Subgroups — C₂×D₃×C₁₉×C₄₇ #24924288

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₉×C₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×C₄₇	—	3	1	no	maximal, Hall
4	C₃×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₄₇	—	3	2	no	—
6	C₂×C₁₉×C₄₇	D₃	1	1	yes	characteristic, direct product factor
7	C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×D₃×C₄₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₄₇	C₂×C₁₉	1	1	yes	characteristic, complemented
10	D₃×C₄₇	C₂×C₁₉	1	2	yes	direct product factor
11	C₂×D₃×C₁₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₄₇	—	3	1	no	Hall
13	C₃×C₄₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₉	C₂×C₄₇	1	1	yes	characteristic, complemented
15	D₃×C₁₉	C₂×C₄₇	1	2	yes	direct product factor
16	C₂×C₄₇	—	3	2	no	—
17	C₂×C₄₇	D₃×C₁₉	1	1	yes	characteristic, direct product factor
18	C₂²×C₁₉	—	3	1	no	Hall
19	C₃×C₁₉	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
20	C₄₇	C₂×D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₁₉	—	3	2	no	—
22	C₂×C₁₉	D₃×C₄₇	1	1	yes	characteristic, direct product factor
23	C₁₉	C₂×D₃×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃	C₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃	C₂×C₁₉×C₄₇	1	1	yes	characteristic, complemented
26	D₃	C₂×C₁₉×C₄₇	1	2	yes	direct product factor
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₁₉×C₄₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	D₃×C₁₉×C₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₄₇	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₁₉×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₄₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₉×C₄₇

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₉×C₄₇	C₂	direct (N × H)
2. C₂×C₃×C₁₉×C₄₇	C₂	semidirect
4. C₃×C₁₉×C₄₇	C₂²	semidirect
6. C₂×C₁₉×C₄₇	D₃	direct (N × H)
7. C₁₉×C₄₇	C₂×D₃	direct (N × H)
8. C₂×D₃×C₄₇	C₁₉	direct (N × H)
9. C₂×C₃×C₄₇	C₂×C₁₉	semidirect
10. D₃×C₄₇	C₂×C₁₉	direct (N × H)
11. C₂×D₃×C₁₉	C₄₇	direct (N × H)
13. C₃×C₄₇	C₂²×C₁₉	semidirect
14. C₂×C₃×C₁₉	C₂×C₄₇	semidirect
15. D₃×C₁₉	C₂×C₄₇	direct (N × H)
17. C₂×C₄₇	D₃×C₁₉	direct (N × H)
19. C₃×C₁₉	C₂²×C₄₇	semidirect
20. C₄₇	C₂×D₃×C₁₉	direct (N × H)
22. C₂×C₁₉	D₃×C₄₇	direct (N × H)
23. C₁₉	C₂×D₃×C₄₇	direct (N × H)
24. C₂×D₃	C₁₉×C₄₇	direct (N × H)
25. C₂×C₃	C₂×C₁₉×C₄₇	semidirect
26. D₃	C₂×C₁₉×C₄₇	direct (N × H)
28. C₃	C₂²×C₁₉×C₄₇	semidirect
30. C₂	D₃×C₁₉×C₄₇	direct (N × H)

Subgroups — C2×D3×C19×C47 #24924288

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₃×C₁₉×C₄₇ #24924288