Subgroups — C₂×C₃×C₅⋊D₅ #64502

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	C₃×C₅⋊D₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅	—	5	6	no	maximal
6	C₂×C₅²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊D₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅	D₅	1	6	yes	complemented
9	C₃×D₅	—	5	12	no	—
10	C₅²	C₂²×C₃	1	1	yes	characteristic, complemented, Sylow
11	C₂×D₅	—	5	6	no	—
12	C₃×C₅	C₂×D₅	1	6	yes	complemented
13	C₂²×C₃	—	25	1	no	Hall
14	C₂×C₅	C₃×D₅	1	6	yes	complemented
15	D₅	—	5	12	no	—
16	C₂×C₃	—	25	2	no	—
17	C₂×C₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
18	C₅	C₂×C₃×D₅	1	6	yes	complemented
19	C₂²	—	25	1	no	Sylow
20	C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	—	25	2	no	—
22	C₂	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃

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.