Subgroups — D₃×D₁₃×C₅₃ #22551981

Order 8268.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₃×C₅₃	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₅₃	—	3	1	no	—
7	D₁₃×C₅₃	—	3	1	no	—
8	D₁₃×C₅₃	D₃	1	1	yes	characteristic, direct product factor
9	C₁₃×C₅₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃×C₅₃	—	13	1	no	maximal, Hall
11	C₂×C₃×C₅₃	—	13	1	no	—
12	D₃×C₅₃	—	13	1	no	—
13	D₃×C₅₃	D₁₃	1	1	yes	characteristic, direct product factor
14	C₂²×C₅₃	—	39	1	no	Hall
15	C₃×C₅₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	D₃×D₁₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅₃	—	3	1	no	—
18	C₂×C₅₃	—	13	1	no	—
19	C₂×C₅₃	—	39	1	no	—
20	D₃₉	C₂×C₅₃	1	1	yes	characteristic, complemented
21	C₃×D₁₃	C₂×C₅₃	1	1	yes	characteristic, complemented
22	D₃×C₁₃	C₂×C₅₃	1	1	yes	characteristic, complemented
23	C₅₃	D₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₁₃	—	3	1	no	Hall
25	C₃×C₁₃	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	3	1	no	—
27	D₁₃	—	3	1	no	—
28	D₁₃	D₃×C₅₃	1	1	yes	characteristic, direct product factor
29	C₁₃	C₂×D₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	13	1	no	Hall
31	C₂×C₃	—	13	1	no	—
32	D₃	—	13	1	no	—
33	D₃	D₁₃×C₅₃	1	1	yes	characteristic, direct product factor
34	C₂²	—	39	1	no	Sylow
35	C₃	C₂×D₁₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	13	1	no	—
38	C₂	—	39	1	no	—

	subgroup	G/H
center, hypercenter	C₅₃	D₃×D₁₃
commutator, hypocenter	C₃×C₁₃	C₂²×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₅₃	C₂²
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₅₃

Complements

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

N	H ≅ G/N	type
1. C₅₃×D₃₉	C₂	semidirect
2. D₃×C₁₃×C₅₃	C₂	semidirect
3. C₃×D₁₃×C₅₃	C₂	semidirect
5. C₃×C₁₃×C₅₃	C₂²	semidirect
8. D₁₃×C₅₃	D₃	direct (N × H)
9. C₁₃×C₅₃	C₂×D₃	semidirect
13. D₃×C₅₃	D₁₃	direct (N × H)
15. C₃×C₅₃	C₂×D₁₃	semidirect
16. D₃×D₁₃	C₅₃	direct (N × H)
20. D₃₉	C₂×C₅₃	semidirect
21. C₃×D₁₃	C₂×C₅₃	semidirect
22. D₃×C₁₃	C₂×C₅₃	semidirect
23. C₅₃	D₃×D₁₃	direct (N × H)
25. C₃×C₁₃	C₂²×C₅₃	semidirect
28. D₁₃	D₃×C₅₃	direct (N × H)
29. C₁₃	C₂×D₃×C₅₃	semidirect
33. D₃	D₁₃×C₅₃	direct (N × H)
35. C₃	C₂×D₁₃×C₅₃	semidirect

Subgroups — D3×D13×C53 #22551981

Conjugacy classes of subgroups

Complements

Subgroups — D₃×D₁₃×C₅₃ #22551981