Group #20290433 — subgroups

Subgroups — #20290433

Order 6784.

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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	#16811582	C₂	1	1	yes	maximal, characteristic
2	#16811559	C₂	1	1	yes	maximal, characteristic
3	(C₂×#6157)⋊C₈	C₂	1	4	yes	maximal
4	C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂×D₅₃⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×#6157	C₂²	1	2	yes	—
7	#13133272	C₄	1	4	yes	complemented
8	(C₂×#6157)⋊C₄	C₄	1	4	yes	—
9	C₂×C₈×D₅₃	C₂²	1	2	yes	—
10	C₄²×D₅₃	C₂²	1	1	yes	characteristic
11	C₄×#88322	C₄	1	1	yes	characteristic, complemented
12	C₈×Dic₅₃	C₄	1	2	yes	complemented
13	C₄×C₈×C₅₃	C₄	1	1	yes	characteristic, complemented
14	C₂²×#6157	C₂×C₄	1	4	yes	—
15	C₂×C₄×D₅₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
17	C₂×#88324	C₂×C₄	1	4	yes	—
18	C₄×#6157	—	2	4	no	—
19	D₅₃⋊C₈	—	2	4	no	—
20	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
21	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₅₃	C₂×C₄	1	2	yes	—
24	C₂×#88322	C₂×C₄	1	2	yes	—
25	C₈×D₅₃	—	2	4	no	—
26	C₂²×D₅₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×#6157	—	2	4	no	—
28	C₂×#6157	—	2	8	no	—
29	C₂×C₄×C₅₃	C₄²	1	2	yes	—
30	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₅₃	C₄²	1	2	yes	—
32	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
33	C₄×D₅₃	—	2	4	no	—
34	C₄×D₅₃	#41	1	4	yes	—
35	#88324	—	2	4	no	—
36	C₈×C₅₃	—	2	2	no	—
37	#88322	—	2	2	no	—
38	C₂²×C₅₃	C₂×C₄²	1	1	yes	characteristic
39	C₂×D₅₃	#117	1	2	yes	—
40	C₂×D₅₃	#131	1	4	yes	—
41	#6157	—	4	4	no	—
42	C₄×C₅₃	—	2	2	no	—
43	C₄×C₅₃	#117	1	2	yes	—
44	Dic₅₃	—	2	2	no	—
45	Dic₅₃	#117	1	2	yes	—
46	#1746	—	53	1	no	maximal, Sylow
47	C₂×C₅₃	#376	1	1	yes	characteristic
48	C₂×C₅₃	#405	1	2	yes	—
49	D₅₃	#433	1	4	yes	—
50	C₂×#97	—	53	1	no	—
51	C₂×C₄×C₈	—	53	1	no	—
52	#376	—	53	1	no	—
53	#336	—	53	4	no	—
54	C₅₃	#1746	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₈	—	53	2	no	—
56	C₂²×C₈	—	53	2	no	—
57	C₂×C₄²	—	53	1	no	—
58	C₂×C₄²	—	53	2	no	—
59	#97	—	53	4	no	—
60	C₄×C₈	—	53	2	no	—
61	C₄×C₈	—	53	1	no	—
62	C₄×C₈	#6157	1	1	yes	characteristic, complemented
63	#95	—	53	4	no	—
64	C₂²×C₄	—	53	1	no	—
65	C₂²×C₄	—	53	2	no	—
66	C₂²×C₄	—	53	4	no	—
67	C₂×C₈	—	53	4	no	—
68	C₂×C₈	—	53	2	no	—
69	C₂×C₈	—	106	4	no	—
70	C₂×C₈	—	106	4	no	—
71	C₂×C₈	C₂×#6157	1	2	yes	—
72	C₄²	—	53	2	no	—
73	C₄²	—	53	1	no	—
74	C₄²	—	106	4	no	—
75	C₄²	C₂×#6157	1	1	yes	characteristic
76	C₂³	—	53	1	no	—
77	C₂×C₄	—	53	1	no	—
78	C₂×C₄	—	53	4	no	—
79	C₂×C₄	—	53	2	no	—
80	C₂×C₄	—	106	4	no	—
81	C₂×C₄	—	106	4	no	—
82	C₂×C₄	—	106	8	no	—
83	C₂×C₄	C₄×#6157	1	2	yes	—
84	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	—	106	4	no	—
87	C₈	—	106	2	no	—
88	C₂²	—	53	2	no	—
89	C₂²	—	53	4	no	—
90	C₂²	C₂×C₄×#6157	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	53	2	no	—
93	C₄	—	106	2	no	—
94	C₄	—	212	4	no	—
95	C₄	#13133296	1	2	yes	—
96	C₂	—	53	4	no	—
97	C₂	#16811559	1	1	yes	characteristic
98	C₂	#16811586	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16811582

