Group #13129909 — subgroups

Subgroups — #13129909

Order 1664.

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

normal subgroups only

This group has 140 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	#11719092	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#106	C₂	1	1	yes	maximal, characteristic
4	#88237	—	2	1	no	—
5	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
6	C₄⋊C₄×D₁₃	—	2	1	no	—
7	#88106	—	2	1	no	—
8	#88102	C₄	1	2	yes	complemented
9	#88101	—	2	1	no	—
10	#88098	C₄	1	2	yes	complemented
11	D₁₃⋊C₁₆	—	2	1	no	—
12	C₁₃×#106	C₄	1	1	yes	characteristic, complemented
13	#88057	C₄	1	1	yes	characteristic, complemented
14	#88048	—	2	1	no	—
15	C₂×C₄×D₁₃	—	4	1	no	—
16	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
17	C₂²⋊#261	—	4	1	no	—
18	C₄⋊#261	—	2	2	no	—
19	C₄×#261	—	4	1	no	—
20	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₁₃×C₄⋊C₄	—	2	1	no	—
22	C₄⋊Dic₁₃	—	2	1	no	—
23	#6101	—	4	1	no	—
24	C₂×#1055	D₄	1	1	yes	characteristic
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	#1386	—	13	1	no	maximal, Sylow
31	C₂²×D₁₃	D₈	1	1	yes	characteristic
32	C₂×#261	—	4	2	no	—
33	C₂×C₄×C₁₃	—	4	1	no	—
34	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₁₃	—	4	1	no	—
36	C₂×Dic₁₃	SD₁₆	1	1	yes	characteristic
37	C₄×D₁₃	—	8	2	no	—
38	C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₁₃	SD₁₆	1	1	yes	characteristic
41	C₄×D₁₃	Q₁₆	1	1	yes	characteristic
42	C₈×C₁₃	C₄²	1	1	yes	characteristic
43	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
44	#1055	C₂²⋊C₄	1	1	yes	characteristic
45	#1055	C₄⋊C₄	1	1	yes	characteristic
46	C₂×M₃₂	—	13	1	no	—
47	#427	—	13	1	no	—
48	C₂×#106	—	13	1	no	—
49	C₂²×C₁₃	#102	1	1	yes	characteristic
50	C₂×D₁₃	—	2	2	no	—
51	C₂×D₁₃	#102	1	1	yes	characteristic
52	C₂×D₁₃	#107	1	1	yes	characteristic
53	#261	—	8	2	no	—
54	C₄×C₁₃	—	8	1	no	—
55	C₄×C₁₃	#95	1	1	yes	characteristic
56	C₄×C₁₃	#103	1	1	yes	characteristic
57	Dic₁₃	—	8	1	no	—
58	Dic₁₃	#103	1	1	yes	characteristic
59	Dic₁₃	#106	1	1	yes	characteristic
60	C₂²×C₈	—	13	1	no	—
61	#117	—	26	1	no	—
62	C₂×C₄⋊C₄	—	26	1	no	—
63	M₃₂	—	13	2	no	—
64	M₃₂	—	26	1	no	—
65	C₂×C₁₆	—	26	1	no	—
66	#107	—	13	2	no	—
67	#106	—	13	1	no	—
68	#106	—	26	1	no	—
69	#106	—	26	1	no	—
70	#106	#261	1	1	yes	characteristic, complemented
71	C₂×C₁₃	—	2	1	no	—
72	C₂×C₁₃	#340	1	1	yes	characteristic
73	D₁₃	—	2	1	no	—
74	D₁₃	#360	1	2	yes	—
75	C₂²×C₄	—	13	1	no	—
76	C₂²×C₄	—	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	C₂×#261	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	26	2	no	—
85	C₄⋊C₄	—	26	1	no	—
86	C₄⋊C₄	—	52	1	no	—
87	C₂²⋊C₄	—	52	1	no	—
88	C₄²	—	52	1	no	—
89	C₁₆	—	26	2	no	—
90	C₁₃	#1386	1	1	yes	characteristic, complemented, Sylow
91	C₂³	—	13	1	no	—
92	C₂×C₄	—	4	1	no	—
93	C₂×C₄	—	13	1	no	—
94	C₂×C₄	—	13	1	no	—
95	C₂×C₄	—	13	1	no	—
96	C₂×C₄	—	13	1	no	—
97	C₂×C₄	—	13	1	no	—
98	C₂×C₄	—	52	2	no	—
99	C₂×C₄	—	52	1	no	—
100	C₂×C₄	—	104	2	no	—
101	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
102	C₈	—	13	1	no	—
103	C₈	—	13	1	no	—
104	C₈	C₄×#261	1	1	yes	characteristic
105	C₈	C₄⋊#261	1	1	yes	characteristic
106	C₂²	—	13	1	no	—
107	C₂²	—	13	1	no	—
108	C₂²	—	26	2	no	—
109	C₂²	#88115	1	1	yes	characteristic
110	C₄	—	8	1	no	—
111	C₄	—	13	1	no	—
112	C₄	—	13	1	no	—
113	C₄	—	104	1	no	—
114	C₄	—	104	2	no	—
115	C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
116	C₄	#88117	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	13	2	no	—
119	C₂	—	26	1	no	—
120	C₂	#11718246	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11719092

