Subgroups — C₉×C₂₅×C₁₂₅ #72205103

Order 28125.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅²	C₅	1	1	yes	maximal, characteristic
2	C₅×C₉×C₁₂₅	C₅	1	5	yes	maximal
3	C₃×C₂₅×C₁₂₅	C₃	1	1	yes	maximal, characteristic
4	C₂₅×C₁₂₅	C₉	1	1	yes	characteristic, direct product factor, Sylow
5	C₃×C₅×C₁₂₅	C₃×C₅	1	5	yes	—
6	C₃×C₂₅²	C₃×C₅	1	1	yes	characteristic
7	C₅×C₉×C₂₅	C₂₅	1	5	yes	—
8	C₅×C₉×C₂₅	C₅²	1	1	yes	characteristic
9	C₉×C₁₂₅	C₂₅	1	25	yes	direct product factor
10	C₅×C₁₂₅	C₅×C₉	1	5	yes	—
11	C₂₅²	C₅×C₉	1	1	yes	characteristic
12	C₃×C₅×C₂₅	C₃×C₂₅	1	5	yes	—
13	C₃×C₅×C₂₅	C₃×C₅²	1	1	yes	characteristic
14	C₃×C₁₂₅	C₃×C₂₅	1	25	yes	—
15	C₅²×C₉	C₅×C₂₅	1	1	yes	characteristic
16	C₉×C₂₅	C₁₂₅	1	25	yes	direct product factor
17	C₉×C₂₅	C₅×C₂₅	1	5	yes	—
18	C₅×C₂₅	C₉×C₂₅	1	5	yes	—
19	C₅×C₂₅	C₅²×C₉	1	1	yes	characteristic
20	C₁₂₅	C₉×C₂₅	1	25	yes	direct product factor
21	C₃×C₅²	C₃×C₅×C₂₅	1	1	yes	characteristic
22	C₃×C₂₅	C₃×C₁₂₅	1	25	yes	—
23	C₃×C₂₅	C₃×C₅×C₂₅	1	5	yes	—
24	C₅×C₉	C₂₅²	1	1	yes	characteristic
25	C₅×C₉	C₅×C₁₂₅	1	5	yes	—
26	C₅²	C₅×C₉×C₂₅	1	1	yes	characteristic
27	C₂₅	C₉×C₁₂₅	1	25	yes	direct product factor
28	C₂₅	C₅×C₉×C₂₅	1	5	yes	—
29	C₃×C₅	C₃×C₂₅²	1	1	yes	characteristic
30	C₃×C₅	C₃×C₅×C₁₂₅	1	5	yes	—
31	C₉	C₂₅×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₅	C₅×C₉×C₁₂₅	1	5	yes	—
33	C₅	C₉×C₂₅²	1	1	yes	characteristic
34	C₃	C₃×C₂₅×C₁₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₅×C₂₅	C₃×C₅²
socle, prime radical	C₃×C₅²	C₃×C₅×C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂₅×C₁₂₅	C₉	direct (N × H)
9. C₉×C₁₂₅	C₂₅	direct (N × H)
16. C₉×C₂₅	C₁₂₅	direct (N × H)
20. C₁₂₅	C₉×C₂₅	direct (N × H)
27. C₂₅	C₉×C₁₂₅	direct (N × H)
31. C₉	C₂₅×C₁₂₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×C₂₅²	5
C₅×C₉×C₁₂₅	5
C₃×C₂₅×C₁₂₅	3

Subgroups — C9×C25×C125 #72205103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₂₅×C₁₂₅ #72205103