Subgroups — C₂×C₃×C₅×C₉×C₄₃ #72190045

Order 11610.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₉×C₄₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₉×C₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃²×C₅×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₂×C₅×C₉×C₄₃	C₃	1	3	yes	maximal, direct product factor
5	C₃²×C₅×C₄₃	C₂×C₃	1	1	yes	characteristic
6	C₅×C₉×C₄₃	C₂×C₃	1	3	yes	direct product factor
7	C₂×C₃×C₅×C₄₃	C₉	1	3	yes	direct product factor
8	C₂×C₃×C₅×C₄₃	C₃²	1	1	yes	characteristic
9	C₃×C₉×C₄₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃²×C₄₃	C₃×C₅	1	1	yes	characteristic
11	C₂×C₉×C₄₃	C₃×C₅	1	3	yes	direct product factor
12	C₃×C₅×C₄₃	C₂×C₉	1	3	yes	direct product factor
13	C₃×C₅×C₄₃	C₂×C₃²	1	1	yes	characteristic
14	C₂×C₅×C₄₃	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃²×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic
16	C₉×C₄₃	C₂×C₃×C₅	1	3	yes	direct product factor
17	C₂×C₃×C₅×C₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₃×C₄₃	C₅×C₉	1	3	yes	direct product factor
19	C₂×C₃×C₄₃	C₃²×C₅	1	1	yes	characteristic
20	C₅×C₄₃	C₂×C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅×C₉	C₂×C₄₃	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₄₃	C₂×C₅×C₉	1	3	yes	direct product factor
23	C₃×C₄₃	C₂×C₃²×C₅	1	1	yes	characteristic
24	C₂×C₃²×C₅	C₃×C₄₃	1	1	yes	characteristic
25	C₂×C₅×C₉	C₃×C₄₃	1	3	yes	direct product factor
26	C₂×C₄₃	C₃×C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃×C₉	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
28	C₃²×C₅	C₂×C₃×C₄₃	1	1	yes	characteristic
29	C₅×C₉	C₂×C₃×C₄₃	1	3	yes	direct product factor
30	C₄₃	C₂×C₃×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃×C₅	C₉×C₄₃	1	3	yes	direct product factor
32	C₂×C₃×C₅	C₃²×C₄₃	1	1	yes	characteristic
33	C₃×C₉	C₂×C₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃²	C₃×C₅×C₄₃	1	1	yes	characteristic
35	C₂×C₉	C₃×C₅×C₄₃	1	3	yes	direct product factor
36	C₃×C₅	C₂×C₉×C₄₃	1	3	yes	direct product factor
37	C₃×C₅	C₂×C₃²×C₄₃	1	1	yes	characteristic
38	C₂×C₅	C₃×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
39	C₃²	C₂×C₃×C₅×C₄₃	1	1	yes	characteristic
40	C₉	C₂×C₃×C₅×C₄₃	1	3	yes	direct product factor
41	C₂×C₃	C₅×C₉×C₄₃	1	3	yes	direct product factor
42	C₂×C₃	C₃²×C₅×C₄₃	1	1	yes	characteristic
43	C₅	C₂×C₃×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	C₂×C₅×C₉×C₄₃	1	3	yes	direct product factor
45	C₃	C₂×C₃²×C₅×C₄₃	1	1	yes	characteristic
46	C₂	C₃×C₅×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃²×C₅×C₄₃
socle, prime radical	C₂×C₃²×C₅×C₄₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₉×C₄₃	C₂	direct (N × H)
2. C₂×C₃×C₉×C₄₃	C₅	direct (N × H)
4. C₂×C₅×C₉×C₄₃	C₃	direct (N × H)
6. C₅×C₉×C₄₃	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₄₃	C₉	direct (N × H)
9. C₃×C₉×C₄₃	C₂×C₅	direct (N × H)
11. C₂×C₉×C₄₃	C₃×C₅	direct (N × H)
12. C₃×C₅×C₄₃	C₂×C₉	direct (N × H)
14. C₂×C₅×C₄₃	C₃×C₉	direct (N × H)
16. C₉×C₄₃	C₂×C₃×C₅	direct (N × H)
17. C₂×C₃×C₅×C₉	C₄₃	direct (N × H)
18. C₂×C₃×C₄₃	C₅×C₉	direct (N × H)
20. C₅×C₄₃	C₂×C₃×C₉	direct (N × H)
21. C₃×C₅×C₉	C₂×C₄₃	direct (N × H)
22. C₃×C₄₃	C₂×C₅×C₉	direct (N × H)
25. C₂×C₅×C₉	C₃×C₄₃	direct (N × H)
26. C₂×C₄₃	C₃×C₅×C₉	direct (N × H)
27. C₂×C₃×C₉	C₅×C₄₃	direct (N × H)
29. C₅×C₉	C₂×C₃×C₄₃	direct (N × H)
30. C₄₃	C₂×C₃×C₅×C₉	direct (N × H)
31. C₂×C₃×C₅	C₉×C₄₃	direct (N × H)
33. C₃×C₉	C₂×C₅×C₄₃	direct (N × H)
35. C₂×C₉	C₃×C₅×C₄₃	direct (N × H)
36. C₃×C₅	C₂×C₉×C₄₃	direct (N × H)
38. C₂×C₅	C₃×C₉×C₄₃	direct (N × H)
40. C₉	C₂×C₃×C₅×C₄₃	direct (N × H)
41. C₂×C₃	C₅×C₉×C₄₃	direct (N × H)
43. C₅	C₂×C₃×C₉×C₄₃	direct (N × H)
44. C₃	C₂×C₅×C₉×C₄₃	direct (N × H)
46. C₂	C₃×C₅×C₉×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
C₃×C₅×C₉×C₄₃	2
C₂×C₃×C₉×C₄₃	5
C₂×C₃²×C₅×C₄₃	3
C₂×C₅×C₉×C₄₃	3
C₂×C₃×C₅×C₉	43

Subgroups — C2×C3×C5×C9×C43 #72190045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₉×C₄₃ #72190045