Subgroups — C₂×C₉×C₂₅×C₄₃ #34084010

Order 19350.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅×C₄₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₂₅×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₉×C₄₃	C₅	1	1	yes	maximal, characteristic
4	C₃×C₂₅×C₄₃	C₂×C₃	1	1	yes	characteristic
5	C₂×C₂₅×C₄₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₉×C₄₃	C₂×C₅	1	1	yes	characteristic
7	C₂×C₃×C₅×C₄₃	C₃×C₅	1	1	yes	characteristic
8	C₂₅×C₄₃	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₉×C₄₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic
11	C₂×C₉×C₂₅	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×C₄₃	C₅×C₉	1	1	yes	characteristic
13	C₉×C₄₃	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₄₃	C₃×C₂₅	1	1	yes	characteristic
15	C₉×C₂₅	C₂×C₄₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₄₃	C₂×C₅×C₉	1	1	yes	characteristic
17	C₂×C₃×C₂₅	C₃×C₄₃	1	1	yes	characteristic
18	C₃×C₄₃	C₂×C₃×C₂₅	1	1	yes	characteristic
19	C₂×C₅×C₉	C₅×C₄₃	1	1	yes	characteristic
20	C₂×C₄₃	C₉×C₂₅	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₂₅	C₂×C₃×C₄₃	1	1	yes	characteristic
22	C₂×C₂₅	C₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
23	C₅×C₉	C₂×C₅×C₄₃	1	1	yes	characteristic
24	C₄₃	C₂×C₉×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃×C₅	C₃×C₅×C₄₃	1	1	yes	characteristic
26	C₂₅	C₂×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₉	C₂₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	C₂×C₃×C₅×C₄₃	1	1	yes	characteristic
29	C₂×C₅	C₅×C₉×C₄₃	1	1	yes	characteristic
30	C₉	C₂×C₂₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×C₂₅×C₄₃	1	1	yes	characteristic
32	C₅	C₂×C₅×C₉×C₄₃	1	1	yes	characteristic
33	C₃	C₂×C₃×C₂₅×C₄₃	1	1	yes	characteristic
34	C₂	C₉×C₂₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₅	C₂×C₃×C₅×C₄₃
socle, prime radical	C₂×C₃×C₅×C₄₃	C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×C₂₅×C₄₃	C₂	direct (N × H)
5. C₂×C₂₅×C₄₃	C₉	direct (N × H)
8. C₂₅×C₄₃	C₂×C₉	direct (N × H)
9. C₂×C₉×C₄₃	C₂₅	direct (N × H)
11. C₂×C₉×C₂₅	C₄₃	direct (N × H)
13. C₉×C₄₃	C₂×C₂₅	direct (N × H)
15. C₉×C₂₅	C₂×C₄₃	direct (N × H)
20. C₂×C₄₃	C₉×C₂₅	direct (N × H)
22. C₂×C₂₅	C₉×C₄₃	direct (N × H)
24. C₄₃	C₂×C₉×C₂₅	direct (N × H)
26. C₂₅	C₂×C₉×C₄₃	direct (N × H)
27. C₂×C₉	C₂₅×C₄₃	direct (N × H)
30. C₉	C₂×C₂₅×C₄₃	direct (N × H)
34. C₂	C₉×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
C₉×C₂₅×C₄₃	2
C₂×C₃×C₂₅×C₄₃	3
C₂×C₅×C₉×C₄₃	5
C₂×C₉×C₂₅	43

Subgroups — C2×C9×C25×C43 #34084010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₂₅×C₄₃ #34084010