Subgroups — C₃⋊#26015580 #46802483

Order 34140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₅₆₉	C₂	1	1	yes	maximal, characteristic
2	#26015580	—	3	1	no	maximal, Hall
3	C₃×C₅×C₅₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₇₀₇	—	5	1	no	maximal, Hall
5	D₅×C₅₆₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅₆₉	—	5	1	no	—
7	C₅×C₅₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₅₆₉	—	15	1	no	Hall
9	C₃×C₅₆₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅₆₉	—	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	D₅₆₉	1	1	yes	characteristic
14	AGL(1,𝔽₅)	—	1707	1	no	Hall
15	C₃×C₅	Dic₅₆₉	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	2845	1	no	Hall
17	D₅	D₁₇₀₇	1	1	yes	characteristic
18	C₂×C₃	—	5	1	no	—
19	C₅	Dic₁₇₀₇	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	8535	1	no	Sylow
21	C₃	#26015580	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×C₅₆₉	C₄
prime radical, cosocle	C₃×D₅×C₅₆₉	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.