Subgroups — C₂²×C₉×D₅ #67117

Order 360.

96 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, complemented
2	C₂×C₉×D₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×D₅	C₃	1	1	yes	maximal, characteristic
4	C₂×C₅×C₉	C₂²	1	3	yes	complemented
5	C₉×D₅	C₂²	1	4	yes	direct product factor
6	C₂³×C₉	—	5	1	no	maximal, Hall
7	C₂²×C₃×C₅	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃×D₅	C₂×C₃	1	6	yes	—
9	C₅×C₉	C₂³	1	1	yes	characteristic, complemented, Hall
10	C₂²×D₅	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₉	—	5	6	no	—
12	C₂²×C₉	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₃×C₅	C₂²×C₃	1	3	yes	—
14	C₃×D₅	C₂²×C₃	1	4	yes	—
15	C₂³×C₃	—	5	1	no	—
16	C₂²×C₅	C₂×C₉	1	1	yes	characteristic, complemented
17	C₂×D₅	C₂×C₉	1	6	yes	direct product factor
18	C₂×C₉	—	5	4	no	—
19	C₂×C₉	C₂×D₅	1	3	yes	direct product factor
20	C₃×C₅	C₂³×C₃	1	1	yes	characteristic
21	C₂²×C₃	—	5	6	no	—
22	C₂²×C₃	C₃×D₅	1	1	yes	characteristic
23	C₂×C₅	C₂²×C₉	1	3	yes	complemented
24	D₅	C₂²×C₉	1	4	yes	direct product factor
25	C₉	C₂²×D₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₂³	—	5	1	no	Sylow
27	C₂×C₃	—	5	4	no	—
28	C₂×C₃	C₂×C₃×D₅	1	3	yes	—
29	C₅	C₂³×C₉	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	5	6	no	—
31	C₂²	C₉×D₅	1	1	yes	characteristic, direct product factor
32	C₃	C₂²×C₃×D₅	1	1	yes	characteristic
33	C₂	—	5	4	no	—
34	C₂	C₂×C₉×D₅	1	3	yes	direct product factor

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.