Subgroups — C₂×C₃×D₁₂₅ #13093708

Order 1500.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₂₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₁₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₂₅	—	5	1	no	maximal
6	C₂×C₁₂₅	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₂₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₂₅	D₅	1	1	yes	characteristic
9	C₃×D₂₅	—	5	2	no	—
10	C₁₂₅	C₂²×C₃	1	1	yes	characteristic, complemented, Sylow
11	C₂×D₂₅	—	5	1	no	—
12	C₃×C₂₅	C₂×D₅	1	1	yes	characteristic
13	C₂×C₃×D₅	—	25	1	no	—
14	C₂×C₂₅	C₃×D₅	1	1	yes	characteristic
15	D₂₅	—	5	2	no	—
16	C₂×C₃×C₅	D₂₅	1	1	yes	characteristic
17	C₃×D₅	—	25	2	no	—
18	C₂₅	C₂×C₃×D₅	1	1	yes	characteristic
19	C₂×D₅	—	25	1	no	—
20	C₃×C₅	C₂×D₂₅	1	1	yes	characteristic
21	C₂²×C₃	—	125	1	no	Hall
22	C₂×C₅	C₃×D₂₅	1	1	yes	characteristic
23	D₅	—	25	2	no	—
24	C₂×C₃	—	125	2	no	—
25	C₂×C₃	D₁₂₅	1	1	yes	characteristic, direct product factor
26	C₅	C₂×C₃×D₂₅	1	1	yes	characteristic
27	C₂²	—	125	1	no	Sylow
28	C₃	C₂×D₁₂₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	125	2	no	—
30	C₂	C₃×D₁₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₂₅
commutator, cosocle, hypocenter	C₁₂₅	C₂²×C₃
Frattini	C₂₅	C₂×C₃×D₅
Fitting	C₂×C₃×C₁₂₅	C₂
socle	C₂×C₃×C₅	D₂₅
LCS	G ▷ C₁₂₅
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.