Group #13114522 — subgroups

Subgroups — #13114522

Order 1664.

328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#88055	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₁₃	C₂	1	2	yes	maximal
4	#11718593	C₂	1	1	yes	maximal, characteristic
5	C₂×#88043	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
10	C₂²×#1055	C₂²	1	2	yes	—
11	C₄×C₈×C₁₃	C₄	1	4	yes	complemented
12	#88071	C₄	1	4	yes	—
13	#88055	C₄	1	8	yes	complemented
14	C₈×Dic₁₃	C₄	1	8	yes	complemented
15	#88043	C₄	1	4	yes	complemented
16	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₃	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₄²×C₁₃	C₂×C₄	1	2	yes	—
24	C₄²×C₁₃	C₂×C₄	1	2	yes	—
25	C₄×Dic₁₃	C₂×C₄	1	4	yes	—
26	C₄×Dic₁₃	C₂×C₄	1	4	yes	—
27	C₂×#1055	C₂×C₄	1	4	yes	—
28	C₂×#1055	C₂×C₄	1	4	yes	—
29	C₂×#1055	C₂×C₄	1	4	yes	—
30	#1726	—	13	1	no	maximal, Sylow
31	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	—	2	4	no	—
33	C₂×C₄×C₁₃	C₄²	1	4	yes	—
34	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₁₃	—	2	8	no	—
39	C₂×Dic₁₃	C₄²	1	8	yes	—
40	C₈×C₁₃	C₄²	1	4	yes	—
41	C₈×C₁₃	C₄²	1	4	yes	—
42	#1055	C₄²	1	8	yes	—
43	C₂×#97	—	13	2	no	—
44	C₂×#97	—	13	1	no	—
45	C₂×C₄×C₈	—	13	2	no	—
46	C₂×C₄×C₈	D₁₃	1	1	yes	characteristic
47	#376	—	13	1	no	—
48	C₂²×C₁₃	C₂×C₄²	1	2	yes	—
49	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
50	C₂²×C₁₃	#131	1	4	yes	—
51	C₄×C₁₃	—	2	4	no	—
52	C₄×C₁₃	C₂×C₄²	1	2	yes	—
53	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
54	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
55	Dic₁₃	—	2	8	no	—
56	C₂²×C₈	—	13	2	no	—
57	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
58	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
59	C₂×C₄²	—	13	2	no	—
60	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
61	#97	—	13	8	no	—
62	#97	—	13	4	no	—
63	C₄×C₈	—	13	8	no	—
64	C₄×C₈	Dic₁₃	1	4	yes	complemented
65	#95	—	13	4	no	—
66	C₂×C₁₃	C₄³	1	1	yes	characteristic
67	C₂×C₁₃	#405	1	2	yes	—
68	C₂×C₁₃	#405	1	4	yes	—
69	C₂²×C₄	—	13	4	no	—
70	C₂²×C₄	C₄×D₁₃	1	2	yes	—
71	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
72	C₂×C₈	—	13	4	no	—
73	C₂×C₈	—	13	4	no	—
74	C₂×C₈	—	13	4	no	—
75	C₂×C₈	C₄×D₁₃	1	4	yes	—
76	C₂×C₈	C₄×D₁₃	1	4	yes	—
77	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
78	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
79	C₄²	—	13	4	no	—
80	C₄²	—	13	4	no	—
81	C₄²	C₄×D₁₃	1	2	yes	—
82	C₄²	C₂×Dic₁₃	1	2	yes	—
83	C₁₃	#1726	1	1	yes	characteristic, complemented, Sylow
84	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	13	8	no	—
87	C₂×C₄	—	26	8	no	—
88	C₂×C₄	C₄×Dic₁₃	1	4	yes	—
89	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
91	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
92	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
93	C₈	—	13	8	no	—
94	C₈	C₄×Dic₁₃	1	4	yes	—
95	C₈	C₄×Dic₁₃	1	4	yes	—
96	C₂²	C₄²×D₁₃	1	2	yes	—
97	C₂²	#88155	1	4	yes	—
98	C₂²	C₂×C₄×Dic₁₃	1	1	yes	characteristic
99	C₄	—	2	4	no	—
100	C₄	—	26	8	no	—
101	C₄	C₄²×D₁₃	1	2	yes	—
102	C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
103	C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
104	C₂	#11718350	1	4	yes	—
105	C₂	C₄²×Dic₁₃	1	1	yes	characteristic
106	C₂	#11718762	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₈×C₁₃

