Subgroups — C₉×#674 #10623536

Order 720.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#168	C₂	1	1	yes	maximal, characteristic
2	C₃×#674	C₃	1	1	yes	maximal, characteristic
3	C₄×C₅×C₉	C₄	1	1	yes	characteristic
4	C₉×C₁₆	—	5	1	no	maximal, Hall
5	C₃×#168	C₂×C₃	1	1	yes	characteristic
6	C₂×C₅×C₉	C₈	1	1	yes	characteristic
7	#674	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₈×C₉	—	5	1	no	—
9	C₃×C₄×C₅	C₃×C₄	1	1	yes	characteristic
10	C₃×C₁₆	—	5	1	no	—
11	C₅×C₉	C₁₆	1	1	yes	characteristic, complemented, Hall
12	#168	C₂×C₉	1	1	yes	characteristic
13	C₄×C₉	AGL(1,𝔽₅)	1	1	yes	characteristic
14	C₂×C₃×C₅	C₃×C₈	1	1	yes	characteristic
15	C₃×C₈	—	5	1	no	—
16	C₄×C₅	C₄×C₉	1	1	yes	characteristic
17	C₂×C₉	#170	1	1	yes	characteristic
18	C₁₆	—	5	1	no	Sylow
19	C₃×C₅	C₃×C₁₆	1	1	yes	characteristic
20	C₃×C₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₂×C₅	C₈×C₉	1	1	yes	characteristic
22	C₉	#674	1	1	yes	characteristic, direct product factor, Sylow
23	C₈	—	5	1	no	—
24	C₂×C₃	C₃×#170	1	1	yes	characteristic
25	C₅	C₉×C₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₄	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₃	C₃×#674	1	1	yes	characteristic
28	C₂	C₉×#170	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.