Subgroups — C₉×D₂₅⋊C₅ #72276692

Order 2250.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×5₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₂₅⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×D₅	—	5	1	no	maximal
4	C₉×D₂₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₃×5₋¹⁺²	C₂×C₃	1	1	yes	characteristic
6	D₂₅⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₅²×C₉	D₅	1	1	yes	characteristic
8	C₉×C₂₅	—	2	2	no	—
9	C₉×C₂₅	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×C₅×D₅	—	5	1	no	—
11	C₃×D₂₅	C₃×C₅	1	1	yes	characteristic
12	5₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₅×C₉	—	25	1	no	—
14	C₉×D₅	—	5	1	no	—
15	C₃×C₅²	C₃×D₅	1	1	yes	characteristic
16	C₃×C₂₅	—	2	2	no	—
17	C₃×C₂₅	C₂×C₃×C₅	1	1	yes	characteristic
18	C₅×D₅	—	5	1	no	—
19	D₂₅	C₅×C₉	1	1	yes	characteristic, complemented
20	C₅×C₉	—	5	1	no	—
21	C₅×C₉	C₅×D₅	1	1	yes	characteristic
22	C₂×C₃×C₅	—	25	1	no	—
23	C₃×D₅	—	5	1	no	—
24	C₅²	C₉×D₅	1	1	yes	characteristic
25	C₂₅	—	2	2	no	—
26	C₂₅	C₂×C₅×C₉	1	1	yes	characteristic, complemented
27	C₂×C₉	—	25	1	no	Hall
28	C₃×C₅	—	5	1	no	—
29	C₃×C₅	C₃×C₅×D₅	1	1	yes	characteristic
30	C₂×C₅	—	25	1	no	—
31	D₅	—	5	1	no	—
32	C₉	D₂₅⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃	—	25	1	no	—
34	C₅	—	5	1	no	—
35	C₅	C₅×C₉×D₅	1	1	yes	characteristic
36	C₃	C₃×D₂₅⋊C₅	1	1	yes	characteristic
37	C₂	—	25	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.