Subgroups — C₅×C₃²⋊C₉ #87943

Order 405.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₅	C₃	1	1	yes	maximal, characteristic
2	C₃×C₅×C₉	C₃	1	3	yes	maximal, complemented
3	C₃²⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃²×C₅	—	3	1	no	—
5	C₃²×C₅	—	3	2	no	—
6	C₃²×C₅	C₉	1	3	yes	complemented
7	C₃²×C₅	C₃²	1	1	yes	characteristic
8	C₅×C₉	—	3	3	no	—
9	C₃³	C₃×C₅	1	1	yes	characteristic
10	C₃×C₉	C₃×C₅	1	3	yes	complemented
11	C₃×C₅	—	3	3	no	—
12	C₃×C₅	C₃×C₉	1	1	yes	characteristic
13	C₃×C₅	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃×C₅	3₋¹⁺²	1	2	yes	—
15	C₃²	—	3	1	no	—
16	C₃²	—	3	2	no	—
17	C₃²	C₅×C₉	1	3	yes	complemented
18	C₃²	C₃²×C₅	1	1	yes	characteristic
19	C₉	—	3	3	no	—
20	C₅	C₃²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	3	3	no	—
22	C₃	C₃×C₅×C₉	1	1	yes	characteristic
23	C₃	C₅×H(3,𝔽₃)	1	1	yes	characteristic
24	C₃	C₅×3₋¹⁺²	1	2	yes	—

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.