Subgroups — C₃⋊#1042 #64490

Order 300.

26 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	#1042	—	3	1	no	maximal, Hall
3	C₃×C₅²	C₄	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₁₆)	—	5	1	no	maximal
5	Dic₁₅	—	5	1	no	maximal
6	C₅×D₅	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅	—	5	1	no	—
8	C₃×D₅	D₅	1	1	yes	characteristic
9	C₅²	Dic₃	1	1	yes	characteristic, complemented, Sylow
10	AGL(1,𝔽₅)	—	15	1	no	—
11	Dic₅	—	15	1	no	—
12	C₃×C₅	—	4	1	no	—
13	C₃×C₅	Dic₅	1	1	yes	characteristic, complemented
14	C₃×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	Dic₃	—	25	1	no	Hall
16	C₂×C₅	—	5	1	no	—
17	D₅	D₁₅	1	1	yes	characteristic
18	C₂×C₃	—	5	1	no	—
19	C₅	—	4	1	no	—
20	C₅	Dic₁₅	1	1	yes	characteristic, complemented
21	C₅	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
22	C₄	—	75	1	no	Sylow
23	C₃	#1042	1	1	yes	characteristic, complemented, Sylow
24	C₂	—	5	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.