Subgroups — C₃×D₅₆₆₅ #46800922

Order 33990.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₆₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₁₃₃	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₁₀₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₃×D₅₁₅	—	11	1	no	maximal, Hall
7	D₁₁₃₃	—	5	1	no	Hall
8	C₃×C₅×C₁₀₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₁₀₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅₁₅	—	11	1	no	Hall
11	C₃×D₁₀₃	—	55	1	no	Hall
12	C₅×C₁₀₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×D₅₅	—	103	1	no	maximal, Hall
14	C₃×C₁₀₃	D₅₅	1	1	yes	characteristic, complemented, Hall
15	D₁₀₃	—	55	1	no	Hall
16	C₃×C₅×C₁₁	D₁₀₃	1	1	yes	characteristic, complemented, Hall
17	D₅₅	—	103	1	no	Hall
18	C₁₀₃	C₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₁₁	—	515	1	no	Hall
20	C₅×C₁₁	C₃×D₁₀₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	D₅₁₅	1	1	yes	characteristic, complemented, Hall
22	C₃×D₅	—	1133	1	no	Hall
23	D₁₁	—	515	1	no	Hall
24	C₃×C₅	D₁₁₃₃	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₃×D₅₁₅	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	1133	1	no	Hall
27	C₂×C₃	—	5665	1	no	Hall
28	C₅	C₃×D₁₁₃₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅₆₆₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	5665	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₆₆₅
commutator, cosocle, hypocenter	C₅×C₁₁×C₁₀₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₀₃	C₂
LCS	G ▷ C₅×C₁₁×C₁₀₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₁₀₃	C₂	semidirect
2. D₅₆₆₅	C₃	direct (N × H)
4. C₅×C₁₁×C₁₀₃	C₂×C₃	semidirect
5. C₃×C₁₁×C₁₀₃	D₅	semidirect
8. C₃×C₅×C₁₀₃	D₁₁	semidirect
9. C₁₁×C₁₀₃	C₃×D₅	semidirect
12. C₅×C₁₀₃	C₃×D₁₁	semidirect
14. C₃×C₁₀₃	D₅₅	semidirect
16. C₃×C₅×C₁₁	D₁₀₃	semidirect
18. C₁₀₃	C₃×D₅₅	semidirect
20. C₅×C₁₁	C₃×D₁₀₃	semidirect
21. C₃×C₁₁	D₅₁₅	semidirect
24. C₃×C₅	D₁₁₃₃	semidirect
25. C₁₁	C₃×D₅₁₅	semidirect
28. C₅	C₃×D₁₁₃₃	semidirect
29. C₃	D₅₆₆₅	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×C₁₀₃	2
D₅₆₆₅	3
C₃×D₁₁₃₃	5
C₃×D₅₁₅	11
C₃×D₅₅	103

Subgroups — C3×D5665 #46800922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₆₆₅ #46800922