Subgroups — C₅×C₁₃⋊C₃×D₈₃ #44569167

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, complemented, Hall
2	C₅×C₁₃×D₈₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×D₈₃	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, complemented, Hall
6	C₃×C₅×D₈₃	—	13	1	no	maximal, Hall
7	C₁₃×D₈₃	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	C₅×D₈₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃×D₈₃	—	13	1	no	Hall
12	C₅×C₈₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₁₃⋊C₃	—	83	1	no	maximal, Hall
14	C₃×C₈₃	—	13	1	no	Hall
15	C₅×C₁₃⋊C₃	D₈₃	1	1	yes	characteristic, direct product factor, Hall
16	D₈₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₃	—	83	1	no	Hall
18	C₈₃	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₃⋊C₃	—	83	1	no	Hall
20	C₅×C₁₃	C₃×D₈₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃⋊C₃	C₅×D₈₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅	—	1079	1	no	Hall
23	C₂×C₁₃	—	83	1	no	Hall
24	C₃×C₅	—	13	1	no	Hall
25	C₁₃	C₃×C₅×D₈₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	83	1	no	Hall
27	C₂×C₃	—	1079	1	no	Hall
28	C₅	C₁₃⋊C₃×D₈₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	13	1	no	Sylow
30	C₂	—	83	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₃⋊C₃×D₈₃
commutator, cosocle, hypocenter	C₁₃×C₈₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₈₃	C₂×C₃
LCS	G ▷ C₁₃×C₈₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃⋊C₃×C₈₃	C₂	semidirect
2. C₅×C₁₃×D₈₃	C₃	semidirect
3. C₁₃⋊C₃×D₈₃	C₅	direct (N × H)
4. C₅×C₁₃×C₈₃	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₈₃	C₂×C₅	semidirect
7. C₁₃×D₈₃	C₃×C₅	semidirect
9. C₁₃×C₈₃	C₂×C₃×C₅	semidirect
10. C₅×D₈₃	C₁₃⋊C₃	direct (N × H)
12. C₅×C₈₃	C₂×C₁₃⋊C₃	semidirect
15. C₅×C₁₃⋊C₃	D₈₃	direct (N × H)
16. D₈₃	C₅×C₁₃⋊C₃	direct (N × H)
18. C₈₃	C₂×C₅×C₁₃⋊C₃	semidirect
20. C₅×C₁₃	C₃×D₈₃	semidirect
21. C₁₃⋊C₃	C₅×D₈₃	direct (N × H)
25. C₁₃	C₃×C₅×D₈₃	semidirect
28. C₅	C₁₃⋊C₃×D₈₃	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
C₅×C₁₃×D₈₃	3
C₁₃⋊C₃×D₈₃	5
C₃×C₅×D₈₃	13
C₂×C₅×C₁₃⋊C₃	83

Subgroups — C5×C13⋊C3×D83 #44569167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃⋊C₃×D₈₃ #44569167