Subgroups — C₃⋊#92537 #13093758

Order 1500.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6953	C₂	1	1	yes	maximal, characteristic
2	#92537	—	3	1	no	maximal, Hall
3	C₃×H(3,𝔽₅)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#1042	—	5	6	no	maximal
5	#6953	D₃	1	1	yes	characteristic
6	C₃×C₅×D₅	—	5	6	no	—
7	H(3,𝔽₅)	Dic₃	1	1	yes	characteristic, complemented, Sylow
8	#1042	—	15	6	no	—
9	C₃×C₅²	AGL(1,𝔽₅)	1	6	yes	complemented
10	ΓL(1,𝔽₁₆)	—	25	6	no	—
11	Dic₁₅	—	25	1	no	—
12	C₅×D₅	—	5	6	no	—
13	C₂×C₃×C₅	—	25	1	no	—
14	C₃×D₅	—	5	6	no	—
15	C₅²	ΓL(1,𝔽₁₆)	1	6	yes	complemented
16	AGL(1,𝔽₅)	—	75	6	no	—
17	Dic₅	—	75	1	no	—
18	C₃×C₅	—	5	6	no	—
19	C₃×C₅	#1043	1	1	yes	characteristic
20	Dic₃	—	125	1	no	Hall
21	C₂×C₅	—	25	1	no	—
22	D₅	—	5	6	no	—
23	C₂×C₃	—	25	1	no	—
24	C₅	—	5	6	no	—
25	C₅	C₃⋊#1043	1	1	yes	characteristic
26	C₄	—	375	1	no	Sylow
27	C₃	#92537	1	1	yes	characteristic, complemented, Sylow
28	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃×H(3,𝔽₅)	C₄
Frattini	C₅	C₃⋊#1043
socle	C₃×C₅	#1043
prime radical, cosocle	C₃×#6953	C₂
LCS	G ▷ C₃×H(3,𝔽₅)
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.