Subgroups — C₃⋊#1044 #64492

Order 300.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	#1044	—	3	1	no	maximal, Hall
3	C₃×C₅²	C₄	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₁₆)	—	5	2	no	maximal
5	C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₃×D₅	—	5	2	no	—
7	C₃×D₅	—	10	2	no	—
8	C₅²	Dic₃	1	1	yes	characteristic, complemented, Sylow
9	AGL(1,𝔽₅)	—	15	2	no	—
10	C₃×C₅	—	2	2	no	—
11	C₃×C₅	AGL(1,𝔽₅)	1	2	yes	complemented
12	Dic₃	—	25	1	no	Hall
13	D₅	—	5	2	no	—
14	D₅	—	10	2	no	—
15	C₂×C₃	—	25	1	no	—
16	C₅	—	2	2	no	—
17	C₅	ΓL(1,𝔽₁₆)	1	2	yes	complemented
18	C₄	—	75	1	no	Sylow
19	C₃	#1044	1	1	yes	characteristic, complemented, Sylow
20	C₂	—	25	1	no	—

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