Group #13114162 — subgroups

Subgroups — #13114162

Order 1664.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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⋊#564	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#491	C₂	1	1	yes	maximal, characteristic
3	#11718741	C₂	1	2	yes	maximal
4	#11718135	C₂	1	1	yes	maximal, characteristic
5	#11718057	C₂	1	2	yes	maximal
6	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₁₃×#125	C₂²	1	1	yes	characteristic
8	#88144	—	2	2	no	—
9	#88143	—	2	2	no	—
10	#88143	—	2	2	no	—
11	#88124	C₂²	1	2	yes	—
12	C₁₃×#103	—	2	2	no	—
13	C₁₃×#97	C₂²	1	1	yes	characteristic
14	#88048	—	2	2	no	—
15	#88047	—	2	2	no	—
16	#88043	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₃	—	2	1	no	—
18	C₂×C₈×C₁₃	—	2	1	no	—
19	C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₁₃×C₄⋊C₄	—	2	2	no	—
21	C₁₃×C₄⋊C₄	D₄	1	2	yes	—
22	C₄²×C₁₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₁₃	—	2	2	no	—
24	C₄⋊Dic₁₃	D₄	1	2	yes	—
25	C₄⋊Dic₁₃	D₄	1	2	yes	—
26	#6101	—	2	2	no	—
27	#6101	—	2	2	no	—
28	#6101	—	2	2	no	—
29	#6101	—	2	2	no	—
30	C₄×Dic₁₃	—	2	2	no	—
31	C₂×#1055	—	2	2	no	—
32	#1663	—	13	1	no	maximal, Sylow
33	Q₈×C₁₃	—	4	2	no	—
34	C₂×C₄×C₁₃	—	2	2	no	—
35	C₂×C₄×C₁₃	—	4	1	no	—
36	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₁₃	—	2	2	no	—
39	C₂×Dic₁₃	—	2	2	no	—
40	C₈×C₁₃	—	4	1	no	—
41	#1055	—	2	4	no	—
42	#564	—	13	1	no	—
43	#501	—	13	2	no	—
44	#491	D₁₃	1	1	yes	characteristic
45	#330	—	13	1	no	—
46	#330	—	13	2	no	—
47	C₂²×C₁₃	#120	1	1	yes	characteristic
48	C₄×C₁₃	—	2	1	no	—
49	C₄×C₁₃	—	2	2	no	—
50	C₄×C₁₃	—	4	2	no	—
51	C₄×C₁₃	—	8	1	no	—
52	Dic₁₃	—	4	2	no	—
53	Dic₁₃	—	4	2	no	—
54	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
55	#125	—	13	2	no	—
56	#125	—	26	2	no	—
57	#125	—	26	2	no	—
58	#125	—	26	2	no	—
59	#125	C₂×D₁₃	1	1	yes	characteristic
60	#107	—	26	2	no	—
61	#106	—	26	2	no	—
62	#103	—	2	2	no	—
63	#97	—	13	2	no	—
64	#97	C₂×D₁₃	1	1	yes	characteristic
65	C₂×C₁₃	#454	1	1	yes	characteristic
66	C₂×C₁₃	#456	1	2	yes	—
67	C₂×Q₈	—	2	1	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	26	2	no	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	13	2	no	—
73	C₄⋊C₄	—	13	2	no	—
74	C₄⋊C₄	—	26	2	no	—
75	C₄⋊C₄	—	26	2	no	—
76	C₄⋊C₄	—	26	2	no	—
77	C₄⋊C₄	—	26	2	no	—
78	C₄⋊C₄	—	26	2	no	—
79	C₄⋊C₄	C₂²⋊D₁₃	1	2	yes	—
80	C₄²	—	26	2	no	—
81	C₄²	C₂²×D₁₃	1	1	yes	characteristic
82	C₁₃	#1663	1	1	yes	characteristic, complemented, Sylow
83	Q₈	—	4	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	26	2	no	—
87	C₂×C₄	—	26	2	no	—
88	C₂×C₄	D₄×D₁₃	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
90	C₈	—	4	1	no	—
91	C₈	—	26	4	no	—
92	C₂²	#88191	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	8	1	no	—
97	C₄	—	52	2	no	—
98	C₄	—	52	2	no	—
99	C₂	#11718723	1	1	yes	characteristic
100	C₂	#11718866	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃⋊#564

C₂

yes

maximal, characteristic

C₁₃×#491

C₂

yes

maximal, characteristic

#11718741

C₂

yes

maximal

#11718135

C₂

yes

maximal, characteristic

#11718057

C₂

yes

maximal

C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₁₃×#125

C₂²

yes

—

—

—

C₂²

yes

—

C₁₃×#103

—

C₁₃×#97

C₂²

yes

—

—

C₂²

yes

—

C₂×Q₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

D₄

yes

—

C₄²×C₁₃

C₂³

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

D₄

yes

—

C₄⋊Dic₁₃

D₄

yes

—

—

—

—

—

C₄×Dic₁₃

—

C₂×#1055

—

#1663

—

maximal, Sylow

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

—

—

—

D₁₃

yes

characteristic

#330

—

#330

—

C₂²×C₁₃

#120

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

C₄⋊Q₈

C₂×D₁₃

yes

—

—

—

—

C₂×D₁₃

yes

—

—

—

—

C₂×D₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₁₃

yes

—

C₄²

—

C₄²

C₂²×D₁₃

yes

characteristic

C₁₃

#1663

yes

characteristic, complemented, Sylow

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₃

yes

—

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

C₈

—

C₈

—

C₂²

#88191

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

#11718723

yes

characteristic

100

C₂

#11718866

yes

—

	subgroup	G/H
center	C₂²	#88191
commutator, cosocle	C₄²×C₁₃	C₂³
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#491	C₂
socle, prime radical	C₂²×C₁₃	#120
hypercenter	#491	D₁₃
hypocenter	C₁₃	#1663
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #491

subgroup

G/H

center

C₂²

#88191

commutator, cosocle

C₄²×C₁₃

C₂³

Frattini

C₄²

C₂²×D₁₃

Fitting

C₁₃×#491

C₂

C₂²×C₁₃

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #491

N	H ≅ G/N	type
82. C₁₃	#1663	semidirect

H ≅ G/N

type

82. C₁₃

#1663

semidirect

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

subgroup	index
C₁₃⋊#564	2
C₁₃×#491	2
#11718741	2
#11718135	2
#11718057	2
#1663	13

subgroup

index

C₁₃⋊#564

C₁₃×#491

Subgroups — #13114162

Conjugacy classes of subgroups

Complements

Maximal subgroups