Group #13130753 — subgroups

Subgroups — #13130753

Order 1664.

260 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 114 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×C₄⋊#1057	C₂	1	2	yes	maximal
2	C₄²×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#11718290	C₂	1	4	yes	maximal
4	C₂²×#1057	C₂²	1	4	yes	—
5	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₃	C₄	1	2	yes	—
7	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
9	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₄⋊#1057	—	2	4	no	—
11	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
15	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
16	C₂×#1057	—	2	4	no	—
17	C₂×#1057	—	2	8	no	—
18	C₄²×C₁₃	—	2	2	no	—
19	C₄×Dic₁₃	—	2	4	no	—
20	C₄×Dic₁₃	—	2	4	no	—
21	C₄×Dic₁₃	C₈	1	4	yes	complemented
22	C₄×Dic₁₃	D₄	1	2	yes	—
23	C₄×Dic₁₃	Q₈	1	2	yes	—
24	#1831	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	—	2	2	no	—
27	C₂×C₄×C₁₃	—	2	2	no	—
28	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₁₃	M₁₆	1	4	yes	—
31	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
32	C₂×Dic₁₃	—	2	2	no	—
33	C₂×Dic₁₃	—	2	2	no	—
34	C₂×Dic₁₃	—	2	2	no	—
35	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
36	C₂×Dic₁₃	C₂×C₈	1	4	yes	—
37	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×Dic₁₃	#41	1	4	yes	—
40	#1057	—	4	4	no	—
41	C₂×C₄⋊C₈	—	13	2	no	—
42	C₄³	—	13	1	no	—
43	#336	—	13	4	no	—
44	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₁₃	#117	1	2	yes	—
46	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
47	C₂²×C₁₃	C₂×M₁₆	1	2	yes	—
48	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₁₃	—	2	4	no	—
50	C₄×C₁₃	C₄⋊C₈	1	4	yes	—
51	Dic₁₃	—	2	2	no	—
52	Dic₁₃	—	2	4	no	—
53	Dic₁₃	#124	1	2	yes	—
54	Dic₁₃	#125	1	2	yes	—
55	C₂²×C₈	—	13	4	no	—
56	C₂×C₄²	—	13	1	no	—
57	C₂×C₄²	—	13	1	no	—
58	C₂×C₄²	—	13	2	no	—
59	C₂×C₄²	—	13	2	no	—
60	C₂×C₄²	#261	1	1	yes	characteristic
61	C₄⋊C₈	—	26	4	no	—
62	C₂×C₁₃	#382	1	1	yes	characteristic
63	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
64	C₂×C₁₃	#423	1	1	yes	characteristic
65	C₂×C₁₃	#431	1	2	yes	—
66	C₂×C₁₃	#432	1	2	yes	—
67	C₂²×C₄	—	13	1	no	—
68	C₂²×C₄	—	13	2	no	—
69	C₂²×C₄	—	13	1	no	—
70	C₂²×C₄	C₂×#261	1	2	yes	—
71	C₂²×C₄	C₂×#261	1	1	yes	characteristic
72	C₂×C₈	—	26	4	no	—
73	C₂×C₈	—	26	8	no	—
74	C₄²	—	2	2	no	—
75	C₄²	—	13	4	no	—
76	C₄²	—	13	2	no	—
77	C₄²	—	13	2	no	—
78	C₄²	—	26	4	no	—
79	C₄²	—	26	4	no	—
80	C₁₃	#1831	1	1	yes	characteristic, complemented, Sylow
81	C₂³	C₂²×#261	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	13	1	no	—
85	C₂×C₄	—	13	1	no	—
86	C₂×C₄	—	13	4	no	—
87	C₂×C₄	—	13	4	no	—
88	C₂×C₄	—	13	2	no	—
89	C₂×C₄	—	26	2	no	—
90	C₂×C₄	—	26	2	no	—
91	C₂×C₄	—	26	2	no	—
92	C₂×C₄	D₁₃⋊C₈	1	2	yes	—
93	C₂×C₄	#6118	1	4	yes	—
94	C₂×C₄	C₄⋊#261	1	2	yes	—
95	C₂×C₄	#6122	1	2	yes	—
96	C₈	—	52	4	no	—
97	C₂²	C₂×D₁₃⋊C₈	1	1	yes	characteristic
98	C₂²	C₂×#6118	1	2	yes	—
99	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
100	C₂²	#88237	1	2	yes	—
101	C₂²	C₂×#6122	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	13	2	no	—
104	C₄	—	13	2	no	—
105	C₄	—	26	4	no	—
106	C₄	—	26	2	no	—
107	C₄	#88112	1	4	yes	—
108	C₂	#11719051	1	2	yes	—
109	C₂	#11719052	1	1	yes	characteristic
110	C₂	#11719060	1	1	yes	characteristic
111	C₂	C₂×#88112	1	1	yes	characteristic
112	C₂	#11719130	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#1057

