Subgroups — C₃⋊(C₁₀₇⋊#1044) #44545702

Order 32100.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇⋊#1044	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₁₀₇⋊AGL(1,𝔽₅))	—	5	2	no	maximal
5	C₅⋊D₅×C₁₀₇	D₃	1	1	yes	characteristic
6	C₃×D₅×C₁₀₇	—	5	2	no	—
7	C₃×D₅×C₁₀₇	—	10	2	no	—
8	C₅²×C₁₀₇	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₁₀₇⋊AGL(1,𝔽₅)	—	15	2	no	—
10	C₃×C₅×C₁₀₇	—	2	2	no	—
11	C₃×C₅×C₁₀₇	AGL(1,𝔽₅)	1	2	yes	complemented
12	Dic₃₂₁	—	25	1	no	Hall
13	D₅×C₁₀₇	—	5	2	no	—
14	D₅×C₁₀₇	—	10	2	no	—
15	C₂×C₃×C₁₀₇	—	25	1	no	—
16	C₅×C₁₀₇	—	2	2	no	—
17	C₅×C₁₀₇	ΓL(1,𝔽₁₆)	1	2	yes	complemented
18	Dic₁₀₇	—	75	1	no	Hall
19	C₃×C₁₀₇	#1044	1	1	yes	characteristic, complemented, Hall
20	C₃⋊#1044	—	107	1	no	maximal, Hall
21	C₂×C₁₀₇	—	25	1	no	—
22	C₃×C₅⋊D₅	D₁₀₇	1	1	yes	characteristic
23	C₁₀₇	C₃⋊#1044	1	1	yes	characteristic, complemented, Sylow
24	#1044	—	321	1	no	Hall
25	C₃×C₅²	Dic₁₀₇	1	1	yes	characteristic, complemented, Hall
26	ΓL(1,𝔽₁₆)	—	535	2	no	—
27	C₅⋊D₅	D₃₂₁	1	1	yes	characteristic
28	C₃×D₅	—	5	2	no	—
29	C₃×D₅	—	10	2	no	—
30	C₅²	Dic₃₂₁	1	1	yes	characteristic, complemented, Sylow
31	AGL(1,𝔽₅)	—	1605	2	no	—
32	C₃×C₅	—	2	2	no	—
33	C₃×C₅	C₁₀₇⋊AGL(1,𝔽₅)	1	2	yes	complemented
34	Dic₃	—	2675	1	no	Hall
35	D₅	—	5	2	no	—
36	D₅	—	10	2	no	—
37	C₂×C₃	—	25	1	no	—
38	C₅	—	2	2	no	—
39	C₅	C₃⋊(C₁₀₇⋊AGL(1,𝔽₅))	1	2	yes	complemented
40	C₄	—	8025	1	no	Sylow
41	C₃	C₁₀₇⋊#1044	1	1	yes	characteristic, complemented, Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₁₀₇	C₄
prime radical, cosocle	C₃×C₅⋊D₅×C₁₀₇	C₂
LCS	G ▷ C₃×C₅²×C₁₀₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₁₀₇	C₄	semidirect
8. C₅²×C₁₀₇	Dic₃	semidirect
11. C₃×C₅×C₁₀₇	AGL(1,𝔽₅)	semidirect
17. C₅×C₁₀₇	ΓL(1,𝔽₁₆)	semidirect
19. C₃×C₁₀₇	#1044	semidirect
23. C₁₀₇	C₃⋊#1044	semidirect
25. C₃×C₅²	Dic₁₀₇	semidirect
30. C₅²	Dic₃₂₁	semidirect
33. C₃×C₅	C₁₀₇⋊AGL(1,𝔽₅)	semidirect
39. C₅	C₃⋊(C₁₀₇⋊AGL(1,𝔽₅))	semidirect
41. C₃	C₁₀₇⋊#1044	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅⋊D₅×C₁₀₇	2
C₁₀₇⋊#1044	3
C₃⋊(C₁₀₇⋊AGL(1,𝔽₅))	5
C₃⋊#1044	107

Subgroups — C3⋊(C107⋊#1044) #44545702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₁₀₇⋊#1044) #44545702