Subgroups — C₂×Dic₄₅ #67098

Order 360.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	Dic₄₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×Dic₁₅	—	3	1	no	maximal
4	C₂×C₅×C₉	C₄	1	2	yes	complemented
5	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₂×Dic₉	—	5	1	no	maximal, Hall
7	C₂²×C₃×C₅	D₃	1	1	yes	characteristic
8	Dic₁₅	—	3	2	no	—
9	C₅×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×Dic₅	—	9	1	no	Hall
11	C₂²×C₉	D₅	1	1	yes	characteristic
12	Dic₉	—	5	2	no	—
13	C₂×C₃×C₅	Dic₃	1	2	yes	—
14	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
15	C₂×Dic₃	—	15	1	no	—
16	C₂²×C₅	D₉	1	1	yes	characteristic
17	Dic₅	—	9	2	no	—
18	C₂×C₉	Dic₅	1	2	yes	complemented
19	C₂×C₉	C₂×D₅	1	1	yes	characteristic
20	C₃×C₅	C₂×Dic₃	1	1	yes	characteristic
21	C₂²×C₃	D₁₅	1	1	yes	characteristic
22	Dic₃	—	15	2	no	—
23	C₂×C₅	Dic₉	1	2	yes	complemented
24	C₂×C₅	C₂×D₉	1	1	yes	characteristic
25	C₉	C₂×Dic₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	45	1	no	Sylow
27	C₂×C₃	Dic₁₅	1	2	yes	—
28	C₂×C₃	C₂×D₁₅	1	1	yes	characteristic
29	C₅	C₂×Dic₉	1	1	yes	characteristic, complemented, Sylow
30	C₂²	D₄₅	1	1	yes	characteristic
31	C₄	—	45	2	no	—
32	C₃	C₂×Dic₁₅	1	1	yes	characteristic
33	C₂	Dic₄₅	1	2	yes	direct product factor
34	C₂	C₂×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.