Subgroups — D₃×D₂₅ #64464

Order 300.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₅	—	3	1	no	maximal, Hall
5	C₃×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅	—	5	1	no	maximal
7	C₂×C₂₅	—	3	1	no	—
8	D₂₅	—	3	1	no	—
9	D₂₅	D₃	1	1	yes	characteristic, direct product factor
10	D₁₅	—	5	1	no	—
11	C₃×D₅	—	5	1	no	—
12	C₅×D₃	D₅	1	1	yes	characteristic
13	C₂₅	C₂×D₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×D₅	—	15	1	no	—
15	C₃×C₅	C₂×D₅	1	1	yes	characteristic
16	C₂×D₃	—	25	1	no	Hall
17	C₂×C₅	—	3	1	no	—
18	D₅	—	5	1	no	—
19	D₅	—	15	1	no	—
20	C₂×C₃	—	25	1	no	—
21	D₃	—	25	1	no	—
22	D₃	D₂₅	1	1	yes	characteristic, direct product factor
23	C₅	D₃×D₅	1	1	yes	characteristic
24	C₂²	—	75	1	no	Sylow
25	C₃	C₂×D₂₅	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, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₂₅	C₂²
Frattini	C₅	D₃×D₅
socle	C₃×C₅	C₂×D₅
LCS	G ▷ C₃×C₂₅
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.