C₂

yes

maximal

C₄²×Dic₁₃

C₂

yes

maximal, characteristic

#11718290

C₂

yes

maximal

C₂²×#1057

C₂²

yes

—

C₂×C₄²×C₁₃

C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₄

yes

—

C₂×C₄×Dic₁₃

C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₄⋊#1057

—

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×#1057

—

C₂×#1057

—

C₄²×C₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₈

yes

complemented

C₄×Dic₁₃

D₄

yes

—

C₄×Dic₁₃

Q₈

yes

—

#1831

—

maximal, Sylow

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

M₁₆

yes

—

C₂×C₄×C₁₃

M₁₆

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₂×C₈

yes

—

C₂×Dic₁₃

C₂×D₄

yes

characteristic

C₂×Dic₁₃

C₂×Q₈

yes

characteristic

C₂×Dic₁₃

#41

yes

—

#1057

—

C₂×C₄⋊C₈

—

C₄³

—

#336

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#117

yes

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₂²×C₁₃

C₂×M₁₆

yes

—

C₂²×C₁₃

C₂×M₁₆

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

C₄⋊C₈

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

#124

yes

—

Dic₁₃

#125

yes

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#261

yes

characteristic

C₄⋊C₈

—

C₂×C₁₃

#382

yes

characteristic

C₂×C₁₃

C₂×C₄⋊C₈

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×C₁₃

#432

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#261

yes

—

C₂²×C₄

C₂×#261

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1831

yes

characteristic, complemented, Sylow

C₂³

C₂²×#261

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₃⋊C₈

yes

—

C₂×C₄

#6118

yes

—

C₂×C₄

C₄⋊#261

yes

—

C₂×C₄

#6122

yes

—

C₈

—

C₂²

C₂×D₁₃⋊C₈

yes

characteristic

C₂²

C₂×#6118

yes

—

C₂²

C₂×C₄⋊#261

yes

characteristic

100

C₂²

#88237

yes

—

101

C₂²

C₂×#6122

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

#88112

yes

—

108

C₂

#11719051

yes

—

109

C₂

#11719052

yes

characteristic

110

C₂

#11719060

yes

characteristic

111

C₂

C₂×#88112

yes

characteristic

112

C₂

#11719130

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#261
commutator	C₂²×C₁₃	C₂²×C₈
Fitting	C₂×C₄²×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×Dic₁₃	C₂³
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	#1831
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

subgroup

G/H

center, Frattini

C₂³

C₂²×#261

commutator

C₂²×C₁₃

C₂²×C₈

Fitting

C₂×C₄²×C₁₃

C₄

socle, prime radical

C₂³×C₁₃

C₂²×C₄

cosocle

C₂²×Dic₁₃

C₂³

C₂×C₄²

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ C₂×C₄²

N	H ≅ G/N	type
21. C₄×Dic₁₃	C₈	semidirect
80. C₁₃	#1831	semidirect

H ≅ G/N

type

21. C₄×Dic₁₃

C₈

semidirect

80. C₁₃

#1831

semidirect

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

subgroup	index
C₂×C₄⋊#1057	2
C₄²×Dic₁₃	2
#11718290	2
#1831	13

subgroup

index

C₂×C₄⋊#1057

C₄²×Dic₁₃

#11718290

#1831

Subgroups — #13130753

Conjugacy classes of subgroups

Complements

Maximal subgroups