Group #20277041 — subgroups

Subgroups — C₂×#16810468 #20277041

Order 6784.

840 conjugacy classes of subgroups; only the 405 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 405 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	C₂²×C₄×Dic₅₃	C₂	1	3	yes	maximal
2	#16810468	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13133124	C₂	1	3	yes	maximal
4	C₂×#95×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₅₃	C₂²	1	3	yes	—
6	C₂³×Dic₅₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₅₃	C₄	1	24	yes	complemented
8	C₂×C₄×Dic₅₃	C₂²	1	12	yes	—
9	#13133124	C₂²	1	12	yes	—
10	C₂³×C₄×C₅₃	C₂²	1	3	yes	—
11	#95×C₅₃	C₂²	1	4	yes	—
12	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
13	C₂²×C₄×C₅₃	—	2	12	no	—
14	C₂²×C₄×C₅₃	C₂×C₄	1	12	yes	—
15	C₂²×C₄×C₅₃	C₂³	1	6	yes	—
16	C₂²×Dic₅₃	—	2	6	no	—
17	C₂²×Dic₅₃	—	2	6	no	—
18	C₂²×Dic₅₃	C₂×C₄	1	12	yes	—
19	C₂²×Dic₅₃	C₂×C₄	1	12	yes	—
20	C₂²×Dic₅₃	C₂³	1	6	yes	—
21	C₂²×Dic₅₃	C₂³	1	2	yes	—
22	C₄×Dic₅₃	C₂×C₄	1	48	yes	complemented
23	C₂³×C₅₃	C₂²×C₄	1	6	yes	—
24	C₂³×C₅₃	#41	1	6	yes	—
25	C₂³×C₅₃	#41	1	2	yes	—
26	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
27	C₂×C₄×C₅₃	—	2	24	no	—
28	C₂×C₄×C₅₃	—	2	12	no	—
29	C₂×C₄×C₅₃	C₂²×C₄	1	12	yes	—
30	C₂×Dic₅₃	—	2	24	no	—
31	C₂×Dic₅₃	—	2	6	no	—
32	C₂×Dic₅₃	—	2	6	no	—
33	C₂×Dic₅₃	C₄²	1	16	yes	—
34	C₂×Dic₅₃	C₂²×C₄	1	12	yes	—
35	C₂×Dic₅₃	C₂²×C₄	1	12	yes	—
36	C₂²×C₅₃	C₂×C₄²	1	4	yes	—
37	C₂²×C₅₃	#117	1	12	yes	—
38	C₂²×C₅₃	#117	1	12	yes	—
39	C₂²×C₅₃	C₂³×C₄	1	3	yes	—
40	C₂²×C₅₃	C₂×#41	1	3	yes	—
41	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
42	C₄×C₅₃	—	2	12	no	—
43	Dic₅₃	—	2	12	no	—
44	Dic₅₃	C₂×C₄²	1	8	yes	—
45	C₂×#376	—	53	1	no	maximal, Sylow
46	C₂×C₅₃	#376	1	8	yes	complemented
47	C₂×C₅₃	C₂²×C₄²	1	1	yes	characteristic
48	C₂×C₅₃	C₂×#117	1	3	yes	—
49	C₂×C₅₃	C₂×#117	1	3	yes	—
50	C₂²×C₄²	—	53	3	no	—
51	#376	—	53	8	no	—
52	C₂×#95	—	53	3	no	—
53	C₂×#95	D₅₃	1	1	yes	characteristic
54	C₅₃	C₂×#376	1	1	yes	characteristic, complemented, Sylow
55	C₂³×C₄	—	53	1	no	—
56	C₂³×C₄	—	53	3	no	—
57	C₂³×C₄	C₂×D₅₃	1	3	yes	—
58	C₂×C₄²	—	53	24	no	—
59	C₂×C₄²	—	53	12	no	—
60	#95	—	53	12	no	—
61	#95	C₂×D₅₃	1	4	yes	—
62	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
63	C₂²×C₄	—	2	12	no	—
64	C₂²×C₄	—	53	12	no	—
65	C₂²×C₄	—	53	2	no	—
66	C₂²×C₄	—	53	12	no	—
67	C₂²×C₄	—	53	6	no	—
68	C₂²×C₄	—	106	6	no	—
69	C₂²×C₄	—	106	6	no	—
70	C₂²×C₄	C₄×D₅₃	1	12	yes	—
71	C₂²×C₄	C₂²×D₅₃	1	6	yes	—
72	C₄²	—	53	48	no	—
73	C₂³	C₂×C₄×D₅₃	1	6	yes	—
74	C₂³	#11719947	1	6	yes	—
75	C₂³	#11719949	1	2	yes	—
76	C₂³	C₂³×D₅₃	1	1	yes	characteristic
77	C₂×C₄	—	2	24	no	—
78	C₂×C₄	—	2	12	no	—
79	C₂×C₄	—	53	16	no	—
80	C₂×C₄	—	53	12	no	—
81	C₂×C₄	—	53	12	no	—
82	C₂×C₄	—	106	24	no	—
83	C₂×C₄	—	106	6	no	—
84	C₂×C₄	—	106	6	no	—
85	C₂×C₄	C₂×C₄×D₅₃	1	12	yes	—
86	C₂²	C₄²×D₅₃	1	4	yes	—
87	C₂²	#13133173	1	12	yes	—
88	C₂²	#13133175	1	12	yes	—
89	C₂²	C₂²×C₄×D₅₃	1	3	yes	—
90	C₂²	C₂×#11719947	1	3	yes	—
91	C₂²	C₂×#11719949	1	1	yes	characteristic
92	C₄	—	2	12	no	—
93	C₄	—	53	8	no	—
94	C₄	—	106	12	no	—
95	C₂	#16810468	1	8	yes	direct product factor
96	C₂	C₂×C₄²×D₅₃	1	1	yes	characteristic
97	C₂	C₂×#13133173	1	3	yes	—
98	C₂	C₂×#13133175	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×Dic₅₃

