Subgroups — D₃×C₅⋊D₅ #64495

Order 300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊D₅	—	3	1	no	maximal, Hall
5	C₃×C₅²	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅	—	5	6	no	maximal
7	C₂×C₅²	—	3	1	no	—
8	C₅⋊D₅	—	3	1	no	—
9	C₅⋊D₅	D₃	1	1	yes	characteristic, direct product factor
10	D₁₅	—	5	6	no	—
11	C₃×D₅	—	5	6	no	—
12	C₅×D₃	D₅	1	6	yes	complemented
13	C₅²	C₂×D₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×D₅	—	15	6	no	—
15	C₃×C₅	C₂×D₅	1	6	yes	complemented
16	C₂×D₃	—	25	1	no	Hall
17	C₂×C₅	—	3	6	no	—
18	D₅	—	5	6	no	—
19	D₅	—	15	6	no	—
20	C₂×C₃	—	25	1	no	—
21	D₃	—	25	1	no	—
22	D₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
23	C₅	D₃×D₅	1	6	yes	complemented
24	C₂²	—	75	1	no	Sylow
25	C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
26	C₂	—	3	1	no	—
27	C₂	—	25	1	no	—
28	C₂	—	75	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁

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.