Subgroups — C₁₀₇×C₃⋊#1039 #44545639

Order 32100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	#1039×C₁₀₇	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₅×C₁₀₇	—	5	6	no	maximal
5	C₂×C₅²×C₁₀₇	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₁₀₇	D₅	1	6	yes	—
7	C₅²×C₁₀₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₅×C₁₀₇	—	15	6	no	—
9	C₃×C₅×C₁₀₇	Dic₅	1	6	yes	complemented
10	Dic₃×C₁₀₇	—	25	1	no	Hall
11	C₂×C₅×C₁₀₇	D₁₅	1	6	yes	—
12	C₂×C₃×C₁₀₇	C₅⋊D₅	1	1	yes	characteristic
13	C₅×C₁₀₇	Dic₁₅	1	6	yes	complemented
14	C₄×C₁₀₇	—	75	1	no	Hall
15	C₃×C₁₀₇	#1039	1	1	yes	characteristic, complemented, Hall
16	C₃⋊#1039	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
18	C₂×C₃×C₅²	C₂×C₁₀₇	1	1	yes	characteristic
19	C₁₀₇	C₃⋊#1039	1	1	yes	characteristic, direct product factor, Sylow
20	#1039	—	3	1	no	Hall
21	C₃×C₅²	C₄×C₁₀₇	1	1	yes	characteristic, complemented, Hall
22	Dic₁₅	—	5	6	no	—
23	C₂×C₅²	D₃×C₁₀₇	1	1	yes	characteristic
24	C₂×C₃×C₅	D₅×C₁₀₇	1	6	yes	—
25	C₅²	Dic₃×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
26	Dic₅	—	15	6	no	—
27	C₃×C₅	Dic₅×C₁₀₇	1	6	yes	complemented
28	Dic₃	—	25	1	no	Hall
29	C₂×C₅	D₁₅×C₁₀₇	1	6	yes	—
30	C₂×C₃	C₅⋊D₅×C₁₀₇	1	1	yes	characteristic
31	C₅	Dic₁₅×C₁₀₇	1	6	yes	complemented
32	C₄	—	75	1	no	Sylow
33	C₃	#1039×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₁₀₇×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₁₀₇	C₄	semidirect
7. C₅²×C₁₀₇	Dic₃	semidirect
9. C₃×C₅×C₁₀₇	Dic₅	semidirect
13. C₅×C₁₀₇	Dic₁₅	semidirect
15. C₃×C₁₀₇	#1039	semidirect
16. C₃⋊#1039	C₁₀₇	direct (N × H)
19. C₁₀₇	C₃⋊#1039	direct (N × H)
21. C₃×C₅²	C₄×C₁₀₇	semidirect
25. C₅²	Dic₃×C₁₀₇	semidirect
27. C₃×C₅	Dic₅×C₁₀₇	semidirect
31. C₅	Dic₁₅×C₁₀₇	semidirect
33. C₃	#1039×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×C₁₀₇	2
#1039×C₁₀₇	3
Dic₁₅×C₁₀₇	5
C₃⋊#1039	107

Subgroups — C107×C3⋊#1039 #44545639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×C₃⋊#1039 #44545639