Subgroups — C₄×C₅³×C₂₅ #72190843

Order 12500.

6528 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅⁴	C₅	1	1	yes	maximal, characteristic
2	C₄×C₅²×C₂₅	C₅	1	155	yes	maximal, direct product factor
3	C₂×C₅³×C₂₅	C₂	1	1	yes	maximal, characteristic
4	C₅³×C₂₅	C₄	1	1	yes	characteristic, direct product factor, Sylow
5	C₂×C₅⁴	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅²×C₂₅	C₂×C₅	1	155	yes	—
7	C₅⁴	C₄×C₅	1	1	yes	characteristic
8	C₅²×C₂₅	C₄×C₅	1	155	yes	direct product factor
9	C₄×C₅³	C₂₅	1	125	yes	direct product factor
10	C₄×C₅³	C₅²	1	31	yes	—
11	C₄×C₅×C₂₅	C₅²	1	775	yes	direct product factor
12	C₂×C₅³	C₂×C₂₅	1	125	yes	—
13	C₂×C₅³	C₂×C₅²	1	31	yes	—
14	C₂×C₅×C₂₅	C₂×C₅²	1	775	yes	—
15	C₅³	C₄×C₂₅	1	125	yes	direct product factor
16	C₅³	C₄×C₅²	1	31	yes	—
17	C₅×C₂₅	C₄×C₅²	1	775	yes	direct product factor
18	C₄×C₅²	C₅×C₂₅	1	775	yes	direct product factor
19	C₄×C₅²	C₅³	1	31	yes	—
20	C₄×C₂₅	C₅³	1	125	yes	direct product factor
21	C₂×C₅²	C₂×C₅×C₂₅	1	775	yes	—
22	C₂×C₅²	C₂×C₅³	1	31	yes	—
23	C₂×C₂₅	C₂×C₅³	1	125	yes	—
24	C₅²	C₄×C₅×C₂₅	1	775	yes	direct product factor
25	C₅²	C₄×C₅³	1	31	yes	—
26	C₂₅	C₄×C₅³	1	125	yes	direct product factor
27	C₄×C₅	C₅²×C₂₅	1	155	yes	direct product factor
28	C₄×C₅	C₅⁴	1	1	yes	characteristic
29	C₂×C₅	C₂×C₅²×C₂₅	1	155	yes	—
30	C₂×C₅	C₂×C₅⁴	1	1	yes	characteristic
31	C₅	C₄×C₅²×C₂₅	1	155	yes	direct product factor
32	C₅	C₄×C₅⁴	1	1	yes	characteristic
33	C₄	C₅³×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅³×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₅⁴
socle, prime radical	C₂×C₅⁴	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₅²×C₂₅	C₅	direct (N × H)
4. C₅³×C₂₅	C₄	direct (N × H)
8. C₅²×C₂₅	C₄×C₅	direct (N × H)
9. C₄×C₅³	C₂₅	direct (N × H)
11. C₄×C₅×C₂₅	C₅²	direct (N × H)
15. C₅³	C₄×C₂₅	direct (N × H)
17. C₅×C₂₅	C₄×C₅²	direct (N × H)
18. C₄×C₅²	C₅×C₂₅	direct (N × H)
20. C₄×C₂₅	C₅³	direct (N × H)
24. C₅²	C₄×C₅×C₂₅	direct (N × H)
26. C₂₅	C₄×C₅³	direct (N × H)
27. C₄×C₅	C₅²×C₂₅	direct (N × H)
31. C₅	C₄×C₅²×C₂₅	direct (N × H)
33. C₄	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
C₄×C₅⁴	5
C₄×C₅²×C₂₅	5
C₂×C₅³×C₂₅	2

Subgroups — C4×C53×C25 #72190843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅³×C₂₅ #72190843