Subgroups — C₃×D₁₉×D₄₇ #24924275

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₈₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₈₉₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×D₄₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₉×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₄₇	—	19	1	no	maximal, Hall
11	C₂×C₃×C₄₇	—	19	1	no	—
12	C₃×D₄₇	—	19	1	no	—
13	C₃×D₄₇	D₁₉	1	1	yes	characteristic, direct product factor
14	C₂×C₃×D₁₉	—	47	1	no	maximal, Hall
15	C₂×D₄₇	—	19	1	no	Hall
16	C₃×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₉	—	47	1	no	—
18	C₃×D₁₉	—	47	1	no	—
19	C₃×D₁₉	D₄₇	1	1	yes	characteristic, direct product factor
20	C₂×C₄₇	—	19	1	no	—
21	D₄₇	—	19	1	no	—
22	D₄₇	C₃×D₁₉	1	1	yes	characteristic, direct product factor
23	C₂×D₁₉	—	47	1	no	Hall
24	C₃×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
25	C₄₇	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₉	—	47	1	no	—
27	D₁₉	—	47	1	no	—
28	D₁₉	C₃×D₄₇	1	1	yes	characteristic, direct product factor
29	C₁₉	C₂×C₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	893	1	no	Hall
31	C₂×C₃	—	19	1	no	—
32	C₂×C₃	—	47	1	no	—
33	C₂×C₃	—	893	1	no	—
34	C₂²	—	893	1	no	Sylow
35	C₃	D₁₉×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	19	1	no	—
37	C₂	—	47	1	no	—
38	C₂	—	893	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₉×D₄₇
commutator, cosocle, hypocenter	C₁₉×C₄₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₄₇	C₂²
LCS	G ▷ C₁₉×C₄₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₈₉₃	C₂	semidirect
2. C₃×D₁₉×C₄₇	C₂	semidirect
3. C₃×C₁₉×D₄₇	C₂	semidirect
4. D₁₉×D₄₇	C₃	direct (N × H)
5. C₃×C₁₉×C₄₇	C₂²	semidirect
6. D₈₉₃	C₂×C₃	semidirect
7. C₁₉×D₄₇	C₂×C₃	semidirect
8. D₁₉×C₄₇	C₂×C₃	semidirect
9. C₁₉×C₄₇	C₂²×C₃	semidirect
13. C₃×D₄₇	D₁₉	direct (N × H)
16. C₃×C₄₇	C₂×D₁₉	semidirect
19. C₃×D₁₉	D₄₇	direct (N × H)
22. D₄₇	C₃×D₁₉	direct (N × H)
24. C₃×C₁₉	C₂×D₄₇	semidirect
25. C₄₇	C₂×C₃×D₁₉	semidirect
28. D₁₉	C₃×D₄₇	direct (N × H)
29. C₁₉	C₂×C₃×D₄₇	semidirect
35. C₃	D₁₉×D₄₇	direct (N × H)

Subgroups — C3×D19×D47 #24924275

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₉×D₄₇ #24924275