Subgroups — C₅×C₉×C₆₂₅ #72205102

Order 28125.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₂₅	C₅	1	1	yes	maximal, characteristic
2	C₉×C₆₂₅	C₅	1	5	yes	maximal, direct product factor
3	C₃×C₅×C₆₂₅	C₃	1	1	yes	maximal, characteristic
4	C₅×C₆₂₅	C₉	1	1	yes	characteristic, direct product factor, Sylow
5	C₃×C₅×C₁₂₅	C₃×C₅	1	1	yes	characteristic
6	C₃×C₆₂₅	C₃×C₅	1	5	yes	—
7	C₅×C₉×C₂₅	C₂₅	1	1	yes	characteristic
8	C₉×C₁₂₅	C₂₅	1	4	yes	—
9	C₉×C₁₂₅	C₅²	1	1	yes	characteristic
10	C₅×C₁₂₅	C₅×C₉	1	1	yes	characteristic
11	C₆₂₅	C₅×C₉	1	5	yes	direct product factor
12	C₃×C₅×C₂₅	C₃×C₂₅	1	1	yes	characteristic
13	C₃×C₁₂₅	C₃×C₂₅	1	4	yes	—
14	C₃×C₁₂₅	C₃×C₅²	1	1	yes	characteristic
15	C₅²×C₉	C₁₂₅	1	1	yes	characteristic
16	C₉×C₂₅	C₁₂₅	1	4	yes	—
17	C₉×C₂₅	C₅×C₂₅	1	1	yes	characteristic
18	C₅×C₂₅	C₉×C₂₅	1	1	yes	characteristic
19	C₁₂₅	C₉×C₂₅	1	4	yes	—
20	C₁₂₅	C₅²×C₉	1	1	yes	characteristic
21	C₃×C₅²	C₃×C₁₂₅	1	1	yes	characteristic
22	C₃×C₂₅	C₃×C₁₂₅	1	4	yes	—
23	C₃×C₂₅	C₃×C₅×C₂₅	1	1	yes	characteristic
24	C₅×C₉	C₆₂₅	1	5	yes	direct product factor
25	C₅×C₉	C₅×C₁₂₅	1	1	yes	characteristic
26	C₅²	C₉×C₁₂₅	1	1	yes	characteristic
27	C₂₅	C₉×C₁₂₅	1	4	yes	—
28	C₂₅	C₅×C₉×C₂₅	1	1	yes	characteristic
29	C₃×C₅	C₃×C₆₂₅	1	5	yes	—
30	C₃×C₅	C₃×C₅×C₁₂₅	1	1	yes	characteristic
31	C₉	C₅×C₆₂₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₅	C₉×C₆₂₅	1	5	yes	direct product factor
33	C₅	C₅×C₉×C₁₂₅	1	1	yes	characteristic
34	C₃	C₃×C₅×C₆₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₂₅	C₃×C₅²
socle, prime radical	C₃×C₅²	C₃×C₁₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₆₂₅	C₅	direct (N × H)
4. C₅×C₆₂₅	C₉	direct (N × H)
11. C₆₂₅	C₅×C₉	direct (N × H)
24. C₅×C₉	C₆₂₅	direct (N × H)
31. C₉	C₅×C₆₂₅	direct (N × H)
32. C₅	C₉×C₆₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₂₅	5
C₉×C₆₂₅	5
C₃×C₅×C₆₂₅	3

Subgroups — C5×C9×C625 #72205102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₆₂₅ #72205102