Subgroups — C₃×C₁₀₇⋊#1035 #44545613

Order 32100.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇⋊#1035	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₅×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₀₇⋊AGL(1,𝔽₅)	—	5	1	no	maximal
5	D₂₅×C₁₀₇	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₁₀₇	—	5	1	no	—
7	C₂₅×C₁₀₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₁₀₇⋊AGL(1,𝔽₅)	—	5	1	no	—
9	C₃×C₅×C₁₀₇	AGL(1,𝔽₅)	1	1	yes	characteristic
10	C₃×Dic₁₀₇	—	25	1	no	Hall
11	D₅×C₁₀₇	—	5	1	no	—
12	C₂×C₃×C₁₀₇	—	25	1	no	—
13	C₅×C₁₀₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
14	Dic₁₀₇	—	25	1	no	Hall
15	C₃×C₁₀₇	#1035	1	1	yes	characteristic, complemented, Hall
16	C₃×#1035	—	107	1	no	maximal, Hall
17	C₂×C₁₀₇	—	25	1	no	—
18	C₃×D₂₅	D₁₀₇	1	1	yes	characteristic
19	C₁₀₇	C₃×#1035	1	1	yes	characteristic, complemented, Sylow
20	#1035	—	107	1	no	Hall
21	C₃×C₂₅	Dic₁₀₇	1	1	yes	characteristic, complemented, Hall
22	C₃×AGL(1,𝔽₅)	—	535	1	no	—
23	D₂₅	C₃×D₁₀₇	1	1	yes	characteristic
24	C₃×D₅	—	5	1	no	—
25	C₂₅	C₃×Dic₁₀₇	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	535	1	no	—
27	C₃×C₅	C₁₀₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₃×C₄	—	2675	1	no	Hall
29	D₅	—	5	1	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃×C₁₀₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₄	—	2675	1	no	Sylow
33	C₃	C₁₀₇⋊#1035	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₁₀₇⋊#1035
commutator, hypocenter	C₂₅×C₁₀₇	C₃×C₄
Frattini	C₅	C₃×C₁₀₇⋊AGL(1,𝔽₅)
Fitting	C₃×C₂₅×C₁₀₇	C₄
socle	C₃×C₅×C₁₀₇	AGL(1,𝔽₅)
prime radical	C₃×D₂₅×C₁₀₇	C₂
cosocle	D₂₅×C₁₀₇	C₂×C₃
LCS	G ▷ C₂₅×C₁₀₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₁₀₇⋊#1035	C₃	direct (N × H)
3. C₃×C₂₅×C₁₀₇	C₄	semidirect
7. C₂₅×C₁₀₇	C₃×C₄	semidirect
15. C₃×C₁₀₇	#1035	semidirect
19. C₁₀₇	C₃×#1035	semidirect
21. C₃×C₂₅	Dic₁₀₇	semidirect
25. C₂₅	C₃×Dic₁₀₇	semidirect
33. C₃	C₁₀₇⋊#1035	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×D₂₅×C₁₀₇	2
C₁₀₇⋊#1035	3
C₃×C₁₀₇⋊AGL(1,𝔽₅)	5
C₃×#1035	107

Subgroups — C3×C107⋊#1035 #44545613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₀₇⋊#1035 #44545613