Subgroups — C₂×D₇₅ #64468

Order 300.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₅	—	3	1	no	maximal, Hall
4	C₃×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₅	—	5	1	no	maximal
6	C₂×C₂₅	D₃	1	1	yes	characteristic, complemented
7	D₂₅	—	3	2	no	—
8	C₂×C₃×C₅	D₅	1	1	yes	characteristic
9	D₁₅	—	5	2	no	—
10	C₂₅	C₂×D₃	1	1	yes	characteristic, complemented, Sylow
11	C₂×D₅	—	15	1	no	—
12	C₃×C₅	C₂×D₅	1	1	yes	characteristic
13	C₂×D₃	—	25	1	no	Hall
14	C₂×C₅	D₁₅	1	1	yes	characteristic
15	D₅	—	15	2	no	—
16	C₂×C₃	D₂₅	1	1	yes	characteristic, complemented
17	D₃	—	25	2	no	—
18	C₅	C₂×D₁₅	1	1	yes	characteristic
19	C₂²	—	75	1	no	Sylow
20	C₃	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	75	2	no	—
22	C₂	D₇₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂²
Frattini	C₅	C₂×D₁₅
Fitting	C₂×C₃×C₂₅	C₂
socle	C₂×C₃×C₅	D₅
LCS	G ▷ C₃×C₂₅
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.