Subgroups — C₅×D₃×C₂₈₉ #22575992

Order 8670.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅×C₂₈₉	—	3	1	no	maximal, Hall
3	D₃×C₂₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₂₈₉	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₂₈₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₂₈₉	—	3	1	no	Hall
7	C₅×D₃×C₁₇	C₁₇	1	1	yes	maximal, characteristic
8	C₂₈₉	C₅×D₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×C₅×C₁₇	C₂×C₁₇	1	1	yes	characteristic
10	C₂×C₅×C₁₇	—	3	1	no	—
11	D₃×C₁₇	C₅×C₁₇	1	1	yes	characteristic
12	C₅×C₁₇	D₃×C₁₇	1	1	yes	characteristic
13	C₃×C₁₇	C₂×C₅×C₁₇	1	1	yes	characteristic
14	C₂×C₁₇	—	3	1	no	—
15	C₅×D₃	C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
16	C₁₇	C₅×D₃×C₁₇	1	1	yes	characteristic
17	C₃×C₅	C₂×C₂₈₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅	—	3	1	no	Hall
19	D₃	C₅×C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
20	C₅	D₃×C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂×C₅×C₂₈₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

Splittings G = N ⋊ H with N normal; H ≅ G/N.