Subgroups — C₉⋊#170 #67076

Order 360.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#170	—	3	1	no	maximal
3	C₂×C₅×C₉	C₄	1	1	yes	characteristic
4	C₉⋊C₈	—	5	1	no	maximal, Hall
5	C₃×Dic₅	D₃	1	1	yes	characteristic
6	C₅×C₉	C₈	1	1	yes	characteristic, complemented, Hall
7	#170	—	9	1	no	Hall
8	C₄×C₉	—	5	1	no	—
9	C₂×C₃×C₅	Dic₃	1	1	yes	characteristic
10	C₃⋊C₈	—	15	1	no	—
11	Dic₅	D₉	1	1	yes	characteristic
12	C₂×C₉	AGL(1,𝔽₅)	1	1	yes	characteristic
13	C₃×C₅	C₃⋊C₈	1	1	yes	characteristic
14	C₃×C₄	—	5	1	no	—
15	C₂×C₅	Dic₉	1	1	yes	characteristic
16	C₉	#170	1	1	yes	characteristic, complemented, Sylow
17	C₈	—	45	1	no	Sylow
18	C₂×C₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
19	C₅	C₉⋊C₈	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	5	1	no	—
21	C₃	C₃⋊#170	1	1	yes	characteristic
22	C₂	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic

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.