Subgroups — C₂²×C₅×C₁₃×C₄₃⋊C₃ #46776598

Order 33540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×C₄₃⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅×C₁₃×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₁₃×C₄₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₃×C₄₃	C₂×C₃	1	3	yes	complemented
6	C₂×C₁₃×C₄₃⋊C₃	C₂×C₅	1	3	yes	direct product factor
7	C₅×C₁₃×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₅×C₄₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₁₃×C₄₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₁₃×C₄₃⋊C₃	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₄₃⋊C₃	C₂×C₁₃	1	3	yes	direct product factor
12	C₂×C₁₃×C₄₃	C₂×C₃×C₅	1	3	yes	complemented
13	C₂²×C₅×C₄₃	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₃×C₅×C₁₃	—	43	1	no	maximal, Hall
15	C₅×C₄₃⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₁₃×C₄₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₄₃⋊C₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₄₃	C₂×C₃×C₁₃	1	3	yes	complemented
19	C₂×C₃×C₅×C₁₃	—	43	3	no	—
20	C₂²×C₅×C₁₃	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₄₃⋊C₃	C₂×C₅×C₁₃	1	3	yes	direct product factor
22	C₅×C₄₃	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	—	43	1	no	Hall
24	C₂²×C₄₃	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₃×C₁₃	—	43	1	no	Hall
26	C₂×C₅×C₁₃	C₂×C₄₃⋊C₃	1	3	yes	direct product factor
27	C₄₃⋊C₃	C₂²×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₄₃	C₂×C₃×C₅×C₁₃	1	3	yes	complemented
29	C₂×C₃×C₁₃	—	43	3	no	—
30	C₅×C₁₃	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂²×C₃×C₅	—	43	1	no	Hall
32	C₂²×C₁₃	C₅×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
33	C₄₃	C₂²×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₃	—	43	1	no	Hall
35	C₂×C₃×C₅	—	43	3	no	—
36	C₂×C₁₃	C₂×C₅×C₄₃⋊C₃	1	3	yes	direct product factor
37	C₂²×C₅	C₁₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	—	43	1	no	Hall
39	C₁₃	C₂²×C₅×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²×C₃	—	43	1	no	Hall
41	C₂×C₅	C₂×C₁₃×C₄₃⋊C₃	1	3	yes	direct product factor
42	C₂×C₃	—	43	3	no	—
43	C₅	C₂²×C₁₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	C₅×C₁₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	43	1	no	Sylow
46	C₂	C₂×C₅×C₁₃×C₄₃⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅×C₁₃	C₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₂²×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃×C₄₃	C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂²×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₃×C₄₃⋊C₃	C₂	direct (N × H)
2. C₂²×C₅×C₁₃×C₄₃	C₃	semidirect
3. C₅×C₁₃×C₄₃⋊C₃	C₂²	direct (N × H)
4. C₂²×C₁₃×C₄₃⋊C₃	C₅	direct (N × H)
5. C₂×C₅×C₁₃×C₄₃	C₂×C₃	semidirect
6. C₂×C₁₃×C₄₃⋊C₃	C₂×C₅	direct (N × H)
7. C₅×C₁₃×C₄₃	C₂²×C₃	semidirect
8. C₂²×C₅×C₄₃⋊C₃	C₁₃	direct (N × H)
9. C₂²×C₁₃×C₄₃	C₃×C₅	semidirect
10. C₁₃×C₄₃⋊C₃	C₂²×C₅	direct (N × H)
11. C₂×C₅×C₄₃⋊C₃	C₂×C₁₃	direct (N × H)
12. C₂×C₁₃×C₄₃	C₂×C₃×C₅	semidirect
13. C₂²×C₅×C₄₃	C₃×C₁₃	semidirect
15. C₅×C₄₃⋊C₃	C₂²×C₁₃	direct (N × H)
16. C₁₃×C₄₃	C₂²×C₃×C₅	semidirect
17. C₂²×C₄₃⋊C₃	C₅×C₁₃	direct (N × H)
18. C₂×C₅×C₄₃	C₂×C₃×C₁₃	semidirect
20. C₂²×C₅×C₁₃	C₄₃⋊C₃	direct (N × H)
21. C₂×C₄₃⋊C₃	C₂×C₅×C₁₃	direct (N × H)
22. C₅×C₄₃	C₂²×C₃×C₁₃	semidirect
24. C₂²×C₄₃	C₃×C₅×C₁₃	semidirect
26. C₂×C₅×C₁₃	C₂×C₄₃⋊C₃	direct (N × H)
27. C₄₃⋊C₃	C₂²×C₅×C₁₃	direct (N × H)
28. C₂×C₄₃	C₂×C₃×C₅×C₁₃	semidirect
30. C₅×C₁₃	C₂²×C₄₃⋊C₃	direct (N × H)
32. C₂²×C₁₃	C₅×C₄₃⋊C₃	direct (N × H)
33. C₄₃	C₂²×C₃×C₅×C₁₃	semidirect
36. C₂×C₁₃	C₂×C₅×C₄₃⋊C₃	direct (N × H)
37. C₂²×C₅	C₁₃×C₄₃⋊C₃	direct (N × H)
39. C₁₃	C₂²×C₅×C₄₃⋊C₃	direct (N × H)
41. C₂×C₅	C₂×C₁₃×C₄₃⋊C₃	direct (N × H)
43. C₅	C₂²×C₁₃×C₄₃⋊C₃	direct (N × H)
44. C₂²	C₅×C₁₃×C₄₃⋊C₃	direct (N × H)
46. C₂	C₂×C₅×C₁₃×C₄₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₃×C₄₃⋊C₃	2
C₂²×C₅×C₁₃×C₄₃	3
C₂²×C₁₃×C₄₃⋊C₃	5
C₂²×C₅×C₄₃⋊C₃	13
C₂²×C₃×C₅×C₁₃	43

Subgroups — C22×C5×C13×C43⋊C3 #46776598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₁₃×C₄₃⋊C₃ #46776598