Group #13114953 — subgroups

Subgroups — #13114953

Order 1664.

260 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#1055	C₂	1	2	yes	maximal
3	#11718116	C₂	1	4	yes	maximal
4	C₂×C₄²×C₁₃	C₄	1	2	yes	—
5	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#1055	C₂²	1	4	yes	—
10	C₄⋊#1055	—	2	4	no	—
11	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₄²×C₁₃	—	2	4	no	—
17	C₄²×C₁₃	—	2	2	no	—
18	C₄²×C₁₃	—	2	4	no	—
19	C₄²×C₁₃	C₈	1	4	yes	complemented
20	C₄²×C₁₃	D₄	1	2	yes	—
21	C₄²×C₁₃	Q₈	1	2	yes	—
22	C₂×#1055	—	2	4	no	—
23	C₂×#1055	—	2	8	no	—
24	#1831	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	—	2	2	no	—
27	C₂×C₄×C₁₃	—	2	2	no	—
28	C₂×C₄×C₁₃	—	2	2	no	—
29	C₂×C₄×C₁₃	—	2	2	no	—
30	C₂×C₄×C₁₃	—	2	2	no	—
31	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₁₃	C₂×C₈	1	4	yes	—
34	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
35	C₂×C₄×C₁₃	M₁₆	1	4	yes	—
36	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
37	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₃	#41	1	4	yes	—
40	#1055	—	4	4	no	—
41	C₂×C₄⋊C₈	—	13	2	no	—
42	C₄³	D₁₃	1	1	yes	characteristic
43	#336	—	13	4	no	—
44	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₁₃	#117	1	2	yes	—
46	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
47	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
48	C₂²×C₁₃	C₂×M₁₆	1	2	yes	—
49	C₄×C₁₃	—	2	2	no	—
50	C₄×C₁₃	—	2	4	no	—
51	C₄×C₁₃	—	2	4	no	—
52	C₄×C₁₃	C₄⋊C₈	1	4	yes	—
53	C₄×C₁₃	#124	1	2	yes	—
54	C₄×C₁₃	#125	1	2	yes	—
55	C₂²×C₈	—	13	4	no	—
56	C₂×C₄²	Dic₁₃	1	2	yes	—
57	C₂×C₄²	Dic₁₃	1	1	yes	characteristic
58	C₂×C₄²	Dic₁₃	1	1	yes	characteristic
59	C₂×C₄²	C₂×D₁₃	1	2	yes	—
60	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
61	C₄⋊C₈	—	26	4	no	—
62	C₂×C₁₃	#382	1	1	yes	characteristic
63	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
64	C₂×C₁₃	#423	1	1	yes	characteristic
65	C₂×C₁₃	#431	1	2	yes	—
66	C₂×C₁₃	#432	1	2	yes	—
67	C₂²×C₄	C₂×Dic₁₃	1	2	yes	—
68	C₂²×C₄	C₂×Dic₁₃	1	2	yes	—
69	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
70	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
71	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
72	C₂×C₈	—	26	4	no	—
73	C₂×C₈	—	26	8	no	—
74	C₄²	—	2	4	no	—
75	C₄²	—	2	2	no	—
76	C₄²	—	2	4	no	—
77	C₄²	#1055	1	4	yes	complemented
78	C₄²	Dic₂₆	1	2	yes	—
79	C₄²	D₅₂	1	2	yes	—
80	C₁₃	#1831	1	1	yes	characteristic, complemented, Sylow
81	C₂³	C₂²×Dic₁₃	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	C₂×#1055	1	4	yes	—
88	C₂×C₄	C₂×#1055	1	2	yes	—
89	C₂×C₄	#6099	1	4	yes	—
90	C₂×C₄	#6099	1	2	yes	—
91	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
92	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
93	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
94	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
95	C₂×C₄	#6127	1	4	yes	—
96	C₈	—	52	4	no	—
97	C₂²	C₂²×#1055	1	1	yes	characteristic
98	C₂²	C₂×#6099	1	1	yes	characteristic
99	C₂²	C₂×#6099	1	2	yes	—
100	C₂²	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
101	C₂²	#88180	1	2	yes	—
102	C₄	—	2	2	no	—
103	C₄	—	2	4	no	—
104	C₄	—	2	4	no	—
105	C₄	C₄⋊#1055	1	4	yes	—
106	C₄	#88124	1	2	yes	—
107	C₄	#88129	1	2	yes	—
108	C₂	C₂×C₄⋊#1055	1	1	yes	characteristic
109	C₂	#11718585	1	1	yes	characteristic
110	C₂	#11718586	1	2	yes	—
111	C₂	#11718587	1	2	yes	—
112	C₂	#11718597	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄³×C₁₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#1055

