Subgroups — C₂²×C₃×C₂₅×C₄₃ #27166344

Order 12900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₅×C₄₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₂₅×C₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₅×C₄₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃×C₅×C₄₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₂₅×C₄₃	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₅×C₄₃	C₂×C₅	1	3	yes	—
7	C₂₅×C₄₃	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₅×C₄₃	C₃×C₅	1	1	yes	characteristic
9	C₃×C₅×C₄₃	C₂²×C₅	1	1	yes	characteristic
10	C₂²×C₃×C₄₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₄₃	C₂×C₃×C₅	1	3	yes	—
12	C₂²×C₃×C₂₅	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₄₃	C₂×C₂₅	1	3	yes	direct product factor
14	C₅×C₄₃	C₂²×C₃×C₅	1	1	yes	characteristic
15	C₂²×C₄₃	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₂₅	C₂×C₄₃	1	3	yes	direct product factor
17	C₃×C₄₃	C₂²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₂₅	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₄₃	C₂×C₃×C₂₅	1	3	yes	direct product factor
20	C₃×C₂₅	C₂²×C₄₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₃×C₅	C₅×C₄₃	1	1	yes	characteristic
22	C₂×C₂₅	C₂×C₃×C₄₃	1	3	yes	direct product factor
23	C₄₃	C₂²×C₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃×C₅	C₂×C₅×C₄₃	1	3	yes	—
25	C₂₅	C₂²×C₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²×C₅	C₃×C₅×C₄₃	1	1	yes	characteristic
27	C₃×C₅	C₂²×C₅×C₄₃	1	1	yes	characteristic
28	C₂²×C₃	C₂₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅	C₂×C₃×C₅×C₄₃	1	3	yes	—
30	C₂×C₃	C₂×C₂₅×C₄₃	1	3	yes	direct product factor
31	C₅	C₂²×C₃×C₅×C₄₃	1	1	yes	characteristic
32	C₂²	C₃×C₂₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₂₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₃×C₂₅×C₄₃	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₃×C₅×C₄₃
socle, prime radical	C₂²×C₃×C₅×C₄₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂₅×C₄₃	C₂	direct (N × H)
2. C₂²×C₂₅×C₄₃	C₃	direct (N × H)
3. C₃×C₂₅×C₄₃	C₂²	direct (N × H)
5. C₂×C₂₅×C₄₃	C₂×C₃	direct (N × H)
7. C₂₅×C₄₃	C₂²×C₃	direct (N × H)
10. C₂²×C₃×C₄₃	C₂₅	direct (N × H)
12. C₂²×C₃×C₂₅	C₄₃	direct (N × H)
13. C₂×C₃×C₄₃	C₂×C₂₅	direct (N × H)
15. C₂²×C₄₃	C₃×C₂₅	direct (N × H)
16. C₂×C₃×C₂₅	C₂×C₄₃	direct (N × H)
17. C₃×C₄₃	C₂²×C₂₅	direct (N × H)
18. C₂²×C₂₅	C₃×C₄₃	direct (N × H)
19. C₂×C₄₃	C₂×C₃×C₂₅	direct (N × H)
20. C₃×C₂₅	C₂²×C₄₃	direct (N × H)
22. C₂×C₂₅	C₂×C₃×C₄₃	direct (N × H)
23. C₄₃	C₂²×C₃×C₂₅	direct (N × H)
25. C₂₅	C₂²×C₃×C₄₃	direct (N × H)
28. C₂²×C₃	C₂₅×C₄₃	direct (N × H)
30. C₂×C₃	C₂×C₂₅×C₄₃	direct (N × H)
32. C₂²	C₃×C₂₅×C₄₃	direct (N × H)
33. C₃	C₂²×C₂₅×C₄₃	direct (N × H)
34. C₂	C₂×C₃×C₂₅×C₄₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₂₅×C₄₃	2
C₂²×C₂₅×C₄₃	3
C₂²×C₃×C₅×C₄₃	5
C₂²×C₃×C₂₅	43

Subgroups — C22×C3×C25×C43 #27166344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₂₅×C₄₃ #27166344