Group #20290937 — subgroups

Subgroups — #20290937

Order 6784.

160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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	D₅₃⋊M₃₂	C₂	1	2	yes	maximal
2	#16811516	C₂	1	2	yes	maximal, complemented
3	#16811515	C₂	1	2	yes	maximal, complemented
4	#16810577	C₂	1	1	yes	maximal, characteristic
5	#13133292	C₄	1	4	yes	complemented
6	#13133291	C₂²	1	4	yes	—
7	D₅₃⋊C₁₆	C₄	1	4	yes	complemented
8	C₂×#11719912	C₄	1	1	yes	characteristic
9	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic
10	#13133174	C₄	1	1	yes	characteristic
11	#13133128	C₂²	1	1	yes	characteristic
12	#13133127	C₂²	1	1	yes	characteristic
13	C₈×Dic₅₃	C₄	1	1	yes	characteristic
14	C₄×C₈×C₅₃	C₄	1	1	yes	characteristic
15	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
19	#11719921	—	2	1	no	—
20	#11719919	—	2	1	no	—
21	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
22	C₂×#88322	C₂×C₄	1	1	yes	characteristic
23	C₂×#88322	C₂³	1	1	yes	characteristic
24	#11719912	—	2	2	no	—
25	C₈×D₅₃	C₂×C₄	1	2	yes	—
26	C₈×D₅₃	C₂×C₄	1	2	yes	—
27	#11719910	C₂×C₄	1	8	yes	—
28	C₂²×D₅₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₅₃	—	2	1	no	—
30	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₅₃	—	2	1	no	—
32	C₂×Dic₅₃	M₁₆	1	1	yes	characteristic
33	C₄×D₅₃	C₄²	1	2	yes	—
34	C₄×D₅₃	M₁₆	1	2	yes	—
35	C₈×C₅₃	—	2	1	no	—
36	C₈×C₅₃	C₄²	1	1	yes	characteristic
37	C₈×C₅₃	C₄²	1	1	yes	characteristic
38	#88322	—	2	1	no	—
39	#88322	C₂²×C₄	1	2	yes	—
40	C₂²×C₅₃	C₂×M₁₆	1	1	yes	characteristic
41	C₂×D₅₃	—	4	1	no	—
42	C₂×D₅₃	#97	1	2	yes	—
43	C₄×C₅₃	—	4	1	no	—
44	C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
46	Dic₅₃	—	4	1	no	—
47	Dic₅₃	#97	1	2	yes	—
48	#2110	—	53	1	no	maximal, Sylow
49	C₂×C₅₃	—	2	1	no	—
50	C₂×C₅₃	C₂×#97	1	1	yes	characteristic
51	D₅₃	—	2	2	no	—
52	C₂×M₃₂	—	53	2	no	—
53	#405	—	53	1	no	—
54	#347	—	53	2	no	—
55	#347	—	53	2	no	—
56	C₅₃	#2110	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	53	1	no	—
58	C₂²×C₈	—	53	1	no	—
59	#117	—	53	1	no	—
60	M₃₂	—	53	4	no	—
61	M₃₂	—	53	4	no	—
62	C₂×C₁₆	—	53	4	no	—
63	#97	—	53	1	no	—
64	#97	—	53	1	no	—
65	C₄×C₈	—	53	1	no	—
66	C₄×C₈	#6157	1	1	yes	characteristic
67	C₂²×C₄	—	53	1	no	—
68	M₁₆	—	106	2	no	—
69	C₂×C₈	—	53	1	no	—
70	C₂×C₈	—	53	2	no	—
71	C₂×C₈	—	53	2	no	—
72	C₂×C₈	—	53	1	no	—
73	C₂×C₈	C₂×#6157	1	1	yes	characteristic
74	C₂×C₈	C₂×#6157	1	1	yes	characteristic
75	C₄⋊C₄	—	106	1	no	—
76	C₂²⋊C₄	—	106	1	no	—
77	C₄²	—	53	1	no	—
78	C₄²	C₂×#6157	1	1	yes	characteristic
79	C₁₆	—	53	8	no	—
80	C₂³	—	53	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	53	1	no	—
83	C₂×C₄	—	53	2	no	—
84	C₂×C₄	—	53	2	no	—
85	C₂×C₄	—	106	1	no	—
86	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
87	C₈	—	2	1	no	—
88	C₈	—	53	2	no	—
89	C₈	—	106	1	no	—
90	C₈	C₄×#6157	1	1	yes	characteristic
91	C₈	C₄×#6157	1	1	yes	characteristic
92	C₂²	—	53	2	no	—
93	C₂²	—	212	1	no	—
94	C₂²	D₅₃⋊M₁₆	1	1	yes	characteristic
95	C₄	—	4	1	no	—
96	C₄	—	53	2	no	—
97	C₄	—	212	1	no	—
98	C₄	C₂×C₄×#6157	1	1	yes	characteristic
99	C₄	D₅₃⋊M₁₆	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	106	2	no	—
102	C₂	#16811582	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₅₃⋊M₃₂