C₂

yes

maximal

#11718116

C₂

yes

maximal

C₂×C₄²×C₁₃

C₄

yes

—

C₂×C₄²×C₁₃

C₄

yes

characteristic

C₂×C₄²×C₁₃

C₄

yes

characteristic

C₂×C₄²×C₁₃

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂²×#1055

C₂²

yes

—

C₄⋊#1055

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₈

yes

complemented

C₄²×C₁₃

D₄

yes

—

C₄²×C₁₃

Q₈

yes

—

—

—

—

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

M₁₆

yes

—

C₂×C₄×C₁₃

M₁₆

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

#1055

—

C₂×C₄⋊C₈

—

C₄³

D₁₃

yes

characteristic

#336

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#117

yes

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₂²×C₁₃

C₂×M₁₆

yes

characteristic

C₂²×C₁₃

C₂×M₁₆

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₄⋊C₈

yes

—

C₄×C₁₃

#124

yes

—

C₄×C₁₃

#125

yes

—

C₂²×C₈

—

C₂×C₄²

Dic₁₃

yes

—

C₂×C₄²

Dic₁₃

yes

characteristic

C₂×C₄²

Dic₁₃

yes

characteristic

C₂×C₄²

C₂×D₁₃

yes

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

C₄⋊C₈

—

C₂×C₁₃

#382

yes

characteristic

C₂×C₁₃

C₂×C₄⋊C₈

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×C₁₃

#432

yes

—

C₂²×C₄

C₂×Dic₁₃

yes

—

C₂²×C₄

C₂×Dic₁₃

yes

—

C₂²×C₄

C₂×Dic₁₃

yes

characteristic

C₂²×C₄

C₂×Dic₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

#1055

yes

complemented

C₄²

Dic₂₆

yes

—

C₄²

D₅₂

yes

—

C₁₃

#1831

yes

characteristic, complemented, Sylow

C₂³

C₂²×Dic₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#1055

yes

—

C₂×C₄

C₂×#1055

yes

—

C₂×C₄

#6099

yes

—

C₂×C₄

#6099

yes

—

C₂×C₄

C₄⋊Dic₁₃

yes

—

C₂×C₄

C₄⋊Dic₁₃

yes

—

C₂×C₄

C₂×Dic₂₆

yes

characteristic

C₂×C₄

C₂×D₅₂

yes

characteristic

C₂×C₄

#6127

yes

—

C₈

—

C₂²

C₂²×#1055

yes

C₂²

yes

C₂²

yes

—

100

C₂²

C₂×C₄⋊Dic₁₃

yes

characteristic

101

C₂²

#88180

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

C₄⋊#1055

yes

—

106

C₄

#88124

yes

—

107

C₄

#88129

yes

—

108

C₂

C₂×C₄⋊#1055

yes

characteristic

109

C₂

#11718585

yes

characteristic

110

C₂

#11718586

yes

—

111

C₂

#11718587

yes

—

112

C₂

#11718597

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₈
Fitting	C₄³×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₄³	D₁₃
hypocenter	C₁₃	#1831
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₃

commutator

C₂²×C₁₃

C₂²×C₈

Fitting

C₄³×C₁₃

C₂

socle, prime radical

C₂³×C₁₃

C₂²×C₄

cosocle

C₂²×C₄×C₁₃

C₂³

hypercenter

C₄³

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ C₄³

N	H ≅ G/N	type
19. C₄²×C₁₃	C₈	semidirect
77. C₄²	#1055	semidirect
80. C₁₃	#1831	semidirect

H ≅ G/N

type

19. C₄²×C₁₃

C₈

semidirect

77. C₄²

#1055

semidirect

80. C₁₃

#1831

semidirect

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

subgroup	index
C₄³×C₁₃	2
C₂×C₄⋊#1055	2
#11718116	2
#1831	13

subgroup

index

C₄³×C₁₃

C₂×C₄⋊#1055

#11718116

#1831

Subgroups — #13114953

Conjugacy classes of subgroups

Complements

Maximal subgroups