Subgroups — C₂×#16810491 #20277105

Order 6784.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16810491	C₂	1	8	yes	maximal, direct product factor
2	C₂×#13133124	C₂	1	6	yes	maximal
3	C₂²×C₄²×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₅₃	C₂²	1	4	yes	—
5	#13133124	C₂²	1	24	yes	—
6	C₂³×C₄×C₅₃	C₂²	1	3	yes	—
7	C₂×C₄²×C₅₃	C₄	1	8	yes	complemented
8	C₂×C₄²×C₅₃	C₂²	1	4	yes	—
9	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₅₃	—	2	12	no	—
11	C₂²×C₄×C₅₃	C₂×C₄	1	12	yes	—
12	C₂²×C₄×C₅₃	C₂³	1	6	yes	—
13	C₂²×Dic₅₃	—	2	24	no	—
14	C₂²×Dic₅₃	C₂³	1	8	yes	—
15	C₄²×C₅₃	C₂×C₄	1	16	yes	complemented
16	C₂³×C₅₃	C₂²×C₄	1	2	yes	—
17	C₂³×C₅₃	#41	1	12	yes	—
18	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
19	C₂×C₄×C₅₃	—	2	24	no	—
20	C₂×C₄×C₅₃	—	2	12	no	—
21	C₂×C₄×C₅₃	C₂²×C₄	1	12	yes	—
22	C₂×Dic₅₃	—	2	24	no	—
23	C₂×Dic₅₃	—	4	16	no	—
24	C₂²×C₅₃	#117	1	12	yes	—
25	C₂²×C₅₃	#126	1	16	yes	—
26	C₂²×C₅₃	C₂³×C₄	1	1	yes	characteristic
27	C₂²×C₅₃	C₂×#41	1	6	yes	—
28	C₄×C₅₃	—	2	12	no	—
29	Dic₅₃	—	4	8	no	—
30	C₂×#383	—	53	1	no	maximal, Sylow
31	C₂×C₅₃	#383	1	8	yes	complemented
32	C₂×C₅₃	C₂×#117	1	3	yes	—
33	C₂×C₅₃	C₂×#126	1	4	yes	—
34	C₂²×C₄²	D₅₃	1	1	yes	characteristic
35	#383	—	53	8	no	—
36	C₂×#95	—	53	6	no	—
37	C₅₃	C₂×#383	1	1	yes	characteristic, complemented, Sylow
38	C₂³×C₄	—	53	4	no	—
39	C₂³×C₄	C₂×D₅₃	1	3	yes	—
40	C₂×C₄²	Dic₅₃	1	8	yes	complemented
41	C₂×C₄²	C₂×D₅₃	1	4	yes	—
42	#95	—	53	24	no	—
43	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
44	C₂²×C₄	—	2	12	no	—
45	C₂²×C₄	—	53	8	no	—
46	C₂²×C₄	—	106	24	no	—
47	C₂²×C₄	C₂×Dic₅₃	1	12	yes	—
48	C₂²×C₄	C₂²×D₅₃	1	6	yes	—
49	C₄²	C₂×Dic₅₃	1	16	yes	complemented
50	C₂³	#11719945	1	12	yes	—
51	C₂³	C₂²×Dic₅₃	1	2	yes	—
52	C₂³	C₂³×D₅₃	1	1	yes	characteristic
53	C₂×C₄	—	2	24	no	—
54	C₂×C₄	—	2	12	no	—
55	C₂×C₄	—	106	24	no	—
56	C₂×C₄	—	212	16	no	—
57	C₂×C₄	C₂²×Dic₅₃	1	12	yes	—
58	C₂²	#13133176	1	12	yes	—
59	C₂²	#13133211	1	16	yes	—
60	C₂²	C₂³×Dic₅₃	1	1	yes	characteristic
61	C₂²	C₂×#11719945	1	6	yes	—
62	C₄	—	2	12	no	—
63	C₄	—	212	8	no	—
64	C₂	#16810491	1	8	yes	direct product factor
65	C₂	C₂×#13133176	1	3	yes	—
66	C₂	C₂×#13133211	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₅₃
commutator	C₂²×C₅₃	C₂³×C₄
Frattini	C₂³	C₂³×D₅₃
Fitting	C₂²×C₄²×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂³
hypercenter	C₂²×C₄²	D₅₃
hypocenter	C₅₃	C₂×#383
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #16810491	C₂	direct (N × H)
7. C₂×C₄²×C₅₃	C₄	semidirect
15. C₄²×C₅₃	C₂×C₄	semidirect
31. C₂×C₅₃	#383	semidirect
37. C₅₃	C₂×#383	semidirect
40. C₂×C₄²	Dic₅₃	semidirect
49. C₄²	C₂×Dic₅₃	semidirect
64. C₂	#16810491	direct (N × H)

Subgroups — C2×#16810491 #20277105

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810491 #20277105