Subgroups — C₃⋊(C₈₃⋊#1043) #38735289

Order 24900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₈₃⋊#1043	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₈₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₈₃⋊AGL(1,𝔽₅))	—	5	6	no	maximal
5	C₅⋊D₅×C₈₃	D₃	1	1	yes	characteristic
6	C₃×D₅×C₈₃	—	5	6	no	—
7	C₅²×C₈₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₈₃⋊AGL(1,𝔽₅)	—	15	6	no	—
9	C₃×C₅×C₈₃	AGL(1,𝔽₅)	1	6	yes	complemented
10	Dic₂₄₉	—	25	1	no	Hall
11	D₅×C₈₃	—	5	6	no	—
12	C₂×C₃×C₈₃	—	25	1	no	—
13	C₅×C₈₃	ΓL(1,𝔽₁₆)	1	6	yes	complemented
14	Dic₈₃	—	75	1	no	Hall
15	C₃⋊#1043	—	83	1	no	maximal, Hall
16	C₃×C₈₃	#1043	1	1	yes	characteristic, complemented, Hall
17	C₂×C₈₃	—	25	1	no	—
18	C₃×C₅⋊D₅	D₈₃	1	1	yes	characteristic
19	#1043	—	249	1	no	Hall
20	C₈₃	C₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₅²	Dic₈₃	1	1	yes	characteristic, complemented, Hall
22	ΓL(1,𝔽₁₆)	—	415	6	no	—
23	C₅⋊D₅	D₂₄₉	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	Dic₂₄₉	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	1245	6	no	—
27	C₃×C₅	C₈₃⋊AGL(1,𝔽₅)	1	6	yes	complemented
28	Dic₃	—	2075	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃⋊(C₈₃⋊AGL(1,𝔽₅))	1	6	yes	complemented
32	C₄	—	6225	1	no	Sylow
33	C₃	C₈₃⋊#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×C₈₃	C₄
prime radical, cosocle	C₃×C₅⋊D₅×C₈₃	C₂
LCS	G ▷ C₃×C₅²×C₈₃
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.