Subgroups — C₉×D₂₀ #67087

Order 360.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×D₅	C₂	1	2	yes	maximal, complemented
2	C₄×C₅×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₀	C₃	1	1	yes	maximal, characteristic
4	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
5	C₉×D₅	—	2	2	no	—
6	D₄×C₉	—	5	1	no	maximal, Hall
7	C₂×C₃×D₅	C₂×C₃	1	2	yes	—
8	C₃×C₄×C₅	C₂×C₃	1	1	yes	characteristic
9	C₅×C₉	D₄	1	1	yes	characteristic, complemented, Hall
10	D₂₀	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₉	—	5	2	no	—
12	C₄×C₉	D₅	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
14	C₃×D₅	—	2	2	no	—
15	C₃×D₄	—	5	1	no	—
16	C₂×D₅	C₂×C₉	1	2	yes	complemented
17	C₄×C₅	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₉	—	10	2	no	—
19	C₂×C₉	C₂×D₅	1	1	yes	characteristic
20	C₃×C₅	C₃×D₄	1	1	yes	characteristic
21	C₂²×C₃	—	5	2	no	—
22	C₃×C₄	C₃×D₅	1	1	yes	characteristic
23	C₂×C₅	C₂²×C₉	1	1	yes	characteristic
24	D₅	—	2	2	no	—
25	C₉	D₂₀	1	1	yes	characteristic, direct product factor, Sylow
26	D₄	—	5	1	no	Sylow
27	C₂×C₃	—	10	2	no	—
28	C₂×C₃	C₂×C₃×D₅	1	1	yes	characteristic
29	C₅	D₄×C₉	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	5	2	no	—
31	C₄	C₉×D₅	1	1	yes	characteristic, complemented
32	C₃	C₃×D₂₀	1	1	yes	characteristic
33	C₂	—	10	2	no	—
34	C₂	C₂×C₉×D₅	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.