Group #13130100 — subgroups

Subgroups — #13130100

Order 1664.

236 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 64 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×#88141	C₂	1	1	yes	maximal, characteristic
2	#11719128	C₂	1	2	yes	maximal
3	#11718286	C₂	1	4	yes	maximal
4	C₂²×Dic₂₆	C₄	1	1	yes	characteristic
5	C₂×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
6	C₂×#6101	C₂²	1	2	yes	—
7	C₂×C₄×Dic₁₃	C₄	1	2	yes	—
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	#88141	—	2	2	no	—
10	#88141	—	2	2	no	—
11	C₂²⋊#1057	C₂²	1	4	yes	—
12	#88112	—	2	2	no	—
13	#88110	—	2	2	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
18	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₆	—	2	2	no	—
20	C₂×Dic₂₆	—	2	4	no	—
21	C₂×#1057	—	2	4	no	—
22	C₁₃×C₄⋊C₄	—	2	2	no	—
23	#6101	—	2	4	no	—
24	C₄×Dic₁₃	—	2	2	no	—
25	C₄×Dic₁₃	—	2	2	no	—
26	C₄×Dic₁₃	D₄	1	2	yes	—
27	C₄×Dic₁₃	D₄	1	2	yes	—
28	#1467	—	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	—	4	2	no	—
33	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
34	C₂×Dic₁₃	—	2	2	no	—
35	C₂×Dic₁₃	—	2	2	no	—
36	C₂×Dic₁₃	—	2	2	no	—
37	C₂×Dic₁₃	—	4	1	no	—
38	C₂×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×Dic₁₃	M₁₆	1	4	yes	—
41	C₂×Dic₁₃	C₂×D₄	1	2	yes	—
42	Dic₂₆	—	2	8	no	—
43	#1057	—	4	4	no	—
44	C₂×C₄×Q₈	—	13	1	no	—
45	#432	—	13	2	no	—
46	#324	—	13	4	no	—
47	C₂²×C₁₃	—	2	1	no	—
48	C₂²×C₁₃	—	2	1	no	—
49	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₁₃	C₂×M₁₆	1	2	yes	—
51	C₄×C₁₃	—	2	2	no	—
52	C₄×C₁₃	—	4	2	no	—
53	Dic₁₃	—	2	4	no	—
54	Dic₁₃	—	2	2	no	—
55	Dic₁₃	—	2	1	no	—
56	Dic₁₃	#101	1	2	yes	—
57	C₂²×Q₈	—	13	1	no	—
58	C₄×Q₈	—	26	2	no	—
59	C₄×Q₈	—	26	2	no	—
60	C₂×C₄⋊C₄	—	13	2	no	—
61	C₂×C₄⋊C₄	#261	1	1	yes	characteristic
62	C₂×C₄²	—	13	1	no	—
63	C₂×C₄²	—	13	2	no	—
64	C₄⋊C₈	—	26	2	no	—
65	C₂²⋊C₈	—	13	4	no	—
66	#97	—	26	2	no	—
67	C₂×C₁₃	—	2	2	no	—
68	C₂×C₁₃	#407	1	1	yes	characteristic
69	C₂×C₁₃	#410	1	1	yes	characteristic
70	C₂×C₁₃	C₂×#101	1	1	yes	characteristic
71	C₂×Q₈	—	26	4	no	—
72	C₂×Q₈	—	26	2	no	—
73	C₂²×C₄	—	13	1	no	—
74	C₂²×C₄	—	13	2	no	—
75	C₂²×C₄	—	13	1	no	—
76	C₂²×C₄	C₂×#261	1	2	yes	—
77	C₂²×C₄	C₂×#261	1	1	yes	characteristic
78	C₂×C₈	—	26	4	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	26	4	no	—
81	C₄²	—	13	2	no	—
82	C₄²	—	13	2	no	—
83	C₄²	—	26	2	no	—
84	C₄²	—	26	2	no	—
85	C₁₃	#1467	1	1	yes	characteristic, complemented, Sylow
86	C₂³	C₂²×#261	1	1	yes	characteristic
87	Q₈	—	26	8	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	13	1	no	—
92	C₂×C₄	—	13	4	no	—
93	C₂×C₄	—	13	1	no	—
94	C₂×C₄	—	13	2	no	—
95	C₂×C₄	—	26	2	no	—
96	C₂×C₄	—	26	2	no	—
97	C₂×C₄	—	26	2	no	—
98	C₂×C₄	—	52	1	no	—
99	C₂×C₄	C₂²⋊#261	1	2	yes	—
100	C₈	—	52	4	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	2	1	no	—
103	C₂²	D₁₃⋊M₁₆	1	2	yes	—
104	C₂²	C₂×C₂²⋊#261	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	13	2	no	—
108	C₄	—	26	4	no	—
109	C₄	—	26	2	no	—
110	C₄	—	26	1	no	—
111	C₂	—	2	2	no	—
112	C₂	#11719126	1	1	yes	characteristic
113	C₂	#11719142	1	1	yes	characteristic
114	C₂	D₁₃⋊#101	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88141

C₂

yes

maximal, characteristic

#11719128

C₂

yes

maximal

#11718286

C₂

yes

maximal

C₂²×Dic₂₆

C₄

yes

characteristic

C₂×C₁₃×C₄⋊C₄

C₄

yes

characteristic

C₂×#6101

C₂²

yes

—

C₂×C₄×Dic₁₃

C₄

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

#88141

—

#88141

—

C₂²⋊#1057

C₂²

yes

—

#88112

—

#88110

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂²×Dic₁₃

C₂³

yes

characteristic

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×#1057

—

C₁₃×C₄⋊C₄

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

D₄

yes

—

C₄×Dic₁₃

D₄

yes

—

#1467

—

maximal, Sylow

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

M₁₆

yes

—

C₂×Dic₁₃

C₂×D₄

yes

—

Dic₂₆

—

#1057

—

C₂×C₄×Q₈

—

#432

—

#324

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₃

C₂×M₁₆

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

#101

yes

—

C₂²×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

#261

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₂×C₁₃

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#261

yes

—

C₂²×C₄

C₂×#261

yes

characteristic

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1467

yes

characteristic, complemented, Sylow

C₂³

C₂²×#261

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#261

yes

—

100

C₈

—

101

C₂²

—

102

C₂²

—

103

C₂²

D₁₃⋊M₁₆

yes

—

104

C₂²

C₂×C₂²⋊#261

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₂

—

112

C₂

#11719126

yes

characteristic

113

C₂

#11719142

yes

characteristic

114

C₂

D₁₃⋊#101

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#261
commutator, prime radical	C₂³×C₁₃	C₂²×C₄
Frattini	C₂³	C₂²×#261
Fitting	C₂×C₁₃×C₄⋊C₄	C₄
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂²×Dic₁₃	C₂³
hypercenter	C₂×C₄⋊C₄	#261
hypocenter	C₁₃	#1467
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂²

C₂×C₂²⋊#261

commutator, prime radical

C₂³×C₁₃

C₂²×C₄

Frattini

C₂³

C₂²×#261

Fitting

C₂×C₁₃×C₄⋊C₄

C₄

socle

C₂²×C₁₃

C₂×C₂²⋊C₄

cosocle

C₂²×Dic₁₃

C₂³

C₂×C₄⋊C₄

C₁₃

G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
85. C₁₃	#1467	semidirect

H ≅ G/N

type

85. C₁₃

#1467

semidirect

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

subgroup	index
C₂×#88141	2
#11719128	2
#11718286	2
#1467	13

subgroup

index

Subgroups — #13130100

Conjugacy classes of subgroups

Complements

Maximal subgroups