Subgroups — C₂×C₉×Dic₅ #67088

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	C₉×Dic₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×Dic₅	C₃	1	1	yes	maximal, characteristic
4	C₂×C₅×C₉	C₄	1	2	yes	complemented
5	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₉	—	5	1	no	maximal, Hall
7	C₂²×C₃×C₅	C₂×C₃	1	1	yes	characteristic
8	C₃×Dic₅	C₂×C₃	1	2	yes	—
9	C₅×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×Dic₅	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₉	D₅	1	1	yes	characteristic
12	C₄×C₉	—	5	2	no	—
13	C₂×C₃×C₅	C₃×C₄	1	2	yes	—
14	C₂×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₄	—	5	1	no	—
16	C₂²×C₅	C₂×C₉	1	1	yes	characteristic
17	Dic₅	C₂×C₉	1	2	yes	direct product factor
18	C₂×C₉	Dic₅	1	2	yes	direct product factor
19	C₂×C₉	C₂×D₅	1	1	yes	characteristic
20	C₃×C₅	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂²×C₃	C₃×D₅	1	1	yes	characteristic
22	C₃×C₄	—	5	2	no	—
23	C₂×C₅	C₄×C₉	1	2	yes	complemented
24	C₂×C₅	C₂²×C₉	1	1	yes	characteristic
25	C₉	C₂×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₄	—	5	1	no	Sylow
27	C₂×C₃	C₃×Dic₅	1	2	yes	—
28	C₂×C₃	C₂×C₃×D₅	1	1	yes	characteristic
29	C₅	C₂×C₄×C₉	1	1	yes	characteristic, complemented, Sylow
30	C₂²	C₉×D₅	1	1	yes	characteristic
31	C₄	—	5	2	no	—
32	C₃	C₂×C₃×Dic₅	1	1	yes	characteristic
33	C₂	C₉×Dic₅	1	2	yes	direct product factor
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.