Group #13129718 — subgroups

Subgroups — #13129718

Order 1664.

190 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 48 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	D₁₃⋊(C₂²⋊C₈)	C₂	1	2	yes	maximal
2	#11718787	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
4	C₂×D₁₃⋊C₈	—	2	2	no	—
5	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic
6	C₂×#6099	C₄	1	1	yes	characteristic
7	C₂²⋊#1057	—	2	2	no	—
8	#88111	C₄	1	4	yes	—
9	#88060	—	2	2	no	—
10	C₂³×D₁₃	Q₈	1	1	yes	characteristic
11	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₁₃	D₄	1	1	yes	characteristic
13	C₂×C₄×D₁₃	—	4	1	no	—
14	C₂×C₄×D₁₃	—	4	1	no	—
15	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₁₃	D₄	1	2	yes	—
17	C₂×#1057	—	2	4	no	—
18	D₁₃⋊C₈	—	4	2	no	—
19	D₁₃⋊C₈	—	4	2	no	—
20	C₁₃×M₁₆	—	4	1	no	—
21	C₂×C₈×C₁₃	—	2	1	no	—
22	#6099	—	4	1	no	—
23	C₂×#1055	—	2	1	no	—
24	#1298	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×D₁₃	—	2	4	no	—
27	C₂²×D₁₃	—	4	1	no	—
28	C₂²×D₁₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₃	—	2	1	no	—
30	C₂×C₄×C₁₃	—	2	1	no	—
31	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×Dic₁₃	—	4	1	no	—
34	C₂×Dic₁₃	C₂²⋊C₄	1	2	yes	—
35	C₄×D₁₃	—	2	2	no	—
36	C₄×D₁₃	—	2	2	no	—
37	C₄×D₁₃	—	4	2	no	—
38	#1057	—	4	4	no	—
39	C₈×C₁₃	—	4	1	no	—
40	#1055	—	4	1	no	—
41	#407	—	13	1	no	—
42	C₂×C₂²⋊C₈	—	13	2	no	—
43	C₂²×C₁₃	—	2	2	no	—
44	C₂²×C₁₃	—	2	1	no	—
45	C₂²×C₁₃	#95	1	1	yes	characteristic
46	C₂×D₁₃	—	2	2	no	—
47	C₂×D₁₃	—	2	2	no	—
48	C₂×D₁₃	—	4	4	no	—
49	C₂×D₁₃	#108	1	4	yes	—
50	C₄×C₁₃	—	2	1	no	—
51	C₄×C₁₃	#99	1	1	yes	characteristic
52	C₄×C₁₃	#99	1	1	yes	characteristic
53	Dic₁₃	—	2	2	no	—
54	C₂³×C₄	—	13	1	no	—
55	C₂×M₁₆	—	13	1	no	—
56	C₂×M₁₆	#261	1	1	yes	characteristic
57	C₂²×C₈	—	26	2	no	—
58	C₂²⋊C₈	—	13	4	no	—
59	C₂²⋊C₈	—	26	2	no	—
60	C₂²⋊C₈	—	26	2	no	—
61	C₂×C₁₃	—	4	1	no	—
62	C₂×C₁₃	#341	1	2	yes	—
63	C₂×C₁₃	#342	1	1	yes	characteristic
64	D₁₃	—	2	4	no	—
65	C₂⁴	—	13	1	no	—
66	C₂²×C₄	—	13	1	no	—
67	C₂²×C₄	—	13	2	no	—
68	C₂²×C₄	—	13	2	no	—
69	C₂²×C₄	—	52	1	no	—
70	C₂²×C₄	—	52	1	no	—
71	C₂²×C₄	C₂×#261	1	1	yes	characteristic
72	M₁₆	—	4	1	no	—
73	M₁₆	—	52	1	no	—
74	C₂×C₈	—	2	1	no	—
75	C₂×C₈	—	26	4	no	—
76	C₂×C₈	—	26	1	no	—
77	C₂×C₈	—	52	2	no	—
78	C₂×C₈	—	52	2	no	—
79	C₁₃	#1298	1	1	yes	characteristic, complemented, Sylow
80	C₂³	—	13	2	no	—
81	C₂³	—	26	4	no	—
82	C₂³	—	52	1	no	—
83	C₂³	C₄⋊#261	1	1	yes	characteristic
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	13	2	no	—
87	C₂×C₄	—	26	2	no	—
88	C₂×C₄	—	26	2	no	—
89	C₂×C₄	—	52	2	no	—
90	C₂×C₄	—	52	1	no	—
91	C₂×C₄	C₄×#261	1	1	yes	characteristic
92	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
93	C₈	—	4	1	no	—
94	C₈	—	52	4	no	—
95	C₈	—	52	1	no	—
96	C₂²	—	2	2	no	—
97	C₂²	—	2	1	no	—
98	C₂²	—	13	4	no	—
99	C₂²	—	26	2	no	—
100	C₂²	—	26	2	no	—
101	C₂²	—	52	4	no	—
102	C₂²	(C₂×#261)⋊C₄	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	26	2	no	—
105	C₄	#88107	1	1	yes	characteristic
106	C₄	#88119	1	1	yes	characteristic
107	C₂	—	4	1	no	—
108	C₂	—	26	4	no	—
109	C₂	#11718273	1	2	yes	—
110	C₂	#11718289	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₁₃⋊(C₂²⋊C₈)

