Subgroups — C₃⋊#19129042 #30633271

Order 16140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₂₆₉	C₂	1	1	yes	maximal, characteristic
2	#19129042	—	3	1	no	maximal, Hall
3	C₃×C₅×C₂₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₈₀₇	—	5	1	no	maximal, Hall
5	D₅×C₂₆₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₂₆₉	—	5	1	no	—
7	C₅×C₂₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₂₆₉	—	15	1	no	Hall
9	C₃×C₂₆₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₂×C₂₆₉	—	5	1	no	—
11	C₂₆₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
12	ΓL(1,𝔽₁₆)	—	269	1	no	maximal, Hall
13	C₃×D₅	D₂₆₉	1	1	yes	characteristic
14	AGL(1,𝔽₅)	—	807	1	no	Hall
15	C₃×C₅	Dic₂₆₉	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	1345	1	no	Hall
17	D₅	D₈₀₇	1	1	yes	characteristic
18	C₂×C₃	—	5	1	no	—
19	C₅	Dic₈₀₇	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	4035	1	no	Sylow
21	C₃	#19129042	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₂₆₉	C₄
prime radical, cosocle	C₃×D₅×C₂₆₉	C₂
LCS	G ▷ C₃×C₅×C₂₆₉
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.