Subgroups — C₂×D₉×C₁₉×C₄₃ #44440899

Order 29412.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉×C₁₉×C₄₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₉×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₉×C₄₃	—	3	1	no	maximal
4	C₉×C₁₉×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₁₉×C₄₃	—	3	2	no	—
6	C₂×C₃×C₁₉×C₄₃	D₃	1	1	yes	characteristic
7	C₂²×C₁₉×C₄₃	—	9	1	no	Hall
8	C₃×C₁₉×C₄₃	C₂×D₃	1	1	yes	characteristic
9	C₂×C₁₉×C₄₃	—	9	2	no	—
10	C₂×C₁₉×C₄₃	D₉	1	1	yes	characteristic, direct product factor
11	C₂×D₉×C₄₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₉×C₄₃	C₂×D₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₉×C₄₃	C₂×C₁₉	1	1	yes	characteristic, complemented
14	D₉×C₄₃	C₂×C₁₉	1	2	yes	direct product factor
15	C₂×D₉×C₁₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×D₃×C₄₃	—	3	1	no	—
17	C₉×C₄₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₉×C₁₉	C₂×C₄₃	1	1	yes	characteristic, complemented
19	D₉×C₁₉	C₂×C₄₃	1	2	yes	direct product factor
20	C₂×C₃×C₄₃	D₃×C₁₉	1	1	yes	characteristic
21	D₃×C₄₃	—	3	2	no	—
22	C₂×D₃×C₁₉	—	3	1	no	—
23	C₂²×C₄₃	—	9	1	no	Hall
24	C₉×C₁₉	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₃	C₂×D₃×C₁₉	1	1	yes	characteristic
26	C₂×C₃×C₁₉	D₃×C₄₃	1	1	yes	characteristic
27	D₃×C₁₉	—	3	2	no	—
28	C₂×C₄₃	—	9	2	no	—
29	C₂×C₄₃	D₉×C₁₉	1	1	yes	characteristic, direct product factor
30	C₂²×C₁₉	—	9	1	no	Hall
31	C₃×C₁₉	C₂×D₃×C₄₃	1	1	yes	characteristic
32	C₄₃	C₂×D₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₁₉	—	9	2	no	—
34	C₂×C₁₉	D₉×C₄₃	1	1	yes	characteristic, direct product factor
35	C₂×D₉	C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
36	C₁₉	C₂×D₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₉	C₂×C₁₉×C₄₃	1	1	yes	characteristic, complemented
38	D₉	C₂×C₁₉×C₄₃	1	2	yes	direct product factor
39	C₂×D₃	—	3	1	no	—
40	C₉	C₂²×C₁₉×C₄₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃×C₁₉×C₄₃	1	1	yes	characteristic
42	D₃	—	3	2	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₉×C₄₃	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	D₉×C₁₉×C₄₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₄₃	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₁₉×C₄₃
Frattini	C₃	C₂×D₃×C₁₉×C₄₃
Fitting	C₂×C₉×C₁₉×C₄₃	C₂
socle	C₂×C₃×C₁₉×C₄₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉×C₄₃

Complements

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

N	H ≅ G/N	type
1. D₉×C₁₉×C₄₃	C₂	direct (N × H)
2. C₂×C₉×C₁₉×C₄₃	C₂	semidirect
4. C₉×C₁₉×C₄₃	C₂²	semidirect
10. C₂×C₁₉×C₄₃	D₉	direct (N × H)
11. C₂×D₉×C₄₃	C₁₉	direct (N × H)
12. C₁₉×C₄₃	C₂×D₉	direct (N × H)
13. C₂×C₉×C₄₃	C₂×C₁₉	semidirect
14. D₉×C₄₃	C₂×C₁₉	direct (N × H)
15. C₂×D₉×C₁₉	C₄₃	direct (N × H)
17. C₉×C₄₃	C₂²×C₁₉	semidirect
18. C₂×C₉×C₁₉	C₂×C₄₃	semidirect
19. D₉×C₁₉	C₂×C₄₃	direct (N × H)
24. C₉×C₁₉	C₂²×C₄₃	semidirect
29. C₂×C₄₃	D₉×C₁₉	direct (N × H)
32. C₄₃	C₂×D₉×C₁₉	direct (N × H)
34. C₂×C₁₉	D₉×C₄₃	direct (N × H)
35. C₂×D₉	C₁₉×C₄₃	direct (N × H)
36. C₁₉	C₂×D₉×C₄₃	direct (N × H)
37. C₂×C₉	C₂×C₁₉×C₄₃	semidirect
38. D₉	C₂×C₁₉×C₄₃	direct (N × H)
40. C₉	C₂²×C₁₉×C₄₃	semidirect
46. C₂	D₉×C₁₉×C₄₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₉×C₁₉×C₄₃	2
C₂×C₉×C₁₉×C₄₃	2
C₂×D₃×C₁₉×C₄₃	3
C₂×D₉×C₄₃	19
C₂×D₉×C₁₉	43

Subgroups — C2×D9×C19×C43 #44440899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉×C₁₉×C₄₃ #44440899