Subgroups — C₄³×D₅₃ #20277036

Order 6784.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₅₃	C₂	1	7	yes	maximal
2	C₄²×Dic₅₃	C₂	1	7	yes	maximal, complemented
3	C₄³×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₅₃	C₂²	1	7	yes	—
5	C₂×C₄×Dic₅₃	C₂²	1	21	yes	—
6	C₄²×D₅₃	C₄	1	56	yes	direct product factor
7	C₂×C₄²×C₅₃	C₂²	1	7	yes	—
8	C₂³×D₅₃	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₅₃	C₂³	1	7	yes	—
10	C₂²×Dic₅₃	C₂³	1	7	yes	—
11	C₂×C₄×D₅₃	C₂×C₄	1	84	yes	—
12	C₄²×C₅₃	C₂×C₄	1	28	yes	complemented
13	C₄×Dic₅₃	C₂×C₄	1	84	yes	complemented
14	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
15	C₂²×D₅₃	C₂²×C₄	1	14	yes	—
16	C₂×C₄×C₅₃	C₂²×C₄	1	42	yes	—
17	C₂×Dic₅₃	C₂²×C₄	1	42	yes	—
18	C₄×D₅₃	C₄²	1	112	yes	direct product factor
19	C₂²×C₅₃	C₂³×C₄	1	7	yes	—
20	C₂×D₅₃	C₂×C₄²	1	28	yes	—
21	C₄×C₅₃	C₂×C₄²	1	28	yes	complemented
22	Dic₅₃	C₂×C₄²	1	28	yes	complemented
23	C₂×C₄³	—	53	1	no	maximal, Sylow
24	C₂×C₅₃	C₂²×C₄²	1	7	yes	—
25	D₅₃	C₄³	1	8	yes	direct product factor
26	C₂²×C₄²	—	53	7	no	—
27	C₄³	—	53	7	no	—
28	C₄³	D₅₃	1	1	yes	characteristic, direct product factor
29	C₅₃	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
30	C₂³×C₄	—	53	7	no	—
31	C₂×C₄²	—	53	21	no	—
32	C₂×C₄²	—	53	56	no	—
33	C₂×C₄²	C₂×D₅₃	1	7	yes	—
34	C₂⁴	—	53	1	no	—
35	C₂²×C₄	—	53	7	no	—
36	C₂²×C₄	—	53	84	no	—
37	C₂²×C₄	C₂²×D₅₃	1	7	yes	—
38	C₄²	—	53	84	no	—
39	C₄²	C₄×D₅₃	1	28	yes	direct product factor
40	C₂³	—	53	14	no	—
41	C₂³	C₂³×D₅₃	1	1	yes	characteristic
42	C₂×C₄	—	53	42	no	—
43	C₂×C₄	—	53	112	no	—
44	C₂×C₄	C₂×C₄×D₅₃	1	42	yes	—
45	C₂²	—	53	28	no	—
46	C₂²	C₂²×C₄×D₅₃	1	7	yes	—
47	C₄	—	53	28	no	—
48	C₄	C₄²×D₅₃	1	28	yes	direct product factor
49	C₂	—	53	8	no	—
50	C₂	C₂×C₄²×D₅₃	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₅₃
commutator, hypocenter	C₅₃	C₂×C₄³
Frattini	C₂³	C₂³×D₅₃
Fitting	C₄³×C₅₃	C₂
socle	C₂³×C₅₃	C₂⁴
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₄²×Dic₅₃	C₂	semidirect
3. C₄³×C₅₃	C₂	semidirect
6. C₄²×D₅₃	C₄	direct (N × H)
12. C₄²×C₅₃	C₂×C₄	semidirect
13. C₄×Dic₅₃	C₂×C₄	semidirect
18. C₄×D₅₃	C₄²	direct (N × H)
21. C₄×C₅₃	C₂×C₄²	semidirect
22. Dic₅₃	C₂×C₄²	semidirect
25. D₅₃	C₄³	direct (N × H)
28. C₄³	D₅₃	direct (N × H)
29. C₅₃	C₂×C₄³	semidirect
39. C₄²	C₄×D₅₃	direct (N × H)
48. C₄	C₄²×D₅₃	direct (N × H)

Subgroups — C43×D53 #20277036

Conjugacy classes of subgroups

Complements

Subgroups — C₄³×D₅₃ #20277036