Group #13131046 — subgroups

Subgroups — #13131046

Order 1664.

184 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 102 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×#88098	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#11718369	C₂	1	1	yes	maximal, characteristic
4	#11718258	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718257	C₂	1	1	yes	maximal, characteristic, complemented
6	#11718231	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#6092	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#6094	C₄	1	1	yes	characteristic
9	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	#88126	C₄	1	1	yes	characteristic
11	C₂×#6092	C₂²	1	1	yes	characteristic
12	C₂×#6092	C₂²	1	1	yes	characteristic
13	C₂×#6092	C₂²	1	1	yes	characteristic
14	C₂×#6092	C₂²	1	1	yes	characteristic
15	#88098	C₄	1	4	yes	complemented
16	D₁₃⋊C₁₆	C₄	1	4	yes	complemented
17	C₁₃×#97	C₄	1	1	yes	characteristic
18	#88055	C₄	1	1	yes	characteristic
19	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
20	C₄×#1055	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	#6103	C₈	1	2	yes	—
26	#6101	C₈	1	2	yes	—
27	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×#1055	C₂×C₄	1	1	yes	characteristic
29	C₂×#1055	C₂³	1	1	yes	characteristic
30	#6094	C₈	1	4	yes	—
31	C₈×D₁₃	C₂×C₄	1	2	yes	—
32	C₈×D₁₃	C₂×C₄	1	2	yes	—
33	#6092	C₂×C₄	1	2	yes	—
34	#6092	C₂×C₄	1	2	yes	—
35	#6092	C₂×C₄	1	2	yes	—
36	#6092	C₂×C₄	1	2	yes	—
37	#2108	—	13	1	no	maximal, Sylow
38	C₂²×D₁₃	C₂×C₈	1	1	yes	characteristic
39	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
40	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₁₃	C₂×C₈	1	2	yes	—
42	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
43	C₄×D₁₃	C₄²	1	2	yes	—
44	C₄×D₁₃	C₂×C₈	1	2	yes	—
45	C₈×C₁₃	C₄²	1	2	yes	—
46	C₈×C₁₃	C₂×C₈	1	2	yes	—
47	#1055	C₂×C₈	1	2	yes	—
48	#1055	C₂²×C₄	1	1	yes	characteristic
49	#1055	C₂²×C₄	1	1	yes	characteristic
50	C₂×M₃₂	—	13	1	no	—
51	C₂²×C₁₆	—	13	1	no	—
52	#405	—	13	1	no	—
53	#346	—	13	1	no	—
54	#346	—	13	1	no	—
55	C₄×C₁₆	—	13	1	no	—
56	C₄×C₁₆	—	13	1	no	—
57	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
58	C₂×D₁₃	—	2	2	no	—
59	C₂×D₁₃	C₄×C₈	1	2	yes	—
60	C₄×C₁₃	—	2	2	no	—
61	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
62	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
63	Dic₁₃	—	2	2	no	—
64	Dic₁₃	C₄×C₈	1	2	yes	—
65	C₂×M₁₆	—	13	1	no	—
66	C₂²×C₈	—	13	1	no	—
67	#117	—	13	1	no	—
68	M₃₂	—	13	4	no	—
69	C₂×C₁₆	—	13	4	no	—
70	C₂×C₁₆	—	13	1	no	—
71	C₂×C₁₆	—	13	1	no	—
72	C₂×C₁₆	—	13	1	no	—
73	C₂×C₁₆	—	13	1	no	—
74	#97	—	13	1	no	—
75	#97	#261	1	1	yes	characteristic
76	C₄×C₈	—	13	1	no	—
77	C₄×C₈	—	13	1	no	—
78	C₂×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
79	C₂×C₁₃	#504	1	2	yes	—
80	D₁₃	—	2	2	no	—
81	C₂²×C₄	—	13	1	no	—
82	M₁₆	—	13	4	no	—
83	C₂×C₈	—	13	1	no	—
84	C₂×C₈	—	13	1	no	—
85	C₂×C₈	—	13	2	no	—
86	C₂×C₈	—	13	2	no	—
87	C₂×C₈	C₂×#261	1	1	yes	characteristic
88	C₂×C₈	C₂×#261	1	1	yes	characteristic
89	C₄⋊C₄	—	13	2	no	—
90	C₂²⋊C₄	—	13	2	no	—
91	C₄²	—	13	1	no	—
92	C₄²	C₂×#261	1	1	yes	characteristic
93	C₁₆	—	13	2	no	—
94	C₁₆	—	13	2	no	—
95	C₁₆	—	13	2	no	—
96	C₁₆	—	13	2	no	—
97	C₁₃	#2108	1	1	yes	characteristic, complemented, Sylow
98	C₂³	—	13	1	no	—
99	C₂×C₄	—	13	1	no	—
100	C₂×C₄	—	13	2	no	—
101	C₂×C₄	—	13	2	no	—
102	C₂×C₄	—	13	2	no	—
103	C₂×C₄	D₁₃⋊C₈	1	2	yes	—
104	C₂×C₄	C₂²×#261	1	1	yes	characteristic
105	C₈	—	13	2	no	—
106	C₈	—	13	1	no	—
107	C₈	—	13	1	no	—
108	C₈	D₁₃⋊C₈	1	2	yes	—
109	C₈	C₄×#261	1	2	yes	—
110	C₂²	—	13	2	no	—
111	C₂²	—	26	2	no	—
112	C₂²	C₂×D₁₃⋊C₈	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	13	2	no	—
115	C₄	—	26	2	no	—
116	C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
117	C₄	C₂×C₄×#261	1	1	yes	characteristic
118	C₂	—	26	2	no	—
119	C₂	C₄×D₁₃⋊C₈	1	1	yes	characteristic
120	C₂	#11719096	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88098

