Subgroups — C₂²×C₅³×C₂₅ #72190851

Order 12500.

10880 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₂₅	C₅	1	155	yes	maximal, direct product factor
2	C₂²×C₅⁴	C₅	1	1	yes	maximal, characteristic
3	C₂×C₅³×C₂₅	C₂	1	3	yes	maximal, direct product factor
4	C₅³×C₂₅	C₂²	1	1	yes	characteristic, direct product factor, Sylow
5	C₂×C₅⁴	C₂×C₅	1	3	yes	—
6	C₂×C₅²×C₂₅	C₂×C₅	1	465	yes	direct product factor
7	C₅⁴	C₂²×C₅	1	1	yes	characteristic
8	C₅²×C₂₅	C₂²×C₅	1	155	yes	direct product factor
9	C₂²×C₅³	C₂₅	1	125	yes	direct product factor
10	C₂²×C₅³	C₅²	1	31	yes	—
11	C₂²×C₅×C₂₅	C₅²	1	775	yes	direct product factor
12	C₂×C₅³	C₂×C₂₅	1	375	yes	direct product factor
13	C₂×C₅³	C₂×C₅²	1	93	yes	—
14	C₂×C₅×C₂₅	C₂×C₅²	1	2325	yes	direct product factor
15	C₅³	C₂²×C₂₅	1	125	yes	direct product factor
16	C₅³	C₂²×C₅²	1	31	yes	—
17	C₅×C₂₅	C₂²×C₅²	1	775	yes	direct product factor
18	C₂²×C₅²	C₅×C₂₅	1	775	yes	direct product factor
19	C₂²×C₅²	C₅³	1	31	yes	—
20	C₂²×C₂₅	C₅³	1	125	yes	direct product factor
21	C₂×C₅²	C₂×C₅×C₂₅	1	2325	yes	direct product factor
22	C₂×C₅²	C₂×C₅³	1	93	yes	—
23	C₂×C₂₅	C₂×C₅³	1	375	yes	direct product factor
24	C₅²	C₂²×C₅×C₂₅	1	775	yes	direct product factor
25	C₅²	C₂²×C₅³	1	31	yes	—
26	C₂₅	C₂²×C₅³	1	125	yes	direct product factor
27	C₂²×C₅	C₅²×C₂₅	1	155	yes	direct product factor
28	C₂²×C₅	C₅⁴	1	1	yes	characteristic
29	C₂×C₅	C₂×C₅²×C₂₅	1	465	yes	direct product factor
30	C₂×C₅	C₂×C₅⁴	1	3	yes	—
31	C₅	C₂²×C₅⁴	1	1	yes	characteristic
32	C₅	C₂²×C₅²×C₂₅	1	155	yes	direct product factor
33	C₂²	C₅³×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅³×C₂₅	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅⁴
socle, prime radical	C₂²×C₅⁴	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅²×C₂₅	C₅	direct (N × H)
3. C₂×C₅³×C₂₅	C₂	direct (N × H)
4. C₅³×C₂₅	C₂²	direct (N × H)
6. C₂×C₅²×C₂₅	C₂×C₅	direct (N × H)
8. C₅²×C₂₅	C₂²×C₅	direct (N × H)
9. C₂²×C₅³	C₂₅	direct (N × H)
11. C₂²×C₅×C₂₅	C₅²	direct (N × H)
12. C₂×C₅³	C₂×C₂₅	direct (N × H)
14. C₂×C₅×C₂₅	C₂×C₅²	direct (N × H)
15. C₅³	C₂²×C₂₅	direct (N × H)
17. C₅×C₂₅	C₂²×C₅²	direct (N × H)
18. C₂²×C₅²	C₅×C₂₅	direct (N × H)
20. C₂²×C₂₅	C₅³	direct (N × H)
21. C₂×C₅²	C₂×C₅×C₂₅	direct (N × H)
23. C₂×C₂₅	C₂×C₅³	direct (N × H)
24. C₅²	C₂²×C₅×C₂₅	direct (N × H)
26. C₂₅	C₂²×C₅³	direct (N × H)
27. C₂²×C₅	C₅²×C₂₅	direct (N × H)
29. C₂×C₅	C₂×C₅²×C₂₅	direct (N × H)
32. C₅	C₂²×C₅²×C₂₅	direct (N × H)
33. C₂²	C₅³×C₂₅	direct (N × H)
34. C₂	C₂×C₅³×C₂₅	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×C₅²×C₂₅	5
C₂²×C₅⁴	5
C₂×C₅³×C₂₅	2

Subgroups — C22×C53×C25 #72190851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅³×C₂₅ #72190851