Subgroups — C₉×A₅ #10587371

Order 540.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×A₅	C₃	1	1	yes	maximal, characteristic
2	C₉×A₄	—	5	1	no	maximal, Hall
3	C₉×D₅	—	6	1	no	maximal
4	A₅	C₉	1	1	yes	characteristic, direct product factor
5	D₃×C₉	—	10	1	no	maximal
6	C₅×C₉	—	6	1	no	—
7	C₃×A₄	—	5	1	no	—
8	C₂²×C₉	—	5	1	no	—
9	C₂²⋊C₉	—	5	2	no	—
10	C₃×D₅	—	6	1	no	—
11	C₃×C₉	—	10	1	no	Sylow
12	C₃×D₃	—	10	1	no	—
13	C₂×C₉	—	15	1	no	—
14	C₃×C₅	—	6	1	no	—
15	C₂²×C₃	—	5	1	no	—
16	A₄	—	5	1	no	—
17	A₄	—	5	2	no	—
18	D₅	—	6	1	no	—
19	C₃²	—	10	1	no	—
20	C₉	—	20	1	no	—
21	C₉	A₅	1	1	yes	maximal normal, characteristic, direct product factor
22	C₂×C₃	—	15	1	no	—
23	D₃	—	10	1	no	—
24	C₅	—	6	1	no	Sylow
25	C₂²	—	5	1	no	Sylow
26	C₃	—	10	1	no	—
27	C₃	—	20	1	no	—
28	C₃	C₃×A₅	1	1	yes	characteristic
29	C₂	—	15	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. A₅	C₉	direct (N × H)
21. C₉	A₅	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.