Subgroups — C₃×#1043×C₁₀₃ #44525511

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	#1043×C₁₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×AGL(1,𝔽₅)×C₁₀₃	—	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	AGL(1,𝔽₅)×C₁₀₃	—	5	6	no	—
9	C₃×C₅×C₁₀₃	AGL(1,𝔽₅)	1	6	yes	complemented
10	C₃×C₄×C₁₀₃	—	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	C₄×C₁₀₃	—	25	1	no	Hall
15	C₃×C₁₀₃	#1043	1	1	yes	characteristic, direct product factor, Hall
16	C₃×#1043	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₃	—	25	1	no	—
18	C₃×C₅⋊D₅	C₂×C₁₀₃	1	1	yes	characteristic
19	C₁₀₃	C₃×#1043	1	1	yes	characteristic, direct product factor, Sylow
20	#1043	C₃×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅²	C₄×C₁₀₃	1	1	yes	characteristic, complemented, Hall
22	C₃×AGL(1,𝔽₅)	—	5	6	no	—
23	C₅⋊D₅	C₂×C₃×C₁₀₃	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	C₃×C₄×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	5	6	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₁₀₃	1	6	yes	complemented
28	C₃×C₄	—	25	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃×AGL(1,𝔽₅)×C₁₀₃	1	6	yes	complemented
32	C₄	—	25	1	no	Sylow
33	C₃	#1043×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. #1043×C₁₀₃	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	direct (N × H)
16. C₃×#1043	C₁₀₃	direct (N × H)
19. C₁₀₃	C₃×#1043	direct (N × H)
20. #1043	C₃×C₁₀₃	direct (N × H)
21. C₃×C₅²	C₄×C₁₀₃	semidirect
25. C₅²	C₃×C₄×C₁₀₃	semidirect
27. C₃×C₅	AGL(1,𝔽₅)×C₁₀₃	semidirect
31. C₅	C₃×AGL(1,𝔽₅)×C₁₀₃	semidirect
33. C₃	#1043×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
C₃×C₅⋊D₅×C₁₀₃	2
#1043×C₁₀₃	3
C₃×AGL(1,𝔽₅)×C₁₀₃	5
C₃×#1043	103

Subgroups — C3×#1043×C103 #44525511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1043×C₁₀₃ #44525511