Group #13117942 — subgroups

Subgroups — #13117942

Order 1664.

448 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 221 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×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
2	#11718642	C₂	1	4	yes	maximal
3	#11718642	C₂	1	4	yes	maximal
4	C₄⋊C₄×Dic₁₃	C₂	1	4	yes	maximal
5	#11718593	C₂	1	2	yes	maximal
6	C₁₃×#125	C₄	1	8	yes	complemented
7	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
11	C₂×C₄×Dic₁₃	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₃	C₂²	1	4	yes	—
13	#88071	C₂²	1	2	yes	—
14	#88071	C₂²	1	2	yes	—
15	#88071	C₂²	1	4	yes	—
16	#88071	C₂²	1	4	yes	—
17	#88071	C₂²	1	4	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
20	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
21	C₂²×Dic₁₃	C₂³	1	4	yes	—
22	C₂²×Dic₁₃	C₂³	1	4	yes	—
23	C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	—
24	C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
25	C₄²×C₁₃	C₂×C₄	1	4	yes	—
26	C₄⋊Dic₁₃	—	2	8	no	—
27	C₄×Dic₁₃	—	2	8	no	—
28	C₄×Dic₁₃	—	2	8	no	—
29	#2371	—	13	1	no	maximal, Sylow
30	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	4	no	—
32	C₂×C₄×C₁₃	—	2	4	no	—
33	C₂×C₄×C₁₃	—	2	4	no	—
34	C₂×C₄×C₁₃	—	2	2	no	—
35	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
36	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₁₃	C₂²×C₄	1	8	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	#41	1	8	yes	—
44	C₂×#125	D₁₃	1	1	yes	characteristic
45	#387	—	13	4	no	—
46	#387	—	13	4	no	—
47	C₄×C₄⋊C₄	—	13	4	no	—
48	#376	—	13	2	no	—
49	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
50	C₂²×C₁₃	C₂×#41	1	4	yes	—
51	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
52	C₄×C₁₃	—	2	4	no	—
53	C₄×C₁₃	—	2	8	no	—
54	C₄×C₁₃	—	2	2	no	—
55	Dic₁₃	—	2	8	no	—
56	Dic₁₃	—	4	4	no	—
57	#125	Dic₁₃	1	8	yes	complemented
58	C₂×C₄⋊C₄	—	13	4	no	—
59	C₂×C₄⋊C₄	C₂×D₁₃	1	4	yes	—
60	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
61	C₂×C₄²	—	13	4	no	—
62	C₂×C₄²	—	13	4	no	—
63	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
64	#95	—	13	2	no	—
65	#95	—	13	4	no	—
66	#95	—	13	2	no	—
67	#95	—	13	4	no	—
68	#95	—	13	4	no	—
69	C₂×C₁₃	C₄×#41	1	2	yes	—
70	C₂×C₁₃	#519	1	1	yes	characteristic
71	C₂×C₁₃	#552	1	4	yes	—
72	C₂²×C₄	—	13	4	no	—
73	C₂²×C₄	—	13	4	no	—
74	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
75	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
76	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
77	C₄⋊C₄	—	26	8	no	—
78	C₄⋊C₄	C₂×Dic₁₃	1	16	yes	—
79	C₄⋊C₄	C₂×Dic₁₃	1	8	yes	—
80	C₄²	—	26	8	no	—
81	C₄²	—	26	8	no	—
82	C₄²	C₂×Dic₁₃	1	4	yes	—
83	C₁₃	#2371	1	1	yes	characteristic, complemented, Sylow
84	C₂³	C₂³×D₁₃	1	1	yes	characteristic
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	13	8	no	—
90	C₂×C₄	—	26	4	no	—
91	C₂×C₄	—	26	4	no	—
92	C₂×C₄	—	26	4	no	—
93	C₂×C₄	—	26	4	no	—
94	C₂×C₄	—	26	4	no	—
95	C₂×C₄	C₂²×Dic₁₃	1	2	yes	—
96	C₂×C₄	C₂²×Dic₁₃	1	4	yes	—
97	C₂×C₄	C₂²×Dic₁₃	1	8	yes	—
98	C₂²	#88254	1	2	yes	—
99	C₂²	#41×D₁₃	1	4	yes	—
100	C₂²	C₂³×Dic₁₃	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	2	4	no	—
103	C₄	—	2	8	no	—
104	C₄	—	26	8	no	—
105	C₄	—	52	4	no	—
106	C₂	#11719398	1	4	yes	—
107	C₂	#11719517	1	1	yes	characteristic
108	C₂	#41×Dic₁₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#125

C₂

yes

maximal, characteristic

#11718642

C₂

yes

maximal

#11718642

C₂

yes

maximal

C₄⋊C₄×Dic₁₃

C₂

yes

maximal

#11718593

C₂

yes

maximal

C₁₃×#125

C₄

yes

complemented

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

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₄²×C₁₃

C₂×C₄

yes

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

#2371

—

maximal, Sylow

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

#41

yes

—

C₂×#125

D₁₃

yes

characteristic

#387

—

#387

—

C₄×C₄⋊C₄

—

#376

—

C₂²×C₁₃

C₂³×C₄

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

2₋¹⁺⁴

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

#125

Dic₁₃

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

—

—

—

—

—

C₂×C₁₃

C₄×#41

yes

—

C₂×C₁₃

#519

yes

characteristic

C₂×C₁₃

#552

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₁₃

yes

—

C₄⋊C₄

C₂×Dic₁₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂×Dic₁₃

yes

—

C₁₃

#2371

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

C₂²×Dic₁₃

yes

—

C₂×C₄

C₂²×Dic₁₃

yes

—

C₂×C₄

C₂²×Dic₁₃

yes

—

C₂²

#88254

yes

—

C₂²

#41×D₁₃

yes

—

100

C₂²

C₂³×Dic₁₃

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₂

#11719398

yes

—

107

C₂

#11719517

yes

characteristic

108

C₂

#41×Dic₁₃

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂³×C₄
Fitting	C₂×C₁₃×#125	C₂
socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
hypercenter	C₂×#125	D₁₃
hypocenter	C₁₃	#2371
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator

C₂²×C₁₃

C₂³×C₄

Fitting

C₂×C₁₃×#125

C₂

socle, prime radical, cosocle

C₂³×C₁₃

C₂⁴

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
6. C₁₃×#125	C₄	semidirect
57. #125	Dic₁₃	semidirect
83. C₁₃	#2371	semidirect

H ≅ G/N

type

6. C₁₃×#125

C₄

semidirect

57. #125

Dic₁₃

semidirect

83. C₁₃

#2371

semidirect

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

subgroup	index
C₂×C₁₃×#125	2
#11718642	2
C₄⋊C₄×Dic₁₃	2
#11718593	2
#2371	13

subgroup

index

C₂×C₁₃×#125

#11718642

C₄⋊C₄×Dic₁₃

#11718593

#2371

Subgroups — #13117942

Conjugacy classes of subgroups

Complements

Maximal subgroups