Group #13120078 — subgroups

Subgroups — #13120078

Order 1664.

380 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 165 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×#384	C₂	1	1	yes	maximal, characteristic
2	#11718647	C₂	1	4	yes	maximal
3	#11718646	C₂	1	4	yes	maximal
4	#11718638	C₂	1	4	yes	maximal
5	C₄×C₄⋊Dic₁₃	C₂	1	2	yes	maximal
6	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
7	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₃	C₂²	1	4	yes	—
13	#88071	C₂²	1	4	yes	—
14	#88071	C₂²	1	4	yes	—
15	#88071	C₂²	1	8	yes	—
16	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
19	C₂²×Dic₁₃	C₂³	1	4	yes	—
20	C₂²×Dic₁₃	C₂³	1	4	yes	—
21	C₁₃×C₄⋊C₄	—	2	8	no	—
22	C₁₃×C₄⋊C₄	—	4	2	no	—
23	C₄²×C₁₃	Q₈	1	4	yes	—
24	C₄⋊Dic₁₃	—	2	4	no	—
25	C₄⋊Dic₁₃	—	2	4	no	—
26	C₄⋊Dic₁₃	—	4	4	no	—
27	C₄×Dic₁₃	—	2	8	no	—
28	#2571	—	13	1	no	maximal, Sylow
29	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₁₃	—	2	1	no	—
31	C₂×C₄×C₁₃	—	2	1	no	—
32	C₂×C₄×C₁₃	—	2	8	no	—
33	C₂×C₄×C₁₃	—	2	4	no	—
34	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
36	C₂×C₄×C₁₃	#41	1	4	yes	—
37	C₂×C₄×C₁₃	#41	1	4	yes	—
38	C₂×Dic₁₃	—	2	4	no	—
39	C₂×Dic₁₃	—	2	4	no	—
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	#400	—	13	4	no	—
45	#389	—	13	4	no	—
46	#384	D₁₃	1	1	yes	characteristic
47	#382	—	13	4	no	—
48	C₄×C₄⋊C₄	—	13	2	no	—
49	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
50	C₂²×C₁₃	C₂×#41	1	2	yes	—
51	C₂²×C₁₃	C₂×#41	1	2	yes	—
52	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
53	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
54	C₄×C₁₃	—	2	2	no	—
55	C₄×C₁₃	—	4	4	no	—
56	C₄×C₁₃	#125	1	8	yes	—
57	Dic₁₃	—	4	4	no	—
58	Dic₁₃	—	4	4	no	—
59	C₂×C₄⋊C₄	—	13	2	no	—
60	C₂×C₄⋊C₄	—	13	2	no	—
61	C₂×C₄⋊C₄	—	13	4	no	—
62	C₂×C₄⋊C₄	C₂×D₁₃	1	4	yes	—
63	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
64	C₂×C₄²	—	13	4	no	—
65	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
66	#95	—	13	4	no	—
67	#95	—	13	4	no	—
68	#95	—	13	8	no	—
69	C₂×C₁₃	C₂×#125	1	2	yes	—
70	C₂×C₁₃	#544	1	1	yes	characteristic
71	C₂×C₁₃	#555	1	1	yes	characteristic
72	C₂×C₁₃	#556	1	2	yes	—
73	C₂×C₁₃	#559	1	1	yes	characteristic
74	C₂²×C₄	—	13	4	no	—
75	C₂²×C₄	—	13	4	no	—
76	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
77	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
78	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
79	C₄⋊C₄	—	2	8	no	—
80	C₄⋊C₄	—	4	2	no	—
81	C₄⋊C₄	—	26	4	no	—
82	C₄⋊C₄	—	26	4	no	—
83	C₄⋊C₄	—	52	4	no	—
84	C₄²	—	26	8	no	—
85	C₄²	Dic₂₆	1	4	yes	—
86	C₁₃	#2571	1	1	yes	characteristic, complemented, Sylow
87	C₂³	C₂³×D₁₃	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	26	4	no	—
93	C₂×C₄	—	26	4	no	—
94	C₂×C₄	—	26	4	no	—
95	C₂×C₄	—	26	4	no	—
96	C₂×C₄	—	26	4	no	—
97	C₂×C₄	—	26	4	no	—
98	C₂×C₄	C₂×Dic₂₆	1	2	yes	—
99	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
100	C₂×C₄	#6129	1	4	yes	—
101	C₂×C₄	#6131	1	4	yes	—
102	C₂²	C₂²×Dic₂₆	1	1	yes	characteristic
103	C₂²	C₂×#6129	1	2	yes	—
104	C₂²	#88251	1	1	yes	characteristic
105	C₂²	C₂×#6131	1	2	yes	—
106	C₂²	#88254	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	—	4	4	no	—
109	C₄	—	52	4	no	—
110	C₄	—	52	4	no	—
111	C₄	#88144	1	8	yes	—
112	C₂	C₂×#88144	1	2	yes	—
113	C₂	#11719205	1	1	yes	characteristic
114	C₂	#11719418	1	1	yes	characteristic
115	C₂	#11719437	1	2	yes	—
116	C₂	#11719439	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#384

C₂

yes

maximal, characteristic

#11718647

C₂

yes

maximal

#11718646

C₂

yes

maximal

#11718638

C₂

yes

maximal

C₄×C₄⋊Dic₁₃

C₂

yes

maximal

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

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×C₄×Dic₁₃

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

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

Q₈

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

#2571

—

maximal, Sylow

C₂³×C₁₃

C₂⁴

yes

characteristic

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×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

#400

—

#389

—

#384

D₁₃

yes

characteristic

#382

—

C₄×C₄⋊C₄

—

C₂²×C₁₃

C₂²×Q₈

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₃

2₋¹⁺⁴

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#125

yes

—

Dic₁₃

—

Dic₁₃

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

—

—

—

C₂×C₁₃

C₂×#125

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×C₁₃

#559

yes

characteristic

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

—

C₄²

—

C₄²

Dic₂₆

yes

—

C₁₃

#2571

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

—

C₂×C₄

—

C₂×C₄

C₂×Dic₂₆

yes

—

C₂×C₄

C₂×Dic₂₆

yes

—

100

C₂×C₄

#6129

yes

—

101

C₂×C₄

#6131

yes

—

102

C₂²

C₂²×Dic₂₆

yes

characteristic

103

C₂²

C₂×#6129

yes

—

104

C₂²

#88251

yes

characteristic

105

C₂²

C₂×#6131

yes

—

106

C₂²

#88254

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#88144

yes

—

112

C₂

C₂×#88144

yes

—

113

C₂

#11719205

yes

characteristic

114

C₂

#11719418

yes

characteristic

115

C₂

#11719437

yes

—

116

C₂

#11719439

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#384	C₂
hypercenter	#384	D₁₃
hypocenter	C₁₃	#2571
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, prime radical, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₁₃×#384

C₂

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
86. C₁₃	#2571	semidirect

H ≅ G/N

type

86. C₁₃

#2571

semidirect

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

subgroup	index
C₁₃×#384	2
#11718647	2
#11718646	2
#11718638	2
C₄×C₄⋊Dic₁₃	2
#2571	13

subgroup

index

C₁₃×#384

C₄×C₄⋊Dic₁₃

Subgroups — #13120078

Conjugacy classes of subgroups

Complements

Maximal subgroups