Subgroups — C₄×C₅×C₆₂₅ #72190839

Order 12500.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₁₂₅	C₅	1	1	yes	maximal, characteristic
2	C₄×C₆₂₅	C₅	1	5	yes	maximal, direct product factor
3	C₂×C₅×C₆₂₅	C₂	1	1	yes	maximal, characteristic
4	C₅×C₆₂₅	C₄	1	1	yes	characteristic, direct product factor, Sylow
5	C₂×C₅×C₁₂₅	C₂×C₅	1	1	yes	characteristic
6	C₂×C₆₂₅	C₂×C₅	1	5	yes	—
7	C₅×C₁₂₅	C₄×C₅	1	1	yes	characteristic
8	C₆₂₅	C₄×C₅	1	5	yes	direct product factor
9	C₄×C₅×C₂₅	C₂₅	1	1	yes	characteristic
10	C₄×C₁₂₅	C₂₅	1	4	yes	—
11	C₄×C₁₂₅	C₅²	1	1	yes	characteristic
12	C₂×C₅×C₂₅	C₂×C₂₅	1	1	yes	characteristic
13	C₂×C₁₂₅	C₂×C₂₅	1	4	yes	—
14	C₂×C₁₂₅	C₂×C₅²	1	1	yes	characteristic
15	C₅×C₂₅	C₄×C₂₅	1	1	yes	characteristic
16	C₁₂₅	C₄×C₂₅	1	4	yes	—
17	C₁₂₅	C₄×C₅²	1	1	yes	characteristic
18	C₄×C₅²	C₁₂₅	1	1	yes	characteristic
19	C₄×C₂₅	C₁₂₅	1	4	yes	—
20	C₄×C₂₅	C₅×C₂₅	1	1	yes	characteristic
21	C₂×C₅²	C₂×C₁₂₅	1	1	yes	characteristic
22	C₂×C₂₅	C₂×C₁₂₅	1	4	yes	—
23	C₂×C₂₅	C₂×C₅×C₂₅	1	1	yes	characteristic
24	C₅²	C₄×C₁₂₅	1	1	yes	characteristic
25	C₂₅	C₄×C₁₂₅	1	4	yes	—
26	C₂₅	C₄×C₅×C₂₅	1	1	yes	characteristic
27	C₄×C₅	C₆₂₅	1	5	yes	direct product factor
28	C₄×C₅	C₅×C₁₂₅	1	1	yes	characteristic
29	C₂×C₅	C₂×C₆₂₅	1	5	yes	—
30	C₂×C₅	C₂×C₅×C₁₂₅	1	1	yes	characteristic
31	C₅	C₄×C₆₂₅	1	5	yes	direct product factor
32	C₅	C₄×C₅×C₁₂₅	1	1	yes	characteristic
33	C₄	C₅×C₆₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅×C₆₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₂₅	C₂×C₅²
socle, prime radical	C₂×C₅²	C₂×C₁₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₆₂₅	C₅	direct (N × H)
4. C₅×C₆₂₅	C₄	direct (N × H)
8. C₆₂₅	C₄×C₅	direct (N × H)
27. C₄×C₅	C₆₂₅	direct (N × H)
31. C₅	C₄×C₆₂₅	direct (N × H)
33. C₄	C₅×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
C₄×C₅×C₁₂₅	5
C₄×C₆₂₅	5
C₂×C₅×C₆₂₅	2

Subgroups — C4×C5×C625 #72190839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₆₂₅ #72190839