Subgroups — C₅×C₉×D₇×C₄₃ #41029068

Order 27090.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₇×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₉×D₇×C₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₄₃	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×C₉×C₄₃	—	7	1	no	maximal, Hall
6	C₅×D₇×C₄₃	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₄₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₄₃	D₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×D₇×C₄₃	C₃×C₅	1	1	yes	characteristic
10	C₅×C₇×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₄₃	—	7	1	no	—
12	C₃×C₇×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic
13	C₂×C₉×C₄₃	—	7	1	no	Hall
14	C₃×C₅×C₄₃	C₃×D₇	1	1	yes	characteristic
15	C₅×C₉×D₇	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	D₇×C₄₃	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₄₃	—	7	1	no	Hall
18	C₉×C₄₃	C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₇×C₉	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
20	C₇×C₄₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₄₃	—	7	1	no	—
22	C₅×C₄₃	C₉×D₇	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×D₇	C₃×C₄₃	1	1	yes	characteristic
24	C₃×C₄₃	C₃×C₅×D₇	1	1	yes	characteristic
25	C₉×D₇	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅×C₇	C₂×C₃×C₄₃	1	1	yes	characteristic
27	C₂×C₅×C₉	—	7	1	no	Hall
28	C₂×C₄₃	—	7	1	no	Hall
29	C₅×D₇	C₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
30	C₇×C₉	C₂×C₅×C₄₃	1	1	yes	characteristic, complemented, Hall
31	C₅×C₉	D₇×C₄₃	1	1	yes	characteristic, direct product factor, Hall
32	C₄₃	C₅×C₉×D₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₃×D₇	C₃×C₅×C₄₃	1	1	yes	characteristic
34	C₅×C₇	C₂×C₉×C₄₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	—	7	1	no	—
36	C₃×C₇	C₂×C₃×C₅×C₄₃	1	1	yes	characteristic
37	C₂×C₉	—	7	1	no	Hall
38	C₃×C₅	C₃×D₇×C₄₃	1	1	yes	characteristic
39	D₇	C₅×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	—	7	1	no	Hall
41	C₉	C₅×D₇×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₅×C₉×C₄₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	7	1	no	—
44	C₅	C₉×D₇×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃×C₅×D₇×C₄₃	1	1	yes	characteristic
46	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉×C₄₃	D₇
commutator, hypocenter	C₇	C₂×C₅×C₉×C₄₃
Frattini	C₃	C₃×C₅×D₇×C₄₃
Fitting	C₅×C₇×C₉×C₄₃	C₂
socle	C₃×C₅×C₇×C₄₃	C₂×C₃
prime radical	C₃×C₅×D₇×C₄₃	C₃
cosocle	C₃×C₇	C₂×C₃×C₅×C₄₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₉×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₄₃	C₂	semidirect
3. C₉×D₇×C₄₃	C₅	direct (N × H)
6. C₅×D₇×C₄₃	C₉	direct (N × H)
7. C₇×C₉×C₄₃	C₂×C₅	semidirect
8. C₅×C₉×C₄₃	D₇	direct (N × H)
10. C₅×C₇×C₄₃	C₂×C₉	semidirect
15. C₅×C₉×D₇	C₄₃	direct (N × H)
16. D₇×C₄₃	C₅×C₉	direct (N × H)
18. C₉×C₄₃	C₅×D₇	direct (N × H)
19. C₅×C₇×C₉	C₂×C₄₃	semidirect
20. C₇×C₄₃	C₂×C₅×C₉	semidirect
22. C₅×C₄₃	C₉×D₇	direct (N × H)
25. C₉×D₇	C₅×C₄₃	direct (N × H)
29. C₅×D₇	C₉×C₄₃	direct (N × H)
30. C₇×C₉	C₂×C₅×C₄₃	semidirect
31. C₅×C₉	D₇×C₄₃	direct (N × H)
32. C₄₃	C₅×C₉×D₇	direct (N × H)
34. C₅×C₇	C₂×C₉×C₄₃	semidirect
39. D₇	C₅×C₉×C₄₃	direct (N × H)
41. C₉	C₅×D₇×C₄₃	direct (N × H)
42. C₇	C₂×C₅×C₉×C₄₃	semidirect
44. C₅	C₉×D₇×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
C₅×C₇×C₉×C₄₃	2
C₃×C₅×D₇×C₄₃	3
C₉×D₇×C₄₃	5
C₂×C₅×C₉×C₄₃	7
C₅×C₉×D₇	43

Subgroups — C5×C9×D7×C43 #41029068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×D₇×C₄₃ #41029068