C₂

yes

maximal, characteristic

#16811559

C₂

yes

maximal, characteristic

(C₂×#6157)⋊C₈

C₂

yes

maximal

C₄×C₈×D₅₃

C₂

yes

maximal, characteristic

C₂×D₅₃⋊C₈

C₂²

yes

—

C₂×C₄×#6157

C₂²

yes

—

#13133272

C₄

yes

complemented

(C₂×#6157)⋊C₄

C₄

yes

—

C₂×C₈×D₅₃

C₂²

yes

—

C₄²×D₅₃

C₂²

yes

characteristic

C₄×#88322

C₄

yes

characteristic, complemented

C₈×Dic₅₃

C₄

yes

complemented

C₄×C₈×C₅₃

C₄

yes

characteristic, complemented

C₂²×#6157

C₂×C₄

yes

—

C₂×C₄×D₅₃

C₂×C₄

yes

—

C₂×C₄×D₅₃

C₂³

yes

characteristic

C₂×#88324

C₂×C₄

yes

—

C₄×#6157

—

D₅₃⋊C₈

—

C₂×C₈×C₅₃

C₂×C₄

yes

—

C₄²×C₅₃

C₂×C₄

yes

characteristic

C₄×Dic₅₃

C₂×C₄

yes

characteristic

C₄×Dic₅₃

C₂×C₄

yes

—

C₂×#88322

C₂×C₄

yes

—

C₈×D₅₃

—

C₂²×D₅₃

C₂²×C₄

yes

characteristic

C₂×#6157

—

C₂×#6157

—

C₂×C₄×C₅₃

C₄²

yes

—

C₂×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂×Dic₅₃

C₄²

yes

—

C₂×Dic₅₃

C₂²×C₄

yes

characteristic

C₄×D₅₃

—

C₄×D₅₃

#41

yes

—

#88324

—

C₈×C₅₃

—

#88322

—

C₂²×C₅₃

C₂×C₄²

yes

characteristic

C₂×D₅₃

#117

yes

—

C₂×D₅₃

#131

yes

—

#6157

—

C₄×C₅₃

—

C₄×C₅₃

#117

yes

—

Dic₅₃

—

Dic₅₃

#117

yes

—

—

C₂×C₅₃

yes

C₂×C₅₃

yes

—

D₅₃

#433

yes

—

C₂×#97

—

C₂×C₄×C₈

—

#376

—

#336

—

C₅₃

#1746

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6157

yes

characteristic, complemented

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

106

—

C₂×C₈

—

106

—

C₂×C₈

C₂×#6157

yes

—

C₄²

—

C₄²

—

C₄²

—

106

—

C₄²

C₂×#6157

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

106

—

C₂×C₄

—

106

—

C₂×C₄

—

106

—

C₂×C₄

C₄×#6157

yes

—

C₂×C₄

C₂²×#6157

yes

characteristic

C₈

—

C₈

—

106

—

C₈

—

106

—

C₂²

—

C₂²

—

C₂²

C₂×C₄×#6157

yes

characteristic

C₄

—

C₄

—

C₄

—

106

—

C₄

—

212

—

C₄

#13133296

yes

—

C₂

—

C₂

#16811559

yes

characteristic

C₂

#16811586

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6157
commutator, socle	C₂²×C₅₃	C₂×C₄²
Fitting	C₄×C₈×C₅₃	C₄
hypercenter	C₄×C₈	#6157
hypocenter	C₅₃	#1746
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6157

commutator, socle

C₂²×C₅₃

C₂×C₄²

Fitting

C₄×C₈×C₅₃

C₄

C₄×C₈

C₅₃

G ▷ C₂²×C₅₃ ▷ C₅₃

C₁ ◁ C₂×C₄ ◁ C₄×C₈

N	H ≅ G/N	type
7. #13133272	C₄	semidirect
11. C₄×#88322	C₄	semidirect
12. C₈×Dic₅₃	C₄	semidirect
13. C₄×C₈×C₅₃	C₄	semidirect
54. C₅₃	#1746	semidirect
62. C₄×C₈	#6157	semidirect

H ≅ G/N

type

7. #13133272

C₄

semidirect

11. C₄×#88322

C₄

semidirect

12. C₈×Dic₅₃

C₄

semidirect

13. C₄×C₈×C₅₃

C₄

semidirect

54. C₅₃

#1746

semidirect

62. C₄×C₈

#6157

semidirect

Subgroups — #20290433

Conjugacy classes of subgroups

Complements