Group #20276303 — subgroups

Subgroups — #346×D₅₃ #20276303

Order 6784.

200 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 117 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×C₁₆×D₅₃	C₂	1	2	yes	maximal
2	C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#16810399	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810398	C₂	1	2	yes	maximal, complemented
5	C₅₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₅₃	C₄	1	1	yes	characteristic
7	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic
8	C₄²×D₅₃	C₄	1	1	yes	characteristic
9	C₂×#11719908	C₂²	1	2	yes	—
10	C₁₆×D₅₃	C₄	1	8	yes	complemented
11	C₄×#88322	C₄	1	1	yes	characteristic
12	C₈×Dic₅₃	C₄	1	1	yes	characteristic
13	C₈×Dic₅₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₅₃	C₂²	1	2	yes	—
15	C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₅₃	C₈	1	2	yes	—
17	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
20	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₅₃	C₈	1	2	yes	—
22	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
23	C₂×#88322	C₂×C₄	1	1	yes	characteristic
24	C₂×#88322	C₂×C₄	1	1	yes	characteristic
25	C₈×D₅₃	C₈	1	4	yes	—
26	C₈×D₅₃	C₂×C₄	1	4	yes	—
27	C₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
28	#11719908	C₂×C₄	1	4	yes	complemented
29	C₂²×D₅₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₅₃	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₅₃	C₂×C₈	1	2	yes	—
33	C₂×Dic₅₃	C₂×C₈	1	1	yes	characteristic
34	C₄×D₅₃	—	2	4	no	—
35	C₄×D₅₃	C₄²	1	2	yes	—
36	C₄×D₅₃	C₂×C₈	1	2	yes	—
37	C₈×C₅₃	C₂×C₈	1	2	yes	—
38	C₈×C₅₃	C₂²×C₄	1	2	yes	—
39	#88322	C₄²	1	2	yes	—
40	#88322	C₂×C₈	1	2	yes	—
41	C₂²×C₅₃	C₂²×C₈	1	1	yes	characteristic
42	C₂×D₅₃	C₄×C₈	1	2	yes	—
43	C₂×D₅₃	M₃₂	1	4	yes	—
44	C₄×C₅₃	—	2	2	no	—
45	C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
46	C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
47	Dic₅₃	—	2	2	no	—
48	Dic₅₃	C₄×C₈	1	2	yes	—
49	C₂×#346	—	53	1	no	maximal, Sylow
50	C₂×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×C₅₃	C₂×M₃₂	1	2	yes	—
52	D₅₃	#346	1	4	yes	direct product factor
53	C₂²×C₁₆	—	53	2	no	—
54	C₂×C₄×C₈	—	53	1	no	—
55	#346	—	53	2	no	—
56	#346	—	53	1	no	—
57	#346	D₅₃	1	1	yes	characteristic, direct product factor
58	C₅₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	—	53	1	no	—
60	C₂²×C₈	—	53	1	no	—
61	C₂×C₄²	—	53	1	no	—
62	C₂×C₁₆	—	53	2	no	—
63	C₂×C₁₆	—	53	8	no	—
64	C₂×C₁₆	C₂×D₅₃	1	2	yes	—
65	C₄×C₈	—	53	1	no	—
66	C₄×C₈	—	53	1	no	—
67	C₄×C₈	—	53	1	no	—
68	C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
69	C₂²×C₄	—	53	1	no	—
70	C₂²×C₄	—	53	2	no	—
71	C₂×C₈	—	53	1	no	—
72	C₂×C₈	—	53	1	no	—
73	C₂×C₈	—	53	4	no	—
74	C₂×C₈	—	53	4	no	—
75	C₂×C₈	C₄×D₅₃	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
77	C₄²	—	53	1	no	—
78	C₄²	—	53	2	no	—
79	C₄²	C₄×D₅₃	1	1	yes	characteristic
80	C₁₆	—	53	4	no	—
81	C₁₆	C₄×D₅₃	1	4	yes	complemented
82	C₂³	—	53	1	no	—
83	C₂×C₄	—	53	1	no	—
84	C₂×C₄	—	53	2	no	—
85	C₂×C₄	—	53	2	no	—
86	C₂×C₄	—	53	2	no	—
87	C₂×C₄	—	106	4	no	—
88	C₂×C₄	C₈×D₅₃	1	2	yes	—
89	C₂×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
90	C₈	—	53	2	no	—
91	C₈	—	53	2	no	—
92	C₈	C₈×D₅₃	1	2	yes	—
93	C₈	C₂×C₄×D₅₃	1	2	yes	—
94	C₂²	—	53	4	no	—
95	C₂²	—	53	2	no	—
96	C₂²	C₂×C₈×D₅₃	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	53	2	no	—
99	C₄	—	106	2	no	—
100	C₄	C₄²×D₅₃	1	1	yes	characteristic
101	C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
102	C₂	—	53	4	no	—
103	C₂	C₄×C₈×D₅₃	1	1	yes	characteristic
104	C₂	M₃₂×D₅₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₅₃

