Subgroups — C₃×#26015578 #46802473

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	#26015578	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₅₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14556189	—	5	1	no	maximal, Hall
5	D₂₈₄₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅₆₉	—	5	1	no	—
7	C₅×C₅₆₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#14556189	—	5	1	no	Hall
9	C₃×C₅₆₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	D₅₆₉	—	5	1	no	—
11	C₅₆₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
12	C₃×AGL(1,𝔽₅)	—	569	1	no	maximal, Hall
13	C₃×D₅	—	569	1	no	—
14	AGL(1,𝔽₅)	—	569	1	no	Hall
15	C₃×C₅	#14556189	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄	—	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	—	2845	1	no	Sylow
21	C₃	#26015578	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	2845	1	no	—

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.