C₂

yes

maximal

#16811516

C₂

yes

maximal, complemented

#16811515

C₂

yes

maximal, complemented

#16810577

C₂

yes

maximal, characteristic

#13133292

C₄

yes

complemented

#13133291

C₂²

yes

—

D₅₃⋊C₁₆

C₄

yes

complemented

C₂×#11719912

C₄

yes

characteristic

C₂×C₈×D₅₃

C₂²

yes

characteristic

#13133174

C₄

yes

characteristic

#13133128

C₂²

yes

characteristic

#13133127

C₂²

yes

characteristic

C₈×Dic₅₃

C₄

yes

characteristic

C₄×C₈×C₅₃

C₄

yes

characteristic

C₂×C₄×D₅₃

C₂×C₄

yes

characteristic

C₂×C₈×C₅₃

C₂×C₄

yes

characteristic

C₂×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄²×C₅₃

C₂×C₄

yes

characteristic

#11719921

—

#11719919

—

C₄×Dic₅₃

C₂×C₄

yes

characteristic

C₂×#88322

C₂×C₄

yes

characteristic

C₂×#88322

C₂³

yes

characteristic

#11719912

—

C₈×D₅₃

C₂×C₄

yes

—

C₈×D₅₃

C₂×C₄

yes

—

#11719910

C₂×C₄

yes

—

C₂²×D₅₃

M₁₆

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

M₁₆

yes

characteristic

C₄×D₅₃

C₄²

yes

—

C₄×D₅₃

M₁₆

yes

—

C₈×C₅₃

—

C₈×C₅₃

C₄²

yes

characteristic

C₈×C₅₃

C₄²

yes

characteristic

#88322

—

#88322

C₂²×C₄

yes

—

C₂²×C₅₃

C₂×M₁₆

yes

characteristic

C₂×D₅₃

—

C₂×D₅₃

#97

yes

—

C₄×C₅₃

—

C₄×C₅₃

C₂×C₄²

yes

characteristic

C₄×C₅₃

C₂×M₁₆

yes

characteristic

Dic₅₃

—

Dic₅₃

#97

yes

—

#2110

—

maximal, Sylow

C₂×C₅₃

—

C₂×C₅₃

C₂×#97

yes

characteristic

D₅₃

—

C₂×M₃₂

—

#405

—

#347

—

#347

—

C₅₃

#2110

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

#6157

yes

characteristic

C₂²×C₄

—

M₁₆

—

106

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

106

—

C₂²⋊C₄

—

106

—

C₄²

—

C₄²

C₂×#6157

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

106

—

C₂×C₄

C₂²×#6157

yes

characteristic

C₈

—

C₈

—

C₈

—

106

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

212

—

C₂²

D₅₃⋊M₁₆

yes

characteristic

C₄

—

C₄

—

C₄

—

212

—

C₄

C₂×C₄×#6157

yes

characteristic

C₄

D₅₃⋊M₁₆

yes

characteristic

100

C₂

—

101

C₂

—

106

—

102

C₂

#16811582

yes

characteristic

	subgroup	G/H
center	C₈	C₄×#6157
commutator	C₄×C₅₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×#6157
Fitting	C₄×C₈×C₅₃	C₄
socle	C₂×C₅₃	C₂×#97
hypercenter	C₄×C₈	#6157
hypocenter	C₅₃	#2110
LCS	G ▷ C₄×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₈ ◁ C₄×C₈

subgroup

G/H

center

C₈

C₄×#6157

commutator

C₄×C₅₃

C₂×C₄²

Frattini

C₂×C₄

C₂²×#6157

Fitting

C₄×C₈×C₅₃

C₄

socle

C₂×C₅₃

C₂×#97

C₄×C₈

C₅₃

G ▷ C₄×C₅₃ ▷ C₅₃

C₁ ◁ C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #16811516	C₂	semidirect
3. #16811515	C₂	semidirect
5. #13133292	C₄	semidirect
7. D₅₃⋊C₁₆	C₄	semidirect
56. C₅₃	#2110	semidirect

H ≅ G/N

type

2. #16811516

C₂

semidirect

3. #16811515

C₂

semidirect

5. #13133292

C₄

semidirect

7. D₅₃⋊C₁₆

C₄

semidirect

56. C₅₃

#2110

semidirect

Subgroups — #20290937

Conjugacy classes of subgroups

Complements