Subgroups — D₃₉×D₅₃ #22551980

Order 8268.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₀₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₅₃	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₆₈₉	—	3	1	no	—
7	C₁₃×D₅₃	D₃	1	1	yes	characteristic, complemented
8	D₁₃×C₅₃	—	3	1	no	—
9	C₁₃×C₅₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₅₃	—	13	1	no	maximal, Hall
11	D₁₅₉	—	13	1	no	—
12	C₃×D₅₃	D₁₃	1	1	yes	characteristic, complemented
13	D₃×C₅₃	—	13	1	no	—
14	C₂×D₅₃	—	39	1	no	Hall
15	C₃×C₅₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₉	—	53	1	no	maximal, Hall
17	C₂×C₅₃	—	39	1	no	—
18	D₅₃	—	39	1	no	—
19	D₅₃	D₃₉	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₁₃	—	53	1	no	—
21	D₃₉	—	53	1	no	—
22	D₃₉	D₅₃	1	1	yes	characteristic, direct product factor
23	C₅₃	C₂×D₃₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₃	—	159	1	no	Hall
25	C₃×C₁₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	53	1	no	—
27	D₁₃	—	3	1	no	—
28	D₁₃	—	159	1	no	—
29	C₁₃	D₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	689	1	no	Hall
31	C₂×C₃	—	53	1	no	—
32	D₃	—	13	1	no	—
33	D₃	—	689	1	no	—
34	C₂²	—	2067	1	no	Sylow
35	C₃	D₁₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	2067	1	no	—
37	C₂	—	39	1	no	—
38	C₂	—	53	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₂₀₆₇	C₂	semidirect
2. C₅₃×D₃₉	C₂	semidirect
3. C₃×C₁₃×D₅₃	C₂	semidirect
5. C₃×C₁₃×C₅₃	C₂²	semidirect
7. C₁₃×D₅₃	D₃	semidirect
9. C₁₃×C₅₃	C₂×D₃	semidirect
12. C₃×D₅₃	D₁₃	semidirect
15. C₃×C₅₃	C₂×D₁₃	semidirect
19. D₅₃	D₃₉	direct (N × H)
22. D₃₉	D₅₃	direct (N × H)
23. C₅₃	C₂×D₃₉	semidirect
25. C₃×C₁₃	C₂×D₅₃	semidirect
29. C₁₃	D₃×D₅₃	semidirect
35. C₃	D₁₃×D₅₃	semidirect

Subgroups — D39×D53 #22551980

Conjugacy classes of subgroups

Complements

Subgroups — D₃₉×D₅₃ #22551980