Group #13123111 — subgroups

Subgroups — #13123111

Order 1664.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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	C₁₃×#382	C₂	1	1	yes	maximal, characteristic
2	#11718645	C₂	1	4	yes	maximal
3	#11718597	C₂	1	2	yes	maximal
4	#11718322	C₂	1	4	yes	maximal
5	#11718318	C₂	1	4	yes	maximal
6	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
11	C₂×#6101	C₂²	1	4	yes	—
12	C₂×#6101	C₂²	1	4	yes	—
13	C₁₃×#95	C₂²	1	4	yes	—
14	#88071	C₂²	1	4	yes	—
15	#88071	C₂²	1	4	yes	—
16	#88071	C₂²	1	4	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
20	C₂²×Dic₁₃	C₂³	1	4	yes	—
21	C₂²×Dic₁₃	C₂³	1	4	yes	—
22	C₁₃×C₄⋊C₄	—	4	2	no	—
23	C₄²×C₁₃	Q₈	1	4	yes	—
24	C₄⋊Dic₁₃	—	4	2	no	—
25	C₄⋊Dic₁₃	—	4	4	no	—
26	C₄⋊Dic₁₃	—	4	2	no	—
27	#6101	—	4	4	no	—
28	#6101	—	4	4	no	—
29	#2845	—	13	1	no	maximal, Sylow
30	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	2	no	—
32	C₂×C₄×C₁₃	—	2	1	no	—
33	C₂×C₄×C₁₃	—	2	1	no	—
34	C₂×C₄×C₁₃	—	2	2	no	—
35	C₂×C₄×C₁₃	—	2	4	no	—
36	C₂×C₄×C₁₃	—	2	4	no	—
37	C₂×C₄×C₁₃	—	2	4	no	—
38	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
39	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
40	C₂×Dic₁₃	—	2	4	no	—
41	C₂×Dic₁₃	—	2	4	no	—
42	C₂×Dic₁₃	—	2	4	no	—
43	C₂×Dic₁₃	—	2	4	no	—
44	C₂×Dic₁₃	—	2	4	no	—
45	C₂×Dic₁₃	—	2	4	no	—
46	#398	—	13	4	no	—
47	#398	—	13	4	no	—
48	#398	—	13	4	no	—
49	#382	—	13	2	no	—
50	#382	D₁₃	1	1	yes	characteristic
51	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
52	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
53	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
54	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
55	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
56	C₄×C₁₃	—	2	2	no	—
57	C₄×C₁₃	—	2	4	no	—
58	C₄×C₁₃	—	4	4	no	—
59	Dic₁₃	—	4	4	no	—
60	Dic₁₃	—	4	4	no	—
61	C₂×C₄⋊C₄	—	13	4	no	—
62	C₂×C₄⋊C₄	—	13	4	no	—
63	C₂×C₄⋊C₄	—	13	2	no	—
64	C₂×C₄⋊C₄	—	13	2	no	—
65	C₂×C₄⋊C₄	—	13	4	no	—
66	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
67	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
68	#95	—	13	4	no	—
69	#95	—	13	4	no	—
70	#95	—	13	4	no	—
71	#95	C₂×D₁₃	1	4	yes	—
72	C₂×C₁₃	#544	1	1	yes	characteristic
73	C₂×C₁₃	#544	1	2	yes	—
74	C₂×C₁₃	#562	1	2	yes	—
75	C₂×C₁₃	#562	1	1	yes	characteristic
76	C₂×C₁₃	#564	1	1	yes	characteristic
77	C₂²×C₄	—	13	4	no	—
78	C₂²×C₄	—	13	4	no	—
79	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
80	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
81	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
82	C₄⋊C₄	—	4	2	no	—
83	C₄⋊C₄	—	52	4	no	—
84	C₄⋊C₄	—	52	4	no	—
85	C₄⋊C₄	—	52	2	no	—
86	C₄⋊C₄	—	52	2	no	—
87	C₄⋊C₄	—	52	4	no	—
88	C₄²	Dic₂₆	1	4	yes	—
89	C₁₃	#2845	1	1	yes	characteristic, complemented, Sylow
90	C₂³	C₂³×D₁₃	1	1	yes	characteristic
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	26	4	no	—
99	C₂×C₄	—	26	4	no	—
100	C₂×C₄	—	26	4	no	—
101	C₂×C₄	—	26	4	no	—
102	C₂×C₄	—	26	4	no	—
103	C₂×C₄	—	26	4	no	—
104	C₂×C₄	C₂×Dic₂₆	1	2	yes	—
105	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
106	C₂²	C₂²×Dic₂₆	1	1	yes	characteristic
107	C₂²	#88251	1	1	yes	characteristic
108	C₂²	#88254	1	1	yes	characteristic
109	C₂²	#88256	1	2	yes	—
110	C₂²	#88257	1	2	yes	—
111	C₄	—	2	2	no	—
112	C₄	—	2	4	no	—
113	C₄	—	4	4	no	—
114	C₄	—	52	4	no	—
115	C₄	—	52	4	no	—
116	C₂	#11719205	1	1	yes	characteristic
117	C₂	#11719224	1	2	yes	—
118	C₂	#11719389	1	2	yes	—
119	C₂	C₁₃⋊#564	1	1	yes	characteristic
120	C₂	#11719405	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#382

C₂

yes

maximal, characteristic

#11718645

C₂

yes

maximal

#11718597

C₂

yes

maximal

#11718322

C₂

yes

maximal

#11718318

C₂

yes

maximal

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

Q₈

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

—

—

—

—

D₁₃

yes

characteristic

C₂²×C₁₃

C₂²×Q₈

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₂²×C₁₃

2₋¹⁺⁴

yes

characteristic

C₂²×C₁₃

2₋¹⁺⁴

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄²

C₂×D₁₃

yes

—

—

—

C₂×D₁₃

yes

—

C₂×C₁₃

#544

yes

characteristic

C₂×C₁₃

#544

yes

—

C₂×C₁₃

#562

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Dic₂₆

yes

—

C₁₃

#2845

yes

characteristic, complemented, Sylow

C₂³

C₂³×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×Dic₂₆

yes

—

105

C₂×C₄

C₂×Dic₂₆

yes

—

106

C₂²

C₂²×Dic₂₆

yes

characteristic

107

C₂²

#88251

yes

characteristic

108

C₂²

#88254

yes

characteristic

109

C₂²

#88256

yes

—

110

C₂²

#88257

yes

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₂

#11719205

yes

characteristic

117

C₂

#11719224

yes

—

118

C₂

#11719389

yes

—

119

C₂

C₁₃⋊#564

yes

characteristic

120

C₂

#11719405

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#382	C₂
hypercenter	#382	D₁₃
hypocenter	C₁₃	#2845
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, prime radical, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₁₃×#382

C₂

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
89. C₁₃	#2845	semidirect

H ≅ G/N

type

89. C₁₃

#2845

semidirect

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

subgroup	index
C₁₃×#382	2
#11718645	2
#11718597	2
#11718322	2
#11718318	2
#2845	13

subgroup

index

C₁₃×#382

Subgroups — #13123111

Conjugacy classes of subgroups

Complements

Maximal subgroups