Subgroups — C₂×C₅×C₁₃⋊C₃×C₈₃ #44569151

Order 32370.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃⋊C₃×C₈₃	C₂	direct (N × H)
2. C₂×C₅×C₁₃×C₈₃	C₃	semidirect
3. C₂×C₁₃⋊C₃×C₈₃	C₅	direct (N × H)
4. C₅×C₁₃×C₈₃	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₈₃	C₂×C₅	direct (N × H)
7. C₂×C₁₃×C₈₃	C₃×C₅	semidirect
9. C₁₃×C₈₃	C₂×C₃×C₅	semidirect
10. C₂×C₅×C₈₃	C₁₃⋊C₃	direct (N × H)
12. C₅×C₈₃	C₂×C₁₃⋊C₃	direct (N × H)
13. C₂×C₅×C₁₃⋊C₃	C₈₃	direct (N × H)
15. C₅×C₁₃⋊C₃	C₂×C₈₃	direct (N × H)
16. C₂×C₈₃	C₅×C₁₃⋊C₃	direct (N × H)
17. C₂×C₅×C₁₃	C₃×C₈₃	semidirect
18. C₈₃	C₂×C₅×C₁₃⋊C₃	direct (N × H)
19. C₂×C₁₃⋊C₃	C₅×C₈₃	direct (N × H)
20. C₅×C₁₃	C₂×C₃×C₈₃	semidirect
21. C₁₃⋊C₃	C₂×C₅×C₈₃	direct (N × H)
23. C₂×C₁₃	C₃×C₅×C₈₃	semidirect
25. C₁₃	C₂×C₃×C₅×C₈₃	semidirect
26. C₂×C₅	C₁₃⋊C₃×C₈₃	direct (N × H)
28. C₅	C₂×C₁₃⋊C₃×C₈₃	direct (N × H)
30. C₂	C₅×C₁₃⋊C₃×C₈₃	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×C₁₃⋊C₃×C₈₃	2
C₂×C₅×C₁₃×C₈₃	3
C₂×C₁₃⋊C₃×C₈₃	5
C₂×C₃×C₅×C₈₃	13
C₂×C₅×C₁₃⋊C₃	83

Subgroups — C2×C5×C13⋊C3×C83 #44569151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₃⋊C₃×C₈₃ #44569151