Subgroups — D₅×Dic₉ #67081

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	1	yes	maximal, characteristic
2	Dic₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×Dic₃	—	3	1	no	maximal
5	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₉×D₅	C₄	1	2	yes	complemented
7	C₂×Dic₉	—	5	1	no	maximal, Hall
8	C₂×C₃×D₅	D₃	1	1	yes	characteristic
9	Dic₁₅	—	3	1	no	—
10	C₅×Dic₃	—	3	1	no	—
11	C₅×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₄×D₅	—	9	1	no	Hall
13	C₂²×C₉	—	5	1	no	—
14	Dic₉	—	5	1	no	—
15	Dic₉	D₅	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
17	C₃×D₅	Dic₃	1	2	yes	—
18	C₂×Dic₃	—	15	1	no	—
19	C₂×D₅	D₉	1	1	yes	characteristic
20	C₄×C₅	—	9	1	no	—
21	Dic₅	—	9	1	no	—
22	C₂×C₉	—	5	2	no	—
23	C₂×C₉	C₂×D₅	1	1	yes	characteristic
24	C₃×C₅	C₂×Dic₃	1	1	yes	characteristic
25	C₂²×C₃	—	5	1	no	—
26	Dic₃	—	3	1	no	—
27	Dic₃	—	15	1	no	—
28	C₂×C₅	C₂×D₉	1	1	yes	characteristic
29	D₅	Dic₉	1	2	yes	direct product factor
30	C₉	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄	—	45	1	no	Sylow
32	C₂×C₃	—	5	2	no	—
33	C₂×C₃	D₃×D₅	1	1	yes	characteristic
34	C₅	C₂×Dic₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	5	1	no	—
36	C₄	—	9	1	no	—
37	C₄	—	45	1	no	—
38	C₃	D₅×Dic₃	1	1	yes	characteristic
39	C₂	—	5	2	no	—
40	C₂	D₅×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.