Subgroups — C₅×C₉⋊C₁₆ #10623532

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	C₅×C₃⋊C₁₆	—	3	1	no	maximal
3	C₄×C₅×C₉	C₄	1	1	yes	characteristic
4	C₉⋊C₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₈	D₃	1	1	yes	characteristic
6	C₂×C₅×C₉	C₈	1	1	yes	characteristic
7	C₅×C₁₆	—	9	1	no	Hall
8	C₈×C₉	C₂×C₅	1	1	yes	characteristic
9	C₃×C₄×C₅	Dic₃	1	1	yes	characteristic
10	C₃⋊C₁₆	—	3	1	no	—
11	C₅×C₉	C₁₆	1	1	yes	characteristic, complemented, Hall
12	C₅×C₈	D₉	1	1	yes	characteristic
13	C₄×C₉	C₄×C₅	1	1	yes	characteristic
14	C₂×C₃×C₅	C₃⋊C₈	1	1	yes	characteristic
15	C₃×C₈	C₅×D₃	1	1	yes	characteristic
16	C₄×C₅	Dic₉	1	1	yes	characteristic
17	C₂×C₉	C₅×C₈	1	1	yes	characteristic
18	C₁₆	—	9	1	no	Sylow
19	C₃×C₅	C₃⋊C₁₆	1	1	yes	characteristic
20	C₃×C₄	C₅×Dic₃	1	1	yes	characteristic
21	C₂×C₅	C₉⋊C₈	1	1	yes	characteristic
22	C₉	C₅×C₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₈	C₅×D₉	1	1	yes	characteristic
24	C₂×C₃	C₅×C₃⋊C₈	1	1	yes	characteristic
25	C₅	C₉⋊C₁₆	1	1	yes	characteristic, direct product factor, Sylow
26	C₄	C₅×Dic₉	1	1	yes	characteristic
27	C₃	C₅×C₃⋊C₁₆	1	1	yes	characteristic
28	C₂	C₅×C₉⋊C₈	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.