Subgroups — C₅×Q₈×C₉ #67102

Order 360.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₉	C₂	1	3	yes	maximal
2	C₃×C₅×Q₈	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
4	Q₈×C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄×C₅	C₂×C₃	1	3	yes	—
6	C₅×C₉	Q₈	1	1	yes	characteristic, direct product factor, Hall
7	C₅×Q₈	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₄×C₉	C₂×C₅	1	3	yes	—
9	C₂×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
10	C₃×Q₈	C₃×C₅	1	1	yes	characteristic
11	C₄×C₅	C₂×C₉	1	3	yes	—
12	C₂×C₉	C₂²×C₅	1	1	yes	characteristic
13	C₃×C₅	C₃×Q₈	1	1	yes	characteristic
14	C₃×C₄	C₂×C₃×C₅	1	3	yes	—
15	C₂×C₅	C₂²×C₉	1	1	yes	characteristic
16	C₉	C₅×Q₈	1	1	yes	characteristic, direct product factor, Sylow
17	Q₈	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃	C₂²×C₃×C₅	1	1	yes	characteristic
19	C₅	Q₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	C₂×C₅×C₉	1	3	yes	—
21	C₃	C₃×C₅×Q₈	1	1	yes	characteristic
22	C₂	C₂²×C₅×C₉	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.