Subgroups — C₅×C₄²⋊C₉ #10623563

Order 720.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₅	C₃	1	1	yes	maximal, characteristic
2	C₅×C₂²⋊C₉	—	4	1	no	maximal
3	C₄²⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅	—	3	1	no	—
5	C₄²×C₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₃×C₅	A₄	1	1	yes	characteristic
7	C₃×C₄×C₅	—	3	2	no	—
8	C₃×C₄²	C₃×C₅	1	1	yes	characteristic
9	C₅×C₉	—	16	1	no	Hall
10	C₂×C₄×C₅	—	3	1	no	—
11	C₂²⋊C₉	—	4	1	no	—
12	C₂×C₃×C₅	—	3	1	no	—
13	C₂×C₃×C₄	—	3	1	no	—
14	C₂²×C₅	C₂²⋊C₉	1	1	yes	characteristic
15	C₄×C₅	—	3	2	no	—
16	C₄²	C₅×C₉	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅	C₄²⋊C₃	1	1	yes	characteristic
18	C₂²×C₃	C₅×A₄	1	1	yes	characteristic
19	C₃×C₄	—	3	2	no	—
20	C₂×C₅	—	3	1	no	—
21	C₉	—	16	1	no	Sylow
22	C₂×C₄	—	3	1	no	—
23	C₂×C₃	—	3	1	no	—
24	C₅	C₄²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²	C₅×C₂²⋊C₉	1	1	yes	characteristic
26	C₄	—	3	2	no	—
27	C₃	C₅×C₄²⋊C₃	1	1	yes	characteristic
28	C₂	—	3	1	no	—

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.