Subgroups — C₃×C₅×#14556189 #46802471

Order 34140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅₆₉	C₂	1	1	yes	maximal, characteristic
2	C₅×#14556189	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₅₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14556189	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×D₅₆₉	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅₆₉	C₂×C₅	1	1	yes	characteristic
7	C₅×C₅₆₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#14556189	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅₆₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	D₅₆₉	C₂×C₃×C₅	1	1	yes	characteristic
11	C₅₆₉	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₅	—	569	1	no	maximal, Hall
13	C₂×C₃×C₅	—	569	1	no	—
14	C₄×C₅	—	569	1	no	Hall
15	C₃×C₅	#14556189	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₄	—	569	1	no	Hall
17	C₂×C₅	—	569	1	no	—
18	C₂×C₃	—	569	1	no	—
19	C₅	C₃×#14556189	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	—	569	1	no	Sylow
21	C₃	C₅×#14556189	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	569	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.