Subgroups — C₂×C₃⋊(C₅⋊D₅) #64505

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	—	3	1	no	maximal, Hall
4	C₃×C₅²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₅	—	5	6	no	maximal
6	C₂×C₅²	D₃	1	1	yes	characteristic, complemented
7	C₅⋊D₅	—	3	2	no	—
8	C₂×C₃×C₅	D₅	1	6	yes	complemented
9	D₁₅	—	5	12	no	—
10	C₅²	C₂×D₃	1	1	yes	characteristic, complemented, Sylow
11	C₂×D₅	—	15	6	no	—
12	C₃×C₅	C₂×D₅	1	6	yes	complemented
13	C₂×D₃	—	25	1	no	Hall
14	C₂×C₅	D₁₅	1	6	yes	complemented
15	D₅	—	15	12	no	—
16	C₂×C₃	C₅⋊D₅	1	1	yes	characteristic, complemented
17	D₃	—	25	2	no	—
18	C₅	C₂×D₁₅	1	6	yes	complemented
19	C₂²	—	75	1	no	Sylow
20	C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	75	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	C₃×C₅²	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂

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.