Group #13129895 — subgroups

Subgroups — #13129895

Order 1664.

128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 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⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#108	C₂	1	1	yes	maximal, characteristic
4	D₁₃⋊M₁₆	—	2	1	no	—
5	M₁₆×D₁₃	—	2	1	no	—
6	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×#6092	—	2	1	no	—
8	#88104	C₄	1	2	yes	—
9	#88103	—	2	1	no	—
10	D₁₃⋊C₁₆	—	2	1	no	—
11	D₁₃⋊C₁₆	C₄	1	2	yes	—
12	C₁₃×#108	C₄	1	1	yes	characteristic
13	#88062	—	2	1	no	—
14	#88059	C₄	1	1	yes	characteristic
15	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
16	#6122	—	4	1	no	—
17	#6118	—	2	2	no	—
18	D₁₃⋊C₈	—	4	1	no	—
19	C₁₃×M₁₆	—	2	1	no	—
20	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	#6099	—	2	1	no	—
22	C₂×#1055	D₄	1	1	yes	characteristic
23	#6094	—	4	1	no	—
24	C₈×D₁₃	—	4	1	no	—
25	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
26	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
27	C₈×D₁₃	D₄	1	1	yes	characteristic
28	C₈×D₁₃	Q₈	1	1	yes	characteristic
29	#6092	—	2	2	no	—
30	#1381	—	13	1	no	maximal, Sylow
31	C₂²×D₁₃	Q₁₆	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×Dic₁₃	SD₁₆	1	1	yes	characteristic
34	C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
36	C₄×D₁₃	D₈	1	1	yes	characteristic
37	C₄×D₁₃	SD₁₆	1	1	yes	characteristic
38	#1057	—	4	2	no	—
39	C₈×C₁₃	—	4	1	no	—
40	C₈×C₁₃	C₄²	1	1	yes	characteristic
41	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
42	#1055	—	4	1	no	—
43	#1055	C₂²⋊C₄	1	1	yes	characteristic
44	#1055	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₁₆	—	13	1	no	—
46	C₂×#108	—	13	1	no	—
47	C₂×#108	—	13	1	no	—
48	C₂²×C₁₃	#103	1	1	yes	characteristic
49	C₂×D₁₃	—	2	2	no	—
50	C₂×D₁₃	#103	1	1	yes	characteristic
51	C₂×D₁₃	#107	1	1	yes	characteristic
52	C₄×C₁₃	#95	1	1	yes	characteristic
53	C₄×C₁₃	#102	1	1	yes	characteristic
54	Dic₁₃	#102	1	1	yes	characteristic
55	Dic₁₃	#106	1	1	yes	characteristic
56	C₂×M₁₆	—	26	1	no	—
57	C₂×M₁₆	—	26	1	no	—
58	C₂²×C₈	—	13	1	no	—
59	C₂×C₁₆	—	13	2	no	—
60	C₂×C₁₆	—	26	1	no	—
61	C₂×C₁₆	—	26	1	no	—
62	#108	—	13	2	no	—
63	#108	—	13	1	no	—
64	#108	—	26	1	no	—
65	#108	—	26	1	no	—
66	#108	#261	1	1	yes	characteristic
67	C₂×C₁₃	—	2	1	no	—
68	C₂×C₁₃	#340	1	1	yes	characteristic
69	D₁₃	—	2	1	no	—
70	D₁₃	#368	1	2	yes	—
71	C₂²×C₄	—	13	1	no	—
72	M₁₆	—	2	1	no	—
73	M₁₆	—	26	2	no	—
74	M₁₆	—	26	1	no	—
75	M₁₆	—	52	1	no	—
76	M₁₆	—	52	1	no	—
77	C₂×C₈	—	13	1	no	—
78	C₂×C₈	—	13	1	no	—
79	C₂×C₈	—	13	1	no	—
80	C₂×C₈	—	13	1	no	—
81	C₂×C₈	—	13	1	no	—
82	C₂×C₈	—	52	1	no	—
83	C₂×C₈	—	52	1	no	—
84	C₂×C₈	C₂×#261	1	1	yes	characteristic
85	C₁₆	—	26	2	no	—
86	C₁₃	#1381	1	1	yes	characteristic, complemented, Sylow
87	C₂³	—	13	1	no	—
88	C₂×C₄	—	13	1	no	—
89	C₂×C₄	—	13	1	no	—
90	C₂×C₄	—	13	1	no	—
91	C₂×C₄	—	13	1	no	—
92	C₂×C₄	—	13	1	no	—
93	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
94	C₈	—	4	1	no	—
95	C₈	—	13	1	no	—
96	C₈	—	13	1	no	—
97	C₈	—	52	2	no	—
98	C₈	—	52	1	no	—
99	C₈	C₄×#261	1	1	yes	characteristic
100	C₈	C₄⋊#261	1	1	yes	characteristic
101	C₂²	—	13	1	no	—
102	C₂²	—	13	1	no	—
103	C₂²	—	26	2	no	—
104	C₂²	#88117	1	1	yes	characteristic
105	C₄	—	13	1	no	—
106	C₄	—	13	1	no	—
107	C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
108	C₄	#88115	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	13	2	no	—
111	C₂	—	26	1	no	—
112	C₂	#11718246	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₁₃⋊#108

