Subgroups — C₃⋊Dic₄₅ #10587366

Order 540.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₁₅	—	3	1	no	maximal
3	Dic₄₅	—	3	3	no	maximal
4	C₃×C₅×C₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃⋊Dic₉	—	5	1	no	maximal, Hall
6	C₂×C₃²×C₅	D₃	1	1	yes	characteristic
7	C₂×C₅×C₉	D₃	1	3	yes	—
8	Dic₁₅	—	9	3	no	—
9	Dic₁₅	—	9	1	no	—
10	C₂×C₃×C₉	D₅	1	1	yes	characteristic
11	C₃²×C₅	Dic₃	1	1	yes	characteristic
12	C₅×C₉	Dic₃	1	3	yes	complemented
13	C₃⋊Dic₃	—	15	1	no	—
14	Dic₉	—	15	3	no	—
15	C₂×C₃×C₅	D₉	1	3	yes	—
16	C₂×C₃×C₅	C₃⋊D₃	1	1	yes	characteristic
17	C₃×C₉	Dic₅	1	1	yes	characteristic, complemented, Sylow
18	Dic₅	—	27	1	no	Hall
19	C₂×C₃²	D₁₅	1	1	yes	characteristic
20	C₂×C₉	D₁₅	1	3	yes	—
21	C₃×C₅	Dic₉	1	3	yes	complemented
22	C₃×C₅	C₃⋊Dic₃	1	1	yes	characteristic
23	Dic₃	—	45	3	no	—
24	Dic₃	—	45	1	no	—
25	C₂×C₅	C₃⋊D₉	1	1	yes	characteristic
26	C₃²	Dic₁₅	1	1	yes	characteristic
27	C₉	Dic₁₅	1	3	yes	complemented
28	C₂×C₃	D₄₅	1	3	yes	—
29	C₂×C₃	C₃⋊D₁₅	1	1	yes	characteristic
30	C₅	C₃⋊Dic₉	1	1	yes	characteristic, complemented, Sylow
31	C₄	—	135	1	no	Sylow
32	C₃	Dic₄₅	1	3	yes	complemented
33	C₃	C₃⋊Dic₁₅	1	1	yes	characteristic
34	C₂	C₃⋊D₄₅	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.