Subgroups — C₉×D₁₆₈₅ #44476751

Order 30330.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₃₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₆₈₅	C₃	1	1	yes	maximal, characteristic
3	C₉×D₃₃₇	—	5	1	no	maximal, Hall
4	C₃×C₅×C₃₃₇	C₂×C₃	1	1	yes	characteristic
5	D₁₆₈₅	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₃₃₇	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃₃₇	—	5	1	no	—
8	C₅×C₃₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₃₇	C₃×D₅	1	1	yes	characteristic
10	D₃₃₇	—	5	1	no	Hall
11	C₃₃₇	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
12	C₉×D₅	—	337	1	no	maximal, Hall
13	C₅×C₉	D₃₃₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅	—	337	1	no	—
15	C₂×C₉	—	1685	1	no	Hall
16	C₃×C₅	C₃×D₃₃₇	1	1	yes	characteristic
17	D₅	—	337	1	no	Hall
18	C₉	D₁₆₈₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	1685	1	no	—
20	C₅	C₉×D₃₃₇	1	1	yes	characteristic, complemented, Sylow
21	C₃	C₃×D₁₆₈₅	1	1	yes	characteristic
22	C₂	—	1685	1	no	Sylow

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.