C₂

yes

maximal

#11718787

C₂

yes

maximal, characteristic

C₂²×C₄×D₁₃

C₂²

yes

characteristic

C₂×D₁₃⋊C₈

—

C₂×C₁₃×M₁₆

C₄

yes

characteristic

C₂×#6099

C₄

yes

characteristic

C₂²⋊#1057

—

#88111

C₄

yes

—

#88060

—

C₂³×D₁₃

Q₈

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

D₄

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₂×C₄

yes

—

C₂×C₄×D₁₃

D₄

yes

—

C₂×#1057

—

D₁₃⋊C₈

—

D₁₃⋊C₈

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

—

—

—

C₂³×C₁₃

C₄⋊C₄

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂²⋊C₄

yes

—

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

#1057

—

C₈×C₁₃

—

#1055

—

#407

—

C₂×C₂²⋊C₈

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#95

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

#108

yes

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

#261

yes

characteristic

C₂²×C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

#341

yes

—

C₂×C₁₃

#342

yes

characteristic

D₁₃

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#261

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₁₃

#1298

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

—

C₂³

C₄⋊#261

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×#261

yes

characteristic

C₂×C₄

C₂²⋊#261

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

(C₂×#261)⋊C₄

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

#88107

yes

characteristic

106

C₄

#88119

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

#11718273

yes

—

110

C₂

#11718289

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#261
commutator	C₂×C₄×C₁₃	C₄²
Frattini	C₂²×C₄	C₂×#261
Fitting	C₂×C₁₃×M₁₆	C₄
socle	C₂²×C₁₃	#95
prime radical	C₂³×D₁₃	Q₈
cosocle	C₂²×C₄×D₁₃	C₂²
hypercenter	C₂×M₁₆	#261
hypocenter	C₁₃	#1298
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₂×C₄

C₂²⋊#261

commutator

C₂×C₄×C₁₃

C₄²

Frattini

C₂²×C₄

C₂×#261

Fitting

C₂×C₁₃×M₁₆

C₄

socle

C₂²×C₁₃

#95

prime radical

C₂³×D₁₃

Q₈

cosocle

C₂²×C₄×D₁₃

C₂²

C₂×M₁₆

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
79. C₁₃	#1298	semidirect

H ≅ G/N

type

79. C₁₃

#1298

semidirect

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

subgroup	index
D₁₃⋊(C₂²⋊C₈)	2
#11718787	2
#1298	13

subgroup

index

D₁₃⋊(C₂²⋊C₈)

#11718787

#1298

Subgroups — #13129718

Conjugacy classes of subgroups

Complements

Maximal subgroups