Group #13120803 — subgroups

Subgroups — #13120803

Order 1664.

352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 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×#401	C₂	1	1	yes	maximal, characteristic
2	C₁₃⋊#401	C₂	1	1	yes	maximal, characteristic
3	#11718321	C₂	1	3	yes	maximal
4	#11718320	C₂	1	3	yes	maximal
5	#11718309	C₂	1	1	yes	maximal, characteristic
6	#11718308	C₂	1	3	yes	maximal
7	#11718307	C₂	1	3	yes	maximal
8	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₃	C₂²	1	3	yes	—
10	C₂×#6101	C₂²	1	3	yes	—
11	C₂×#6101	C₂²	1	3	yes	—
12	C₂×C₄×Dic₁₃	C₂²	1	3	yes	—
13	C₁₃×#95	C₂²	1	3	yes	—
14	C₁₃×#95	C₂²	1	3	yes	—
15	C₁₃×#95	C₂²	1	1	yes	characteristic
16	#88071	C₂²	1	3	yes	—
17	#88071	C₂²	1	3	yes	—
18	#88071	C₂²	1	3	yes	—
19	#88071	C₂²	1	3	yes	—
20	#88071	C₂²	1	3	yes	—
21	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
22	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
24	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₃	C₂³	1	3	yes	—
26	C₂²×Dic₁₃	C₂³	1	3	yes	—
27	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
28	C₂×Dic₂₆	—	2	6	no	—
29	C₄⋊Dic₁₃	—	4	3	no	—
30	#6101	—	2	6	no	—
31	#6101	—	4	3	no	—
32	C₄×Dic₁₃	—	2	6	no	—
33	#2645	—	13	1	no	maximal, Sylow
34	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₁₃	—	2	3	no	—
36	C₂×C₄×C₁₃	—	2	3	no	—
37	C₂×C₄×C₁₃	—	2	3	no	—
38	C₂×C₄×C₁₃	—	2	3	no	—
39	C₂×C₄×C₁₃	—	2	6	no	—
40	C₂×C₄×C₁₃	—	2	3	no	—
41	C₂×Dic₁₃	—	2	3	no	—
42	C₂×Dic₁₃	—	2	3	no	—
43	C₂×Dic₁₃	—	2	3	no	—
44	C₂×Dic₁₃	—	2	3	no	—
45	C₂×Dic₁₃	—	2	3	no	—
46	C₂×Dic₁₃	—	2	3	no	—
47	C₂×Dic₁₃	—	2	3	no	—
48	C₂×Dic₁₃	#41	1	6	yes	—
49	Dic₂₆	—	4	4	no	—
50	#401	—	13	1	no	—
51	#401	D₁₃	1	1	yes	characteristic
52	#400	—	13	3	no	—
53	#400	—	13	3	no	—
54	#391	—	13	3	no	—
55	#389	—	13	3	no	—
56	#376	—	13	1	no	—
57	C₂²×C₁₃	C₂×#41	1	3	yes	—
58	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
59	C₂²×C₁₃	2₋¹⁺⁴	1	3	yes	—
60	C₄×C₁₃	—	4	1	no	—
61	C₄×C₁₃	—	4	3	no	—
62	C₄×C₁₃	—	4	3	no	—
63	Dic₁₃	—	4	1	no	—
64	Dic₁₃	—	4	3	no	—
65	Dic₁₃	—	4	3	no	—
66	Dic₁₃	#126	1	4	yes	—
67	C₂²×Q₈	—	13	1	no	—
68	C₂×C₄⋊C₄	—	13	3	no	—
69	C₂×C₄⋊C₄	—	13	3	no	—
70	C₂×C₄⋊C₄	—	13	3	no	—
71	C₂×C₄²	—	13	3	no	—
72	#95	—	13	3	no	—
73	#95	—	13	3	no	—
74	#95	—	13	3	no	—
75	#95	—	13	3	no	—
76	#95	—	13	3	no	—
77	#95	C₂×D₁₃	1	1	yes	characteristic
78	#95	C₂×D₁₃	1	3	yes	—
79	#95	C₂×D₁₃	1	3	yes	—
80	C₂×C₁₃	C₂×#126	1	1	yes	characteristic
81	C₂×C₁₃	#541	1	3	yes	—
82	C₂×C₁₃	#542	1	3	yes	—
83	C₂×Q₈	—	26	6	no	—
84	C₂²×C₄	—	13	1	no	—
85	C₂²×C₄	—	13	1	no	—
86	C₂²×C₄	—	13	3	no	—
87	C₂²×C₄	—	13	3	no	—
88	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
89	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
90	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
91	C₄⋊C₄	—	26	6	no	—
92	C₄⋊C₄	—	52	3	no	—
93	C₄⋊C₄	—	52	3	no	—
94	C₄²	—	26	6	no	—
95	C₁₃	#2645	1	1	yes	characteristic, complemented, Sylow
96	C₂³	C₂³×D₁₃	1	1	yes	characteristic
97	Q₈	—	52	4	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	2	6	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	13	6	no	—
105	C₂×C₄	—	26	3	no	—
106	C₂×C₄	—	26	3	no	—
107	C₂×C₄	—	26	3	no	—
108	C₂×C₄	—	26	3	no	—
109	C₂×C₄	—	26	3	no	—
110	C₂×C₄	—	26	3	no	—
111	C₂×C₄	—	26	3	no	—
112	C₂²	#41×D₁₃	1	3	yes	—
113	C₂²	#88256	1	1	yes	characteristic
114	C₂²	#88257	1	3	yes	—
115	C₄	—	4	3	no	—
116	C₄	—	4	1	no	—
117	C₄	—	4	3	no	—
118	C₄	—	13	4	no	—
119	C₄	—	52	1	no	—
120	C₄	—	52	3	no	—
121	C₄	—	52	3	no	—
122	C₂	#11719406	1	3	yes	—
123	C₂	D₁₃×#126	1	1	yes	characteristic
124	C₂	#11719415	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#401

