88126	1	1	yes	characteristic
100	C₄	#88131	1	1	yes	characteristic
101	C₄	#88139	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	#11718311	1	1	yes	characteristic
104	C₂	D₁₃×#108	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11718779

C₂

yes

maximal

C₂×C₈×Dic₁₃

C₂

yes

maximal, characteristic

C₁₃×#341

C₂

yes

maximal, characteristic

#11718150

C₂

yes

maximal

#11718144

C₂

yes

maximal, characteristic

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

#88054

—

C₈×Dic₁₃

C₄

yes

—

C₈×Dic₁₃

C₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

Q₈

yes

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

—

—

—

—

—

C₂×C₄

yes

—

#1837

—

maximal, Sylow

C₂³×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#1055

—

#423

—

C₂×C₄×C₈

—

#341

—

#341

—

#341

D₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#125

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

Dic₁₃

#108

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

#382

yes

characteristic

C₂×C₁₃

C₂×#108

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₃

yes

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1837

yes

characteristic, complemented, Sylow

C₂³

Q₈×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

#6127

yes

—

C₂×C₄

D₄×D₁₃

yes

characteristic

C₂×C₄

#6129

yes

—

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#88143

yes

—

C₂²

C₄⋊C₄×D₁₃

yes

characteristic

C₄

—

C₄

—

C₄

#88126

yes

characteristic

100

C₄

#88131

yes

characteristic

101

C₄

#88139

yes

—

102

C₂

—

103

C₂

#11718311

yes

characteristic

104

C₂

D₁₃×#108

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#341	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#341	D₁₃
hypocenter	C₁₃	#1837
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#341

C₂

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂³×C₁₃

C₂×Q₈

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
81. C₁₃	#1837	semidirect

H ≅ G/N

type

81. C₁₃

#1837

semidirect

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

subgroup	index
#11718779	2
C₂×C₈×Dic₁₃	2
C₁₃×#341	2
#11718150	2
#11718144	2
#1837	13

subgroup

index

#11718779

C₂×C₈×Dic₁₃

C₁₃×#341

#11718150

#11718144

#1837

Subgroups — #13114972

Conjugacy classes of subgroups

Complements

Maximal subgroups