Group #13130737 — subgroups

Subgroups — #13130737

Order 1664.

272 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 66 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×#88126	C₂	1	1	yes	maximal, characteristic
2	#11719126	C₂	1	2	yes	maximal
3	#11718291	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
5	C₂×#6122	C₂²	1	4	yes	—
6	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
7	C₂×#6103	C₄	1	2	yes	—
8	C₂×#6101	C₂²	1	2	yes	—
9	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
10	#88126	—	2	4	no	—
11	#88111	—	2	4	no	—
12	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
16	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₄×D₁₃	—	2	4	no	—
18	C₂×C₄×D₁₃	D₄	1	4	yes	—
19	#6122	—	2	8	no	—
20	C₂×#1057	—	2	4	no	—
21	C₄²×C₁₃	—	2	2	no	—
22	#6103	—	2	4	no	—
23	#6101	—	2	4	no	—
24	C₄×Dic₁₃	—	2	2	no	—
25	#1822	—	13	1	no	maximal, Sylow
26	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×D₁₃	—	2	2	no	—
28	C₂²×D₁₃	—	4	2	no	—
29	C₂²×D₁₃	C₂²⋊C₄	1	2	yes	—
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	—	4	2	no	—
36	C₂×Dic₁₃	C₂×D₄	1	2	yes	—
37	C₂×Dic₁₃	#41	1	4	yes	—
38	C₄×D₁₃	—	2	8	no	—
39	#1057	—	4	4	no	—
40	C₂×#117	—	13	1	no	—
41	#407	—	13	2	no	—
42	#343	—	13	4	no	—
43	C₂²×C₁₃	—	2	2	no	—
44	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₁₃	#117	1	2	yes	—
46	C₂×D₁₃	—	2	2	no	—
47	C₂×D₁₃	—	2	4	no	—
48	C₂×D₁₃	—	4	4	no	—
49	C₄×C₁₃	—	2	2	no	—
50	C₄×C₁₃	—	4	2	no	—
51	Dic₁₃	—	4	2	no	—
52	Dic₁₃	#123	1	4	yes	—
53	C₂³×C₄	—	13	1	no	—
54	C₂×M₁₆	—	13	4	no	—
55	#117	—	26	4	no	—
56	C₂×C₄⋊C₄	—	13	2	no	—
57	C₂×C₂²⋊C₄	—	13	2	no	—
58	C₂×C₄²	—	13	1	no	—
59	C₂×C₄²	#261	1	1	yes	characteristic
60	C₂²⋊C₈	—	26	4	no	—
61	C₂×C₁₃	—	2	2	no	—
62	C₂×C₁₃	#381	1	1	yes	characteristic
63	C₂×C₁₃	#413	1	2	yes	—
64	D₁₃	—	4	2	no	—
65	C₂⁴	—	13	1	no	—
66	C₂²×C₄	—	13	1	no	—
67	C₂²×C₄	—	13	4	no	—
68	C₂²×C₄	—	13	2	no	—
69	C₂²×C₄	—	26	4	no	—
70	C₂²×C₄	C₂×#261	1	2	yes	—
71	C₂²×C₄	C₂×#261	1	1	yes	characteristic
72	M₁₆	—	26	8	no	—
73	C₂×C₈	—	26	4	no	—
74	C₄⋊C₄	—	26	4	no	—
75	C₂²⋊C₄	—	26	4	no	—
76	C₄²	—	2	2	no	—
77	C₄²	—	26	2	no	—
78	C₁₃	#1822	1	1	yes	characteristic, complemented, Sylow
79	C₂³	—	13	2	no	—
80	C₂³	—	26	2	no	—
81	C₂³	—	52	2	no	—
82	C₂³	C₂²×#261	1	1	yes	characteristic
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	13	4	no	—
87	C₂×C₄	—	13	2	no	—
88	C₂×C₄	—	26	8	no	—
89	C₂×C₄	—	26	2	no	—
90	C₂×C₄	—	52	2	no	—
91	C₂×C₄	C₂²⋊#261	1	2	yes	—
92	C₈	—	52	4	no	—
93	C₂²	—	2	2	no	—
94	C₂²	—	26	4	no	—
95	C₂²	—	26	2	no	—
96	C₂²	—	52	4	no	—
97	C₂²	#88237	1	2	yes	—
98	C₂²	C₂×C₂²⋊#261	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	4	2	no	—
101	C₄	—	13	4	no	—
102	C₄	—	52	2	no	—
103	C₂	—	2	2	no	—
104	C₂	—	52	2	no	—
105	C₂	#11719132	1	2	yes	—
106	C₂	#11719135	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88126

C₂

yes

maximal, characteristic

#11719126

C₂

yes

maximal

#11718291

C₂

yes

maximal, complemented

C₂²×C₄×D₁₃

C₂²

yes

characteristic

C₂×#6122

C₂²

yes

—

C₂×C₄²×C₁₃

C₄

yes

characteristic

C₂×#6103

C₄

yes

—

C₂×#6101

C₂²

yes

—

C₂×C₄×Dic₁₃

C₄

yes

characteristic

#88126

—

#88111

—

C₂³×D₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂²×Dic₁₃

C₂³

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

D₄

yes

—

#6122

—

C₂×#1057

—

C₄²×C₁₃

—

#6103

—

#6101

—

C₄×Dic₁₃

—

#1822

—

maximal, Sylow

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×D₄

yes

—

C₂×Dic₁₃

#41

yes

—

C₄×D₁₃

—

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₃

#117

yes

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

#123

yes

—

C₂³×C₄

—

C₂×M₁₆

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

#261

yes

characteristic

C₂²⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

#381

yes

characteristic

C₂×C₁₃

#413

yes

—

D₁₃

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#261

yes

—

C₂²×C₄

C₂×#261

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₁₃

#1822

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²×#261

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#261

yes

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#88237

yes

—

C₂²

C₂×C₂²⋊#261

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₂

—

104

C₂

—

105

C₂

#11719132

yes

—

106

C₂

#11719135

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#261
commutator	C₂³×C₁₃	C₂²×C₄
Frattini	C₂³	C₂²×#261
Fitting	C₂×C₄²×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₃	C₂×C₄
cosocle	C₂²×Dic₁₃	C₂³
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	#1822
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄²

subgroup

G/H

center

C₂²

C₂×C₂²⋊#261

commutator

C₂³×C₁₃

C₂²×C₄

Frattini

C₂³

C₂²×#261

Fitting

C₂×C₄²×C₁₃

C₄

socle

C₂²×C₁₃

C₂×C₂²⋊C₄

prime radical

C₂³×D₁₃

C₂×C₄

cosocle

C₂²×Dic₁₃

C₂³

C₂×C₄²

C₁₃

G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄²

N	H ≅ G/N	type
3. #11718291	C₂	semidirect
78. C₁₃	#1822	semidirect

H ≅ G/N

type

3. #11718291

C₂

semidirect

78. C₁₃

#1822

semidirect

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

subgroup	index
C₂×#88126	2
#11719126	2
#11718291	2
#1822	13

subgroup

index

Subgroups — #13130737

Conjugacy classes of subgroups

Complements

Maximal subgroups