C₂

yes

maximal, characteristic

C₂×#88055

C₂

yes

maximal

C₂×C₈×Dic₁₃

C₂

yes

maximal

#11718593

C₂

yes

maximal, characteristic

C₂×#88043

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

—

C₂²×#1055

C₂²

yes

—

C₄×C₈×C₁₃

C₄

yes

complemented

#88071

C₄

yes

—

#88055

C₄

yes

complemented

C₈×Dic₁₃

C₄

yes

complemented

#88043

C₄

yes

complemented

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₄²×C₁₃

C₂×C₄

yes

—

C₄²×C₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

C₂×C₄

yes

—

C₂×#1055

C₂×C₄

yes

—

C₂×#1055

C₂×C₄

yes

—

C₂×#1055

C₂×C₄

yes

—

#1726

—

maximal, Sylow

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄²

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄²

yes

—

C₈×C₁₃

C₄²

yes

—

C₈×C₁₃

C₄²

yes

—

#1055

C₄²

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₁₃

yes

characteristic

#376

—

C₂²×C₁₃

C₂×C₄²

yes

—

C₂²×C₁₃

C₂×C₄²

yes

characteristic

C₂²×C₁₃

#131

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄²

yes

—

C₄×C₁₃

C₂×C₄²

yes

characteristic

C₄×C₁₃

C₂×C₄²

yes

characteristic

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₁₃

yes

complemented

#95

—

C₂×C₁₃

C₄³

yes

characteristic

C₂×C₁₃

#405

yes

—

C₂×C₁₃

#405

yes

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₃

yes

—

C₂×C₈

C₄×D₁₃

yes

—

C₂×C₈

C₂×Dic₁₃

yes

—

C₂×C₈

C₂×Dic₁₃

yes

—

C₄²

—

C₄²

—

C₄²

C₄×D₁₃

yes

—

C₄²

C₂×Dic₁₃

yes

—

C₁₃

#1726

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₁₃

yes

—

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

C₂×C₄×D₁₃

yes

—

C₂×C₄

C₂×C₄×D₁₃

yes

—

C₂×C₄

C₂²×Dic₁₃

yes

characteristic

C₈

—

C₈

C₄×Dic₁₃

yes

—

C₈

C₄×Dic₁₃

yes

—

C₂²

C₄²×D₁₃

yes

—

C₂²

#88155

yes

—

C₂²

C₂×C₄×Dic₁₃

yes

characteristic

C₄

—

100

C₄

—

101

C₄

C₄²×D₁₃

yes

—

102

C₄

C₂×C₄×Dic₁₃

yes

characteristic

103

C₄

C₂×C₄×Dic₁₃

yes

characteristic

104

C₂

#11718350

yes

—

105

C₂

C₄²×Dic₁₃

yes

characteristic

106

C₂

#11718762

yes

—

	subgroup	G/H
center	C₂²×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₄³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₃
hypocenter	C₁₃	#1726
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₈

C₂×D₁₃

commutator

C₂×C₁₃

C₄³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂×C₄×C₈×C₁₃

C₂

socle, prime radical

C₂³×C₁₃

C₂²×C₄

cosocle

C₂²×C₄×C₁₃

C₂³

hypercenter

C₂×C₄×C₈

D₁₃

C₁₃

G ▷ C₂×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
11. C₄×C₈×C₁₃	C₄	semidirect
13. #88055	C₄	semidirect
14. C₈×Dic₁₃	C₄	semidirect
15. #88043	C₄	semidirect
64. C₄×C₈	Dic₁₃	semidirect
83. C₁₃	#1726	semidirect

H ≅ G/N

type

11. C₄×C₈×C₁₃

C₄

semidirect

13. #88055

C₄

semidirect

14. C₈×Dic₁₃

C₄

semidirect

15. #88043

C₄

semidirect

64. C₄×C₈

Dic₁₃

semidirect

83. C₁₃

#1726

semidirect

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

subgroup	index
C₂×C₄×C₈×C₁₃	2
C₂×#88055	2
C₂×C₈×Dic₁₃	2
#11718593	2
C₂×#88043	2
#1726	13

subgroup

index

C₂×C₄×C₈×C₁₃

C₂×C₈×Dic₁₃

Subgroups — #13114522

Conjugacy classes of subgroups

Complements

Maximal subgroups