C₂

yes

maximal, characteristic

C₂×D₁₃⋊C₁₆

C₂

yes

maximal, characteristic

D₁₃×#108

C₂

yes

maximal, characteristic

D₁₃⋊M₁₆

—

M₁₆×D₁₃

—

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₂×#6092

—

#88104

C₄

yes

—

#88103

—

D₁₃⋊C₁₆

—

D₁₃⋊C₁₆

C₄

yes

—

C₁₃×#108

C₄

yes

characteristic

#88062

—

#88059

C₄

yes

characteristic

C₂×C₄×D₁₃

D₄

yes

characteristic

#6122

—

#6118

—

D₁₃⋊C₈

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

#6099

—

C₂×#1055

D₄

yes

characteristic

#6094

—

C₈×D₁₃

—

C₈×D₁₃

C₂×C₄

yes

characteristic

C₈×D₁₃

C₂×C₄

yes

characteristic

C₈×D₁₃

D₄

yes

characteristic

C₈×D₁₃

Q₈

yes

—

—

C₂²×D₁₃

Q₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

SD₁₆

yes

characteristic

C₄×D₁₃

C₂²⋊C₄

yes

characteristic

C₄×D₁₃

C₄⋊C₄

yes

characteristic

C₄×D₁₃

D₈

yes

characteristic

C₄×D₁₃

SD₁₆

yes

characteristic

#1057

—

C₈×C₁₃

—

C₈×C₁₃

C₄²

yes

characteristic

C₈×C₁₃

C₄⋊C₄

yes

characteristic

#1055

—

#1055

C₂²⋊C₄

yes

characteristic

#1055

C₄⋊C₄

yes

characteristic

C₂²×C₁₆

—

C₂×#108

—

C₂×#108

—

C₂²×C₁₃

#103

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

yes

C₂×D₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

yes

Dic₁₃

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

—

—

—

yes

C₂×C₁₃

—

C₂×C₁₃

#340

yes

characteristic

D₁₃

—

D₁₃

#368

yes

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#261

yes

characteristic

C₁₆

—

C₁₃

#1381

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#261

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

C₈

C₄×#261

yes

characteristic

100

C₈

C₄⋊#261

yes

characteristic

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

#88117

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

(C₂×#261)⋊C₄

yes

characteristic

108

C₄

#88115

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

112

C₂

#11718246

yes

characteristic

	subgroup	G/H
center	C₄	#88115
commutator	C₈×C₁₃	C₄²
Frattini	C₂×C₈	C₂×#261
Fitting	C₁₃×#108	C₄
socle	C₂×C₁₃	#340
prime radical	C₂²×D₁₃	Q₁₆
cosocle	C₂×C₈×D₁₃	C₂²
hypercenter	#108	#261
hypocenter	C₁₃	#1381
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

subgroup

G/H

center

C₄

#88115

commutator

C₈×C₁₃

C₄²

Frattini

C₂×C₈

C₂×#261

Fitting

C₁₃×#108

C₄

socle

C₂×C₁₃

#340

prime radical

C₂²×D₁₃

Q₁₆

cosocle

C₂×C₈×D₁₃

C₂²

C₁₃

G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

N	H ≅ G/N	type
86. C₁₃	#1381	semidirect

H ≅ G/N

type

86. C₁₃

#1381

semidirect

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

subgroup	index
D₁₃⋊#108	2
C₂×D₁₃⋊C₁₆	2
D₁₃×#108	2
#1381	13

subgroup

index

D₁₃⋊#108

C₂×D₁₃⋊C₁₆

D₁₃×#108

#1381

Subgroups — #13129895

Conjugacy classes of subgroups

Complements

Maximal subgroups