Subgroups — C₂×C₃×C₁₉×D₄₇ #24924291

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×D₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×D₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₉×D₄₇	C₂×C₃	1	2	yes	direct product factor
7	C₁₉×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₄₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₄₇	C₂×C₁₉	1	1	yes	characteristic, complemented
10	C₃×D₄₇	C₂×C₁₉	1	2	yes	direct product factor
11	C₂²×C₃×C₁₉	—	47	1	no	maximal, Hall
12	C₂×D₄₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₄₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₉	—	47	2	no	—
15	C₂×C₃×C₁₉	D₄₇	1	1	yes	characteristic, direct product factor
16	C₂×C₄₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
17	D₄₇	C₂×C₃×C₁₉	1	2	yes	direct product factor
18	C₂²×C₁₉	—	47	1	no	Hall
19	C₃×C₁₉	C₂×D₄₇	1	1	yes	characteristic, direct product factor, Hall
20	C₄₇	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₉	—	47	2	no	—
22	C₂×C₁₉	C₃×D₄₇	1	1	yes	characteristic, direct product factor
23	C₁₉	C₂×C₃×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃	—	47	1	no	Hall
25	C₂×C₃	—	47	2	no	—
26	C₂×C₃	C₁₉×D₄₇	1	1	yes	characteristic, direct product factor
27	C₂²	—	47	1	no	Sylow
28	C₃	C₂×C₁₉×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	47	2	no	—
30	C₂	C₃×C₁₉×D₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₄₇	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×D₄₇	C₂	direct (N × H)
2. C₂×C₃×C₁₉×C₄₇	C₂	semidirect
3. C₂×C₁₉×D₄₇	C₃	direct (N × H)
4. C₃×C₁₉×C₄₇	C₂²	semidirect
5. C₂×C₁₉×C₄₇	C₂×C₃	semidirect
6. C₁₉×D₄₇	C₂×C₃	direct (N × H)
7. C₁₉×C₄₇	C₂²×C₃	semidirect
8. C₂×C₃×D₄₇	C₁₉	direct (N × H)
9. C₂×C₃×C₄₇	C₂×C₁₉	semidirect
10. C₃×D₄₇	C₂×C₁₉	direct (N × H)
12. C₂×D₄₇	C₃×C₁₉	direct (N × H)
13. C₃×C₄₇	C₂²×C₁₉	semidirect
15. C₂×C₃×C₁₉	D₄₇	direct (N × H)
16. C₂×C₄₇	C₂×C₃×C₁₉	semidirect
17. D₄₇	C₂×C₃×C₁₉	direct (N × H)
19. C₃×C₁₉	C₂×D₄₇	direct (N × H)
20. C₄₇	C₂²×C₃×C₁₉	semidirect
22. C₂×C₁₉	C₃×D₄₇	direct (N × H)
23. C₁₉	C₂×C₃×D₄₇	direct (N × H)
26. C₂×C₃	C₁₉×D₄₇	direct (N × H)
28. C₃	C₂×C₁₉×D₄₇	direct (N × H)
30. C₂	C₃×C₁₉×D₄₇	direct (N × H)

Subgroups — C2×C3×C19×D47 #24924291

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₁₉×D₄₇ #24924291