Subgroups — C₃×D₅×C₁₁×C₁₀₁ #45686779

Order 33330.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₁×C₁₀₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₁₁×C₁₀₁	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₁₀₁	D₅	1	1	yes	characteristic, direct product factor, Hall
6	C₃×D₅×C₁₀₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₁₀₁	—	5	1	no	Hall
8	C₃×C₅×C₁₀₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₁₀₁	C₃×D₅	1	1	yes	characteristic, direct product factor, Hall
10	D₅×C₁₀₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₁₀₁	—	5	1	no	Hall
12	C₅×C₁₀₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×D₅×C₁₁	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₁₀₁	D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₀₁	—	5	1	no	Hall
16	C₃×C₅×C₁₁	C₂×C₁₀₁	1	1	yes	characteristic, complemented, Hall
17	D₅×C₁₁	C₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₀₁	C₃×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃×C₁₁	—	5	1	no	Hall
20	C₅×C₁₁	C₂×C₃×C₁₀₁	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	D₅×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
22	C₃×D₅	C₁₁×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₁	—	5	1	no	Hall
24	C₃×C₅	C₂×C₁₁×C₁₀₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₃×D₅×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	C₃×C₁₁×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	5	1	no	Hall
28	C₅	C₂×C₃×C₁₁×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅×C₁₁×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₁₀₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₁₁×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₀₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₁₁×C₁₀₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₁₀₁	C₂	semidirect
2. D₅×C₁₁×C₁₀₁	C₃	direct (N × H)
4. C₅×C₁₁×C₁₀₁	C₂×C₃	semidirect
5. C₃×C₁₁×C₁₀₁	D₅	direct (N × H)
6. C₃×D₅×C₁₀₁	C₁₁	direct (N × H)
8. C₃×C₅×C₁₀₁	C₂×C₁₁	semidirect
9. C₁₁×C₁₀₁	C₃×D₅	direct (N × H)
10. D₅×C₁₀₁	C₃×C₁₁	direct (N × H)
12. C₅×C₁₀₁	C₂×C₃×C₁₁	semidirect
13. C₃×D₅×C₁₁	C₁₀₁	direct (N × H)
14. C₃×C₁₀₁	D₅×C₁₁	direct (N × H)
16. C₃×C₅×C₁₁	C₂×C₁₀₁	semidirect
17. D₅×C₁₁	C₃×C₁₀₁	direct (N × H)
18. C₁₀₁	C₃×D₅×C₁₁	direct (N × H)
20. C₅×C₁₁	C₂×C₃×C₁₀₁	semidirect
21. C₃×C₁₁	D₅×C₁₀₁	direct (N × H)
22. C₃×D₅	C₁₁×C₁₀₁	direct (N × H)
24. C₃×C₅	C₂×C₁₁×C₁₀₁	semidirect
25. C₁₁	C₃×D₅×C₁₀₁	direct (N × H)
26. D₅	C₃×C₁₁×C₁₀₁	direct (N × H)
28. C₅	C₂×C₃×C₁₁×C₁₀₁	semidirect
29. C₃	D₅×C₁₁×C₁₀₁	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×C₁₁×C₁₀₁	2
D₅×C₁₁×C₁₀₁	3
C₂×C₃×C₁₁×C₁₀₁	5
C₃×D₅×C₁₀₁	11
C₃×D₅×C₁₁	101

Subgroups — C3×D5×C11×C101 #45686779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₁₁×C₁₀₁ #45686779