Subgroups — C₂×C₅²×D₃ #64503

Order 300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅²

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.