Subgroups — C₃×C₁₀₃⋊#1043 #44525512

Order 30900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃⋊#1043	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₀₃⋊AGL(1,𝔽₅)	—	5	6	no	maximal
5	C₅⋊D₅×C₁₀₃	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₁₀₃	—	5	6	no	—
7	C₅²×C₁₀₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₁₀₃⋊AGL(1,𝔽₅)	—	5	6	no	—
9	C₃×C₅×C₁₀₃	AGL(1,𝔽₅)	1	6	yes	complemented
10	C₃×Dic₁₀₃	—	25	1	no	Hall
11	D₅×C₁₀₃	—	5	6	no	—
12	C₂×C₃×C₁₀₃	—	25	1	no	—
13	C₅×C₁₀₃	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
14	Dic₁₀₃	—	25	1	no	Hall
15	C₃×C₁₀₃	#1043	1	1	yes	characteristic, complemented, Hall
16	C₃×#1043	—	103	1	no	maximal, Hall
17	C₂×C₁₀₃	—	25	1	no	—
18	C₃×C₅⋊D₅	D₁₀₃	1	1	yes	characteristic
19	C₁₀₃	C₃×#1043	1	1	yes	characteristic, complemented, Sylow
20	#1043	—	103	1	no	Hall
21	C₃×C₅²	Dic₁₀₃	1	1	yes	characteristic, complemented, Hall
22	C₃×AGL(1,𝔽₅)	—	515	6	no	—
23	C₅⋊D₅	C₃×D₁₀₃	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	C₃×Dic₁₀₃	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	515	6	no	—
27	C₃×C₅	C₁₀₃⋊AGL(1,𝔽₅)	1	6	yes	complemented
28	C₃×C₄	—	2575	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃×C₁₀₃⋊AGL(1,𝔽₅)	1	6	yes	complemented
32	C₄	—	2575	1	no	Sylow
33	C₃	C₁₀₃⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₁₀₃⋊#1043
commutator, hypocenter	C₅²×C₁₀₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₀₃	C₄
prime radical	C₃×C₅⋊D₅×C₁₀₃	C₂
cosocle	C₅⋊D₅×C₁₀₃	C₂×C₃
LCS	G ▷ C₅²×C₁₀₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₁₀₃⋊#1043	C₃	direct (N × H)
3. C₃×C₅²×C₁₀₃	C₄	semidirect
7. C₅²×C₁₀₃	C₃×C₄	semidirect
9. C₃×C₅×C₁₀₃	AGL(1,𝔽₅)	semidirect
13. C₅×C₁₀₃	C₃×AGL(1,𝔽₅)	semidirect
15. C₃×C₁₀₃	#1043	semidirect
19. C₁₀₃	C₃×#1043	semidirect
21. C₃×C₅²	Dic₁₀₃	semidirect
25. C₅²	C₃×Dic₁₀₃	semidirect
27. C₃×C₅	C₁₀₃⋊AGL(1,𝔽₅)	semidirect
31. C₅	C₃×C₁₀₃⋊AGL(1,𝔽₅)	semidirect
33. C₃	C₁₀₃⋊#1043	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⋊D₅×C₁₀₃	2
C₁₀₃⋊#1043	3
C₃×C₁₀₃⋊AGL(1,𝔽₅)	5
C₃×#1043	103

Subgroups — C3×C103⋊#1043 #44525512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₀₃⋊#1043 #44525512