Subgroups — C₃⋊(C₁₀₇⋊#1043) #44545700

Order 32100.

96 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⋊#1043	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₁₀₇⋊AGL(1,𝔽₅))	—	5	6	no	maximal
5	C₅⋊D₅×C₁₀₇	D₃	1	1	yes	characteristic
6	C₃×D₅×C₁₀₇	—	5	6	no	—
7	C₅²×C₁₀₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₁₀₇⋊AGL(1,𝔽₅)	—	15	6	no	—
9	C₃×C₅×C₁₀₇	AGL(1,𝔽₅)	1	6	yes	complemented
10	Dic₃₂₁	—	25	1	no	Hall
11	D₅×C₁₀₇	—	5	6	no	—
12	C₂×C₃×C₁₀₇	—	25	1	no	—
13	C₅×C₁₀₇	ΓL(1,𝔽₁₆)	1	6	yes	complemented
14	Dic₁₀₇	—	75	1	no	Hall
15	C₃×C₁₀₇	#1043	1	1	yes	characteristic, complemented, Hall
16	C₃⋊#1043	—	107	1	no	maximal, Hall
17	C₂×C₁₀₇	—	25	1	no	—
18	C₃×C₅⋊D₅	D₁₀₇	1	1	yes	characteristic
19	C₁₀₇	C₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
20	#1043	—	321	1	no	Hall
21	C₃×C₅²	Dic₁₀₇	1	1	yes	characteristic, complemented, Hall
22	ΓL(1,𝔽₁₆)	—	535	6	no	—
23	C₅⋊D₅	D₃₂₁	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	Dic₃₂₁	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	1605	6	no	—
27	C₃×C₅	C₁₀₇⋊AGL(1,𝔽₅)	1	6	yes	complemented
28	Dic₃	—	2675	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃⋊(C₁₀₇⋊AGL(1,𝔽₅))	1	6	yes	complemented
32	C₄	—	8025	1	no	Sylow
33	C₃	C₁₀₇⋊#1043	1	1	yes	characteristic, complemented, Sylow
34	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

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

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