Subgroups — C₉×#672 #10623533

Order 720.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#672	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×C₅×C₈	C₂×C₃	1	1	yes	characteristic
6	C₂×C₅×C₉	C₈	1	1	yes	characteristic
7	#672	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₈×C₉	D₅	1	1	yes	characteristic
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	C₅×C₈	C₂×C₉	1	1	yes	characteristic
13	C₄×C₉	Dic₅	1	1	yes	characteristic
14	C₂×C₃×C₅	C₃×C₈	1	1	yes	characteristic
15	C₃×C₈	C₃×D₅	1	1	yes	characteristic
16	C₄×C₅	C₄×C₉	1	1	yes	characteristic
17	C₂×C₉	#168	1	1	yes	characteristic
18	C₁₆	—	5	1	no	Sylow
19	C₃×C₅	C₃×C₁₆	1	1	yes	characteristic
20	C₃×C₄	C₃×Dic₅	1	1	yes	characteristic
21	C₂×C₅	C₈×C₉	1	1	yes	characteristic
22	C₉	#672	1	1	yes	characteristic, direct product factor, Sylow
23	C₈	C₉×D₅	1	1	yes	characteristic
24	C₂×C₃	C₃×#168	1	1	yes	characteristic
25	C₅	C₉×C₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₄	C₉×Dic₅	1	1	yes	characteristic
27	C₃	C₃×#672	1	1	yes	characteristic
28	C₂	C₉×#168	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.