Subgroups — C₃⋊#26015579 #46802482

Order 34140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₈₄₅	C₂	1	1	yes	maximal, characteristic
2	#26015579	—	3	1	no	maximal, Hall
3	C₃×C₅×C₅₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#14556189	—	5	1	no	maximal, Hall
5	D₂₈₄₅	D₃	1	1	yes	characteristic
6	C₃×D₅₆₉	—	5	1	no	—
7	C₅×C₅₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#14556189	—	15	1	no	Hall
9	C₃×C₅₆₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	D₅₆₉	—	5	1	no	—
11	C₅₆₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
12	ΓL(1,𝔽₁₆)	—	569	1	no	maximal, Hall
13	C₃×D₅	—	569	1	no	—
14	AGL(1,𝔽₅)	—	1707	1	no	Hall
15	C₃×C₅	#14556189	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	2845	1	no	Hall
17	D₅	—	569	1	no	—
18	C₂×C₃	—	2845	1	no	—
19	C₅	C₃⋊#14556189	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	8535	1	no	Sylow
21	C₃	#26015579	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	2845	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₅₆₉	C₄
prime radical, cosocle	C₃×D₂₈₄₅	C₂
LCS	G ▷ C₃×C₅×C₅₆₉
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.