Subgroups — D₅×3₋¹⁺² #63189

Order 270.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃²×D₅	C₃	1	1	yes	maximal, characteristic
3	C₉×D₅	C₃	1	3	yes	maximal, complemented
4	C₂×3₋¹⁺²	—	5	1	no	maximal, Hall
5	C₃²×C₅	C₂×C₃	1	1	yes	characteristic
6	C₅×C₉	C₂×C₃	1	3	yes	complemented
7	C₃×D₅	—	3	1	no	—
8	C₃×D₅	C₃²	1	1	yes	characteristic
9	3₋¹⁺²	D₅	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₃²	—	5	1	no	—
11	C₂×C₉	—	5	3	no	—
12	C₃×C₅	—	3	1	no	—
13	C₃×C₅	C₂×C₃²	1	1	yes	characteristic
14	D₅	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Hall
15	C₃²	C₃×D₅	1	1	yes	characteristic
16	C₉	C₃×D₅	1	3	yes	complemented
17	C₂×C₃	—	5	1	no	—
18	C₂×C₃	—	15	1	no	—
19	C₅	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
20	C₃	—	3	1	no	—
21	C₃	C₃²×D₅	1	1	yes	characteristic
22	C₂	—	5	1	no	Sylow

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.