C₂

yes

maximal, characteristic

C₂×D₁₃⋊C₁₆

C₂

yes

maximal, characteristic

#11718369

C₂

yes

maximal, characteristic

#11718258

C₂

yes

maximal, characteristic, complemented

#11718257

C₂

yes

maximal, characteristic, complemented

#11718231

C₂

yes

maximal, characteristic, complemented

C₄×#6092

C₂

yes

maximal, characteristic, complemented

C₂×#6094

C₄

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

#88126

C₄

yes

characteristic

C₂×#6092

C₂²

yes

characteristic

C₂×#6092

C₂²

yes

characteristic

C₂×#6092

C₂²

yes

characteristic

C₂×#6092

C₂²

yes

characteristic

#88098

C₄

yes

complemented

D₁₃⋊C₁₆

C₄

yes

complemented

C₁₃×#97

C₄

yes

characteristic

#88055

C₄

yes

characteristic

C₈×Dic₁₃

C₂²

yes

characteristic

C₄×#1055

C₂²

yes

characteristic

C₂×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₄

yes

characteristic

#6103

C₈

yes

—

#6101

C₈

yes

—

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂×#1055

C₂×C₄

yes

characteristic

C₂×#1055

C₂³

yes

characteristic

#6094

C₈

yes

—

C₈×D₁₃

C₂×C₄

yes

—

C₈×D₁₃

C₂×C₄

yes

—

#6092

C₂×C₄

yes

—

#6092

C₂×C₄

yes

—

#6092

C₂×C₄

yes

—

#6092

C₂×C₄

yes

—

#2108

—

maximal, Sylow

C₂²×D₁₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

—

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₄×D₁₃

C₄²

yes

—

C₄×D₁₃

C₂×C₈

yes

—

C₈×C₁₃

C₄²

yes

—

C₈×C₁₃

C₂×C₈

yes

—

#1055

C₂×C₈

yes

—

#1055

C₂²×C₄

yes

characteristic

#1055

C₂²×C₄

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₄×C₈

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄²

yes

characteristic

C₄×C₁₃

C₂²×C₈

yes

characteristic

Dic₁₃

—

Dic₁₃

C₄×C₈

yes

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂×C₁₃

#504

yes

—

D₁₃

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₃

#2108

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

D₁₃⋊C₈

yes

—

104

C₂×C₄

C₂²×#261

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

D₁₃⋊C₈

yes

—

109

C₈

C₄×#261

yes

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂×D₁₃⋊C₈

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

C₂×D₁₃⋊C₈

yes

characteristic

117

C₄

C₂×C₄×#261

yes

characteristic

118

C₂

—

119

C₂

C₄×D₁₃⋊C₈

yes

characteristic

120

C₂

#11719096

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂×C₄×C₈
Fitting	C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂²×C₈
prime radical	C₂²×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂³
hypercenter	#97	#261
hypocenter	C₁₃	#2108
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#261

commutator

C₂×C₁₃

C₂×C₄×C₈

Fitting

C₁₃×#97

C₄

socle

C₂²×C₁₃

C₂²×C₈

prime radical

C₂²×D₁₃

C₂×C₈

C₂³

C₁₃

G ▷ C₂×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
4. #11718258	C₂	semidirect
5. #11718257	C₂	semidirect
6. #11718231	C₂	semidirect
7. C₄×#6092	C₂	semidirect
15. #88098	C₄	semidirect
16. D₁₃⋊C₁₆	C₄	semidirect
97. C₁₃	#2108	semidirect

H ≅ G/N

type

4. #11718258

C₂

semidirect

5. #11718257

C₂

semidirect

6. #11718231

C₂

semidirect

7. C₄×#6092

C₂

semidirect

15. #88098

C₄

semidirect

16. D₁₃⋊C₁₆

C₄

semidirect

97. C₁₃

#2108

semidirect

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

subgroup	index
C₂×#88098	2
C₂×D₁₃⋊C₁₆	2
#11718369	2
#11718258	2
#11718257	2
#11718231	2
C₄×#6092	2
#2108	13

subgroup

index

C₂×D₁₃⋊C₁₆

Subgroups — #13131046

Conjugacy classes of subgroups

Complements

Maximal subgroups