Subgroups — C₅×D₃₉×C₈₃ #44569161

Order 32370.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₃×C₈₃	—	3	1	no	maximal, Hall
3	D₃₉×C₈₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₈₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₈₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×C₈₃	—	13	1	no	maximal, Hall
7	D₁₃×C₈₃	—	3	1	no	Hall
8	C₃×C₅×C₈₃	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₈₃	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₈₃	—	39	1	no	Hall
11	D₃×C₈₃	—	13	1	no	Hall
12	C₅×C₈₃	D₃₉	1	1	yes	characteristic, direct product factor, Hall
13	C₅×D₃₉	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₈₃	C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₃	C₂×C₈₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₈₃	—	39	1	no	Hall
17	C₅×D₁₃	—	3	1	no	Hall
18	C₈₃	C₅×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
19	D₃₉	C₅×C₈₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₃	D₃×C₈₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₃	C₂×C₅×C₈₃	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	13	1	no	Hall
23	D₁₃	—	3	1	no	Hall
24	C₃×C₅	D₁₃×C₈₃	1	1	yes	characteristic, complemented, Hall
25	C₁₃	C₅×D₃×C₈₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	39	1	no	Hall
27	D₃	—	13	1	no	Hall
28	C₅	D₃₉×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₁₃×C₈₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	39	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₈₃	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₅×C₈₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₈₃	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₅×C₈₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×C₈₃	C₂	semidirect
3. D₃₉×C₈₃	C₅	direct (N × H)
4. C₅×C₁₃×C₈₃	D₃	semidirect
5. C₃×C₁₃×C₈₃	C₂×C₅	semidirect
8. C₃×C₅×C₈₃	D₁₃	semidirect
9. C₁₃×C₈₃	C₅×D₃	semidirect
12. C₅×C₈₃	D₃₉	direct (N × H)
13. C₅×D₃₉	C₈₃	direct (N × H)
14. C₃×C₈₃	C₅×D₁₃	semidirect
15. C₃×C₅×C₁₃	C₂×C₈₃	semidirect
18. C₈₃	C₅×D₃₉	direct (N × H)
19. D₃₉	C₅×C₈₃	direct (N × H)
20. C₅×C₁₃	D₃×C₈₃	semidirect
21. C₃×C₁₃	C₂×C₅×C₈₃	semidirect
24. C₃×C₅	D₁₃×C₈₃	semidirect
25. C₁₃	C₅×D₃×C₈₃	semidirect
28. C₅	D₃₉×C₈₃	direct (N × H)
29. C₃	C₅×D₁₃×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₃×C₈₃	2
C₅×D₁₃×C₈₃	3
D₃₉×C₈₃	5
C₅×D₃×C₈₃	13
C₅×D₃₉	83

Subgroups — C5×D39×C83 #44569161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₉×C₈₃ #44569161