Subgroups — D₃×5₋¹⁺² #10625296

Order 750.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×5₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×5₋¹⁺²	—	3	1	no	maximal, Hall
3	C₅²×D₃	C₅	1	1	yes	maximal, characteristic
4	D₃×C₂₅	C₅	1	5	yes	maximal, complemented
5	5₋¹⁺²	D₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃×C₅²	C₂×C₅	1	1	yes	characteristic
7	C₃×C₂₅	C₂×C₅	1	5	yes	complemented
8	C₂×C₅²	—	3	1	no	—
9	C₂×C₂₅	—	3	5	no	—
10	C₅×D₃	—	5	1	no	—
11	C₅×D₃	C₅²	1	1	yes	characteristic
12	C₅²	C₅×D₃	1	1	yes	characteristic
13	C₂₅	C₅×D₃	1	5	yes	complemented
14	C₃×C₅	—	5	1	no	—
15	C₃×C₅	C₂×C₅²	1	1	yes	characteristic
16	C₂×C₅	—	3	1	no	—
17	C₂×C₅	—	15	1	no	—
18	D₃	5₋¹⁺²	1	1	yes	characteristic, direct product factor, Hall
19	C₅	—	5	1	no	—
20	C₅	C₅²×D₃	1	1	yes	characteristic
21	C₃	C₂×5₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	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.