Subgroups — C₁₃×D₇₅ #14519600

Order 1950.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₅	—	3	1	no	maximal, Hall
3	C₁₃×D₁₅	—	5	1	no	maximal
4	C₁₃×C₂₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₃	D₅	1	1	yes	characteristic
6	D₇₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₅×C₁₃	—	15	1	no	—
8	D₃×C₁₃	—	25	1	no	Hall
9	C₃×C₂₅	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₅×C₁₃	D₁₅	1	1	yes	characteristic
11	D₂₅	—	3	1	no	Hall
12	C₃×C₁₃	D₂₅	1	1	yes	characteristic, complemented, Hall
13	D₁₅	—	5	1	no	—
14	C₂×C₁₃	—	75	1	no	Hall
15	C₂₅	D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₅	D₅×C₁₃	1	1	yes	characteristic
17	C₁₃	D₇₅	1	1	yes	characteristic, direct product factor, Sylow
18	D₅	—	15	1	no	—
19	D₃	—	25	1	no	Hall
20	C₅	C₁₃×D₁₅	1	1	yes	characteristic
21	C₃	C₁₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₇₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂×C₁₃
Frattini	C₅	C₁₃×D₁₅
Fitting	C₃×C₁₃×C₂₅	C₂
socle	C₃×C₅×C₁₃	D₅
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₁₃

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.