Subgroups — C₂²×C₂₅×C₁₂₅ #72190847

Order 12500.

380 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₂₅	C₅	1	5	yes	maximal
2	C₂²×C₂₅²	C₅	1	1	yes	maximal, characteristic
3	C₂×C₂₅×C₁₂₅	C₂	1	3	yes	maximal, direct product factor
4	C₂₅×C₁₂₅	C₂²	1	1	yes	characteristic, direct product factor, Sylow
5	C₂×C₅×C₁₂₅	C₂×C₅	1	15	yes	—
6	C₂×C₂₅²	C₂×C₅	1	3	yes	—
7	C₅×C₁₂₅	C₂²×C₅	1	5	yes	—
8	C₂₅²	C₂²×C₅	1	1	yes	characteristic
9	C₂²×C₅×C₂₅	C₂₅	1	5	yes	—
10	C₂²×C₅×C₂₅	C₅²	1	1	yes	characteristic
11	C₂²×C₁₂₅	C₂₅	1	25	yes	direct product factor
12	C₂×C₅×C₂₅	C₂×C₂₅	1	15	yes	—
13	C₂×C₅×C₂₅	C₂×C₅²	1	3	yes	—
14	C₂×C₁₂₅	C₂×C₂₅	1	75	yes	direct product factor
15	C₅×C₂₅	C₂²×C₂₅	1	5	yes	—
16	C₅×C₂₅	C₂²×C₅²	1	1	yes	characteristic
17	C₁₂₅	C₂²×C₂₅	1	25	yes	direct product factor
18	C₂²×C₅²	C₅×C₂₅	1	1	yes	characteristic
19	C₂²×C₂₅	C₁₂₅	1	25	yes	direct product factor
20	C₂²×C₂₅	C₅×C₂₅	1	5	yes	—
21	C₂×C₅²	C₂×C₅×C₂₅	1	3	yes	—
22	C₂×C₂₅	C₂×C₁₂₅	1	75	yes	direct product factor
23	C₂×C₂₅	C₂×C₅×C₂₅	1	15	yes	—
24	C₅²	C₂²×C₅×C₂₅	1	1	yes	characteristic
25	C₂₅	C₂²×C₁₂₅	1	25	yes	direct product factor
26	C₂₅	C₂²×C₅×C₂₅	1	5	yes	—
27	C₂²×C₅	C₂₅²	1	1	yes	characteristic
28	C₂²×C₅	C₅×C₁₂₅	1	5	yes	—
29	C₂×C₅	C₂×C₂₅²	1	3	yes	—
30	C₂×C₅	C₂×C₅×C₁₂₅	1	15	yes	—
31	C₅	C₂²×C₂₅²	1	1	yes	characteristic
32	C₅	C₂²×C₅×C₁₂₅	1	5	yes	—
33	C₂²	C₂₅×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₂₅×C₁₂₅	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅×C₂₅	C₂²×C₅²
socle, prime radical	C₂²×C₅²	C₅×C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₂₅×C₁₂₅	C₂	direct (N × H)
4. C₂₅×C₁₂₅	C₂²	direct (N × H)
11. C₂²×C₁₂₅	C₂₅	direct (N × H)
14. C₂×C₁₂₅	C₂×C₂₅	direct (N × H)
17. C₁₂₅	C₂²×C₂₅	direct (N × H)
19. C₂²×C₂₅	C₁₂₅	direct (N × H)
22. C₂×C₂₅	C₂×C₁₂₅	direct (N × H)
25. C₂₅	C₂²×C₁₂₅	direct (N × H)
33. C₂²	C₂₅×C₁₂₅	direct (N × H)
34. C₂	C₂×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
C₂²×C₅×C₁₂₅	5
C₂²×C₂₅²	5
C₂×C₂₅×C₁₂₅	2

Subgroups — C22×C25×C125 #72190847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₅×C₁₂₅ #72190847