C₂

yes

maximal

C₄×C₈×D₅₃

C₂

yes

maximal, characteristic

#16810399

C₂

yes

maximal, characteristic, complemented

#16810398

C₂

yes

maximal, complemented

C₅₃×#346

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₅₃

C₄

yes

characteristic

C₂×C₈×D₅₃

C₂²

yes

characteristic

C₄²×D₅₃

C₄

yes

characteristic

C₂×#11719908

C₂²

yes

—

C₁₆×D₅₃

C₄

yes

complemented

C₄×#88322

C₄

yes

characteristic

C₈×Dic₅₃

C₄

yes

characteristic

C₈×Dic₅₃

C₂²

yes

characteristic

C₂×C₁₆×C₅₃

C₂²

yes

—

C₄×C₈×C₅₃

C₂²

yes

characteristic

C₂×C₄×D₅₃

C₈

yes

—

C₂×C₄×D₅₃

C₂×C₄

yes

characteristic

C₂×C₈×C₅₃

C₂×C₄

yes

characteristic

C₂×C₈×C₅₃

C₂³

yes

characteristic

C₄²×C₅₃

C₂×C₄

yes

characteristic

C₄×Dic₅₃

C₈

yes

—

C₄×Dic₅₃

C₂×C₄

yes

characteristic

C₂×#88322

C₂×C₄

yes

characteristic

C₂×#88322

C₂×C₄

yes

characteristic

C₈×D₅₃

C₈

yes

—

C₈×D₅₃

C₂×C₄

yes

—

C₁₆×C₅₃

C₂×C₄

yes

complemented

#11719908

C₂×C₄

yes

complemented

C₂²×D₅₃

C₂×C₈

yes

characteristic

C₂×C₄×C₅₃

C₂×C₈

yes

—

C₂×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂×Dic₅₃

C₂×C₈

yes

—

C₂×Dic₅₃

C₂×C₈

yes

characteristic

C₄×D₅₃

—

C₄×D₅₃

C₄²

yes

—

C₄×D₅₃

C₂×C₈

yes

—

C₈×C₅₃

C₂×C₈

yes

—

C₈×C₅₃

C₂²×C₄

yes

—

#88322

C₄²

yes

—

#88322

C₂×C₈

yes

—

C₂²×C₅₃

C₂²×C₈

yes

characteristic

C₂×D₅₃

C₄×C₈

yes

—

C₂×D₅₃

M₃₂

yes

—

C₄×C₅₃

—

C₄×C₅₃

C₂×C₄²

yes

characteristic

C₄×C₅₃

C₂²×C₈

yes

characteristic

Dic₅₃

—

Dic₅₃

C₄×C₈

yes

—

C₂×#346

—

maximal, Sylow

C₂×C₅₃

C₂×C₄×C₈

yes

characteristic

C₂×C₅₃

C₂×M₃₂

yes

—

D₅₃

#346

yes

direct product factor

C₂²×C₁₆

—

C₂×C₄×C₈

—

#346

—

#346

—

#346

D₅₃

yes

characteristic, direct product factor

C₅₃

C₂×#346

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₅₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₅₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₅₃

yes

characteristic

C₂×C₈

C₂²×D₅₃

yes

characteristic

C₄²

—

C₄²

—

C₄²

C₄×D₅₃

yes

characteristic

C₁₆

—

C₁₆

C₄×D₅₃

yes

complemented

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

106

—

C₂×C₄

C₈×D₅₃

yes

—

C₂×C₄

C₂×C₄×D₅₃

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₅₃

yes

—

C₈

C₂×C₄×D₅₃

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₅₃

yes

characteristic

C₄

—

C₄

—

C₄

—

106

—

100

C₄

C₄²×D₅₃

yes

characteristic

101

C₄

C₂×C₈×D₅₃

yes

characteristic

102

C₂

—

103

C₂

C₄×C₈×D₅₃

yes

characteristic

104

C₂

M₃₂×D₅₃

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₅₃
commutator	C₂×C₅₃	C₂×C₄×C₈
Fitting	C₅₃×#346	C₂
socle	C₂²×C₅₃	C₂²×C₈
hypercenter	#346	D₅₃
hypocenter	C₅₃	C₂×#346
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₅₃

commutator

C₂×C₅₃

C₂×C₄×C₈

Fitting

C₅₃×#346

C₂

socle

C₂²×C₅₃

C₂²×C₈

D₅₃

C₅₃

G ▷ C₂×C₅₃ ▷ C₅₃

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
3. #16810399	C₂	semidirect
4. #16810398	C₂	semidirect
5. C₅₃×#346	C₂	semidirect
10. C₁₆×D₅₃	C₄	semidirect
27. C₁₆×C₅₃	C₂×C₄	semidirect
28. #11719908	C₂×C₄	semidirect
52. D₅₃	#346	direct (N × H)
57. #346	D₅₃	direct (N × H)
58. C₅₃	C₂×#346	semidirect
81. C₁₆	C₄×D₅₃	semidirect

H ≅ G/N

type

3. #16810399

C₂

semidirect

4. #16810398

C₂

semidirect

5. C₅₃×#346

C₂

semidirect

10. C₁₆×D₅₃

C₄

semidirect

27. C₁₆×C₅₃

C₂×C₄

semidirect

28. #11719908

C₂×C₄

semidirect

52. D₅₃

#346

direct (N × H)

57. #346

D₅₃

direct (N × H)

58. C₅₃

C₂×#346

semidirect

81. C₁₆

C₄×D₅₃

semidirect

Subgroups — #346×D₅₃ #20276303

Conjugacy classes of subgroups

Complements

Subgroups — #346×D53 #20276303

Conjugacy classes of subgroups

Complements

Subgroups — #346×D₅₃ #20276303