C₂

yes

maximal

#16810468

C₂

yes

maximal, direct product factor

C₂×#13133124

C₂

yes

maximal

C₂×#95×C₅₃

C₂

yes

maximal, characteristic

C₂³×Dic₅₃

C₂²

yes

—

C₂³×Dic₅₃

C₂²

yes

characteristic

C₂×C₄×Dic₅₃

C₄

yes

complemented

C₂×C₄×Dic₅₃

C₂²

yes

—

#13133124

C₂²

yes

—

C₂³×C₄×C₅₃

C₂²

yes

—

#95×C₅₃

C₂²

yes

—

C₂⁴×C₅₃

C₂³

yes

characteristic

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×C₄

yes

—

C₂²×C₄×C₅₃

C₂³

yes

—

C₂²×Dic₅₃

—

C₂²×Dic₅₃

—

C₂²×Dic₅₃

C₂×C₄

yes

—

C₂²×Dic₅₃

C₂×C₄

yes

—

C₂²×Dic₅₃

C₂³

yes

—

C₂²×Dic₅₃

C₂³

yes

—

C₄×Dic₅₃

C₂×C₄

yes

complemented

C₂³×C₅₃

C₂²×C₄

yes

—

C₂³×C₅₃

#41

yes

—

C₂³×C₅₃

#41

yes

—

C₂³×C₅₃

C₂⁴

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂²×C₄

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

C₄²

yes

—

C₂×Dic₅₃

C₂²×C₄

yes

—

C₂×Dic₅₃

C₂²×C₄

yes

—

C₂²×C₅₃

C₂×C₄²

yes

—

C₂²×C₅₃

#117

yes

—

C₂²×C₅₃

#117

yes

—

C₂²×C₅₃

C₂³×C₄

yes

—

C₂²×C₅₃

C₂×#41

yes

—

C₂²×C₅₃

C₂×#41

yes

characteristic

C₄×C₅₃

—

Dic₅₃

—

Dic₅₃

C₂×C₄²

yes

—

—

C₂×C₅₃

yes

C₂×C₅₃

C₂²×C₄²

yes

characteristic

C₂×C₅₃

C₂×#117

yes

—

C₂×C₅₃

C₂×#117

yes

—

C₂²×C₄²

—

#376

—

C₂×#95

—

C₂×#95

D₅₃

yes

characteristic

C₅₃

C₂×#376

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₅₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

#95

—

#95

C₂×D₅₃

yes

—

C₂⁴

C₂²×D₅₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

106

—

C₂²×C₄

—

106

—

C₂²×C₄

C₄×D₅₃

yes

—

C₂²×C₄

C₂²×D₅₃

yes

—

C₄²

—

C₂³

C₂×C₄×D₅₃

yes

—

C₂³

#11719947

yes

—

C₂³

#11719949

yes

—

C₂³

C₂³×D₅₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

106

—

C₂×C₄

—

106

—

C₂×C₄

—

106

—

C₂×C₄

C₂×C₄×D₅₃

yes

—

C₂²

C₄²×D₅₃

yes

—

C₂²

#13133173

yes

—

C₂²

#13133175

yes

—

C₂²

C₂²×C₄×D₅₃

yes

—

C₂²

C₂×#11719947

yes

—

C₂²

C₂×#11719949

yes

characteristic

C₄

—

C₄

—

C₄

—

106

—

C₂

#16810468

yes

direct product factor

C₂

C₂×C₄²×D₅₃

yes

characteristic

C₂

C₂×#13133173

yes

—

C₂

C₂×#13133175

yes

—

	subgroup	G/H
center	C₂⁴	C₂²×D₅₃
commutator	C₂×C₅₃	C₂²×C₄²
Frattini	C₂³	C₂³×D₅₃
Fitting	C₂×#95×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂³
hypercenter	C₂×#95	D₅₃
hypocenter	C₅₃	C₂×#376
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

subgroup

G/H

center

C₂⁴

C₂²×D₅₃

commutator

C₂×C₅₃

C₂²×C₄²

Frattini

C₂³

C₂³×D₅₃

Fitting

C₂×#95×C₅₃

C₂

socle

C₂⁴×C₅₃

C₂³

hypercenter

C₂×#95

D₅₃

C₅₃

G ▷ C₂×C₅₃ ▷ C₅₃

C₁ ◁ C₂⁴ ◁ C₂×#95

N	H ≅ G/N	type
2. #16810468	C₂	direct (N × H)
7. C₂×C₄×Dic₅₃	C₄	semidirect
22. C₄×Dic₅₃	C₂×C₄	semidirect
46. C₂×C₅₃	#376	semidirect
54. C₅₃	C₂×#376	semidirect
95. C₂	#16810468	direct (N × H)

H ≅ G/N

type

2. #16810468

C₂

direct (N × H)

7. C₂×C₄×Dic₅₃

C₄

semidirect

22. C₄×Dic₅₃

C₂×C₄

semidirect

46. C₂×C₅₃

#376

semidirect

54. C₅₃

C₂×#376

semidirect

95. C₂

#16810468

direct (N × H)

Subgroups — C₂×#16810468 #20277041

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16810468 #20277041

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810468 #20277041