C₂

yes

maximal, characteristic

C₁₃⋊#401

C₂

yes

maximal, characteristic

#11718321

C₂

yes

maximal

#11718320

C₂

yes

maximal

#11718309

C₂

yes

maximal, characteristic

#11718308

C₂

yes

maximal

#11718307

C₂

yes

maximal

C₂²×Dic₂₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

C₁₃×#95

C₂²

yes

characteristic

#88071

C₂²

yes

—

#88071

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

characteristic

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

characteristic

C₂×Dic₂₆

—

C₄⋊Dic₁₃

—

#6101

—

#6101

—

C₄×Dic₁₃

—

#2645

—

maximal, Sylow

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

#41

yes

—

Dic₂₆

—

#401

—

#401

D₁₃

yes

—

—

—

—

—

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₃

2₋¹⁺⁴

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

#126

yes

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

—

—

—

C₂×D₁₃

yes

characteristic

#95

C₂×D₁₃

yes

—

#95

C₂×D₁₃

yes

—

C₂×C₁₃

C₂×#126

yes

characteristic

C₂×C₁₃

#541

yes

—

C₂×C₁₃

#542

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

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

—

C₄²

—

C₁₃

#2645

yes

characteristic, complemented, Sylow

C₂³

C₂³×D₁₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂²

#41×D₁₃

yes

—

113

C₂²

#88256

yes

characteristic

114

C₂²

#88257

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₂

#11719406

yes

—

123

C₂

D₁₃×#126

yes

characteristic

124

C₂

#11719415

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#401	C₂
hypercenter	#401	D₁₃
hypocenter	C₁₃	#2645
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #401

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, prime radical, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₁₃×#401

C₂

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #401

N	H ≅ G/N	type
95. C₁₃	#2645	semidirect

H ≅ G/N

type

95. C₁₃

#2645

semidirect

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

subgroup	index
C₁₃×#401	2
C₁₃⋊#401	2
#11718321	2
#11718320	2
#11718309	2
#11718308	2
#11718307	2
#2645	13

subgroup

index

C₁₃×#401

C₁₃⋊#401

Subgroups — #13120803

Conjugacy classes of subgroups

Complements

Maximal subgroups