Subgroups — C₃×C₅×C₁₃×C₁₂₅ #72201664

Order 24375.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₂₅	C₅	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₁₂₅	C₅	1	5	yes	maximal, direct product factor
3	C₅×C₁₃×C₁₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₂₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₃×C₂₅	C₃×C₅	1	1	yes	characteristic
6	C₁₃×C₁₂₅	C₃×C₅	1	5	yes	direct product factor
7	C₃×C₅²×C₁₃	C₂₅	1	1	yes	characteristic
8	C₃×C₁₃×C₂₅	C₂₅	1	4	yes	—
9	C₃×C₁₃×C₂₅	C₅²	1	1	yes	characteristic
10	C₅×C₁₂₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₃×C₅×C₂₅	C₅×C₁₃	1	1	yes	characteristic
12	C₃×C₁₂₅	C₅×C₁₃	1	5	yes	direct product factor
13	C₅²×C₁₃	C₃×C₂₅	1	1	yes	characteristic
14	C₁₃×C₂₅	C₃×C₂₅	1	4	yes	—
15	C₁₃×C₂₅	C₃×C₅²	1	1	yes	characteristic
16	C₃×C₅×C₁₃	C₁₂₅	1	5	yes	direct product factor
17	C₃×C₅×C₁₃	C₅×C₂₅	1	1	yes	characteristic
18	C₅×C₂₅	C₃×C₅×C₁₃	1	1	yes	characteristic
19	C₁₂₅	C₃×C₅×C₁₃	1	5	yes	direct product factor
20	C₃×C₅²	C₁₃×C₂₅	1	1	yes	characteristic
21	C₃×C₂₅	C₁₃×C₂₅	1	4	yes	—
22	C₃×C₂₅	C₅²×C₁₃	1	1	yes	characteristic
23	C₅×C₁₃	C₃×C₁₂₅	1	5	yes	direct product factor
24	C₅×C₁₃	C₃×C₅×C₂₅	1	1	yes	characteristic
25	C₃×C₁₃	C₅×C₁₂₅	1	1	yes	characteristic, direct product factor, Hall
26	C₅²	C₃×C₁₃×C₂₅	1	1	yes	characteristic
27	C₂₅	C₃×C₁₃×C₂₅	1	4	yes	—
28	C₂₅	C₃×C₅²×C₁₃	1	1	yes	characteristic
29	C₃×C₅	C₁₃×C₁₂₅	1	5	yes	direct product factor
30	C₃×C₅	C₅×C₁₃×C₂₅	1	1	yes	characteristic
31	C₁₃	C₃×C₅×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₅	C₃×C₁₃×C₁₂₅	1	5	yes	direct product factor
33	C₅	C₃×C₅×C₁₃×C₂₅	1	1	yes	characteristic
34	C₃	C₅×C₁₃×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₅	C₃×C₅²×C₁₃
socle, prime radical	C₃×C₅²×C₁₃	C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×C₁₂₅	C₅	direct (N × H)
3. C₅×C₁₃×C₁₂₅	C₃	direct (N × H)
4. C₃×C₅×C₁₂₅	C₁₃	direct (N × H)
6. C₁₃×C₁₂₅	C₃×C₅	direct (N × H)
10. C₅×C₁₂₅	C₃×C₁₃	direct (N × H)
12. C₃×C₁₂₅	C₅×C₁₃	direct (N × H)
16. C₃×C₅×C₁₃	C₁₂₅	direct (N × H)
19. C₁₂₅	C₃×C₅×C₁₃	direct (N × H)
23. C₅×C₁₃	C₃×C₁₂₅	direct (N × H)
25. C₃×C₁₃	C₅×C₁₂₅	direct (N × H)
29. C₃×C₅	C₁₃×C₁₂₅	direct (N × H)
31. C₁₃	C₃×C₅×C₁₂₅	direct (N × H)
32. C₅	C₃×C₁₃×C₁₂₅	direct (N × H)
34. C₃	C₅×C₁₃×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
C₃×C₅×C₁₃×C₂₅	5
C₃×C₁₃×C₁₂₅	5
C₅×C₁₃×C₁₂₅	3
C₃×C₅×C₁₂₅	13

Subgroups — C3×C5×C13×C125 #72201664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₃×C₁₂₅ #72201664