Subgroups — C₅×Dic₁₈ #67090

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	1	yes	maximal, characteristic
2	C₅×Dic₉	C₂	1	2	yes	maximal
3	C₅×Dic₆	—	3	1	no	maximal
4	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
5	Dic₁₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₄×C₅	D₃	1	1	yes	characteristic
7	C₅×Dic₃	—	3	2	no	—
8	C₅×C₉	Q₈	1	1	yes	characteristic, complemented, Hall
9	C₅×Q₈	—	9	1	no	Hall
10	C₄×C₉	C₂×C₅	1	1	yes	characteristic
11	Dic₉	C₂×C₅	1	2	yes	—
12	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
13	Dic₆	—	3	1	no	—
14	C₄×C₅	—	9	2	no	—
15	C₄×C₅	D₉	1	1	yes	characteristic
16	C₂×C₉	C₂²×C₅	1	1	yes	characteristic
17	C₃×C₅	Dic₆	1	1	yes	characteristic
18	C₃×C₄	C₅×D₃	1	1	yes	characteristic
19	Dic₃	—	3	2	no	—
20	C₂×C₅	C₂×D₉	1	1	yes	characteristic
21	C₉	C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
22	Q₈	—	9	1	no	Sylow
23	C₂×C₃	C₂×C₅×D₃	1	1	yes	characteristic
24	C₅	Dic₁₈	1	1	yes	characteristic, direct product factor, Sylow
25	C₄	—	9	2	no	—
26	C₄	C₅×D₉	1	1	yes	characteristic
27	C₃	C₅×Dic₆	1	1	yes	characteristic
28	C₂	C₂×C₅×D₉	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.