C₂

yes

maximal, characteristic

D₁₃⋊M₃₂

C₂

yes

maximal, characteristic

D₁₃×#106

C₂

yes

maximal, characteristic

#88237

—

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₄⋊C₄×D₁₃

—

#88106

—

#88102

C₄

yes

complemented

#88101

—

#88098

C₄

yes

complemented

D₁₃⋊C₁₆

—

C₁₃×#106

C₄

yes

characteristic, complemented

#88057

C₄

yes

characteristic, complemented

#88048

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

D₄

yes

characteristic

C₂²⋊#261

—

C₄⋊#261

—

C₄×#261

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₁₃×C₄⋊C₄

—

C₄⋊Dic₁₃

—

#6101

—

C₂×#1055

D₄

yes

characteristic

C₈×D₁₃

C₂×C₄

yes

characteristic

C₈×D₁₃

C₂×C₄

yes

characteristic

C₈×D₁₃

D₄

yes

characteristic

C₈×D₁₃

Q₈

yes

—

—

C₂²×D₁₃

D₈

yes

characteristic

C₂×#261

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

SD₁₆

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

C₂²⋊C₄

yes

characteristic

C₄×D₁₃

C₄⋊C₄

yes

characteristic

C₄×D₁₃

SD₁₆

yes

characteristic

C₄×D₁₃

Q₁₆

yes

characteristic

C₈×C₁₃

C₄²

yes

characteristic

C₈×C₁₃

C₄⋊C₄

yes

characteristic

#1055

C₂²⋊C₄

yes

characteristic

#1055

C₄⋊C₄

yes

characteristic

C₂×M₃₂

—

#427

—

C₂×#106

—

C₂²×C₁₃

#102

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

yes

C₂×D₁₃

yes

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

yes

Dic₁₃

yes

C₂²×C₈

—

#117

—

C₂×C₄⋊C₄

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

—

—

—

yes

characteristic, complemented

C₂×C₁₃

—

C₂×C₁₃

#340

yes

characteristic

D₁₃

—

D₁₃

#360

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#261

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₃

#1386

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

104

—

101

C₂×C₄

C₂²⋊#261

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

C₄×#261

yes

characteristic

105

C₈

C₄⋊#261

yes

characteristic

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

#88115

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

104

—

114

C₄

—

104

—

115

C₄

(C₂×#261)⋊C₄

yes

characteristic

116

C₄

#88117

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#11718246

yes

characteristic

	subgroup	G/H
center	C₂	#11718246
commutator	C₈×C₁₃	C₄²
Frattini	C₂×C₈	C₂×#261
Fitting	C₁₃×#106	C₄
socle	C₂×C₁₃	#340
prime radical	C₂²×D₁₃	D₈
cosocle	C₂×C₈×D₁₃	C₂²
hypercenter	#106	#261
hypocenter	C₁₃	#1386
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

subgroup

G/H

center

C₂

#11718246

commutator

C₈×C₁₃

C₄²

Frattini

C₂×C₈

C₂×#261

Fitting

C₁₃×#106

C₄

socle

C₂×C₁₃

#340

prime radical

C₂²×D₁₃

D₈

cosocle

C₂×C₈×D₁₃

C₂²

C₁₃

G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

N	H ≅ G/N	type
8. #88102	C₄	semidirect
10. #88098	C₄	semidirect
12. C₁₃×#106	C₄	semidirect
13. #88057	C₄	semidirect
70. #106	#261	semidirect
90. C₁₃	#1386	semidirect

H ≅ G/N

type

8. #88102

C₄

semidirect

10. #88098

C₄

semidirect

12. C₁₃×#106

C₄

semidirect

13. #88057

C₄

semidirect

70. #106

#261

semidirect

90. C₁₃

#1386

semidirect

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

subgroup	index
#11719092	2
D₁₃⋊M₃₂	2
D₁₃×#106	2
#1386	13

subgroup

index

#11719092

D₁₃⋊M₃₂

D₁₃×#106

#1386

Subgroups — #13129909

Conjugacy classes of subgroups

Complements

Maximal subgroups