Subgroups — C₃×D₅₁×C₁₀₃ #44538575

Order 31518.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₁×C₁₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₇×C₁₀₃	—	3	1	no	maximal
4	C₃×C₁₇×C₁₀₃	—	2	1	no	—
5	C₃×C₁₇×C₁₀₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₇×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₇×C₁₀₃	—	3	1	no	Hall
8	C₃×D₃×C₁₀₃	—	17	1	no	maximal, Hall
9	C₁₇×C₁₀₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₀₃	D₁₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₀₃	—	51	1	no	—
12	D₃×C₁₀₃	—	17	1	no	—
13	C₃×C₁₀₃	—	2	1	no	—
14	C₃×C₁₀₃	C₃×D₁₇	1	1	yes	characteristic, complemented
15	C₃×C₁₀₃	D₅₁	1	1	yes	characteristic, direct product factor
16	C₃×D₅₁	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₃	—	51	1	no	Hall
18	C₃²×C₁₇	C₂×C₁₀₃	1	1	yes	characteristic, complemented, Hall
19	C₁₀₃	C₃×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
20	D₅₁	C₃×C₁₀₃	1	1	yes	characteristic, direct product factor
21	C₃×D₁₇	—	3	1	no	—
22	C₃×C₁₇	—	2	1	no	—
23	C₃×C₁₇	D₃×C₁₀₃	1	1	yes	characteristic, complemented
24	C₃×C₁₇	C₂×C₃×C₁₀₃	1	1	yes	characteristic, complemented
25	D₁₇	—	3	1	no	Hall
26	C₃×D₃	—	17	1	no	Hall
27	C₁₇	C₃×D₃×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
28	C₃²	D₁₇×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	51	1	no	—
30	D₃	—	17	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₇×C₁₀₃	1	1	yes	characteristic, complemented
33	C₃	D₅₁×C₁₀₃	1	1	yes	characteristic, direct product factor
34	C₂	—	51	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₀₃	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₃×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₁₀₃	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₃×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇×C₁₀₃	C₂	semidirect
2. D₅₁×C₁₀₃	C₃	direct (N × H)
5. C₃×C₁₇×C₁₀₃	D₃	semidirect
6. C₃×C₁₇×C₁₀₃	C₂×C₃	semidirect
9. C₁₇×C₁₀₃	C₃×D₃	semidirect
10. C₃²×C₁₀₃	D₁₇	semidirect
14. C₃×C₁₀₃	C₃×D₁₇	semidirect
15. C₃×C₁₀₃	D₅₁	direct (N × H)
16. C₃×D₅₁	C₁₀₃	direct (N × H)
18. C₃²×C₁₇	C₂×C₁₀₃	semidirect
19. C₁₀₃	C₃×D₅₁	direct (N × H)
20. D₅₁	C₃×C₁₀₃	direct (N × H)
23. C₃×C₁₇	D₃×C₁₀₃	semidirect
24. C₃×C₁₇	C₂×C₃×C₁₀₃	semidirect
27. C₁₇	C₃×D₃×C₁₀₃	semidirect
28. C₃²	D₁₇×C₁₀₃	semidirect
32. C₃	C₃×D₁₇×C₁₀₃	semidirect
33. C₃	D₅₁×C₁₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×C₁₀₃	2
D₅₁×C₁₀₃	3
C₃×D₁₇×C₁₀₃	3
C₃×D₃×C₁₀₃	17
C₃×D₅₁	103

Subgroups — C3×D51×C103 #44538575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₁×C₁₀₃ #44538575