Subgroups — C₅×C₉×C₂₃×C₃₁ #44545539

Order 32085.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×C₃₁	C₃	1	1	yes	maximal, characteristic
2	C₉×C₂₃×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₂₃×C₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₂₃×C₃₁	C₃×C₅	1	1	yes	characteristic
5	C₅×C₉×C₃₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₉×C₂₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂₃×C₃₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₅×C₃₁	C₃×C₂₃	1	1	yes	characteristic
9	C₃×C₅×C₂₃	C₃×C₃₁	1	1	yes	characteristic
10	C₉×C₃₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
11	C₉×C₂₃	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₃₁	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₂₃	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₃₁	C₃×C₅×C₂₃	1	1	yes	characteristic
15	C₃×C₂₃	C₃×C₅×C₃₁	1	1	yes	characteristic
16	C₅×C₉	C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃₁	C₅×C₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂₃	C₅×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	C₃×C₂₃×C₃₁	1	1	yes	characteristic
20	C₉	C₅×C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₉×C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₅×C₂₃×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₂₃×C₃₁
socle, prime radical	C₃×C₅×C₂₃×C₃₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₂₃×C₃₁	C₅	direct (N × H)
3. C₅×C₂₃×C₃₁	C₉	direct (N × H)
5. C₅×C₉×C₃₁	C₂₃	direct (N × H)
6. C₅×C₉×C₂₃	C₃₁	direct (N × H)
7. C₂₃×C₃₁	C₅×C₉	direct (N × H)
10. C₉×C₃₁	C₅×C₂₃	direct (N × H)
11. C₉×C₂₃	C₅×C₃₁	direct (N × H)
12. C₅×C₃₁	C₉×C₂₃	direct (N × H)
13. C₅×C₂₃	C₉×C₃₁	direct (N × H)
16. C₅×C₉	C₂₃×C₃₁	direct (N × H)
17. C₃₁	C₅×C₉×C₂₃	direct (N × H)
18. C₂₃	C₅×C₉×C₃₁	direct (N × H)
20. C₉	C₅×C₂₃×C₃₁	direct (N × H)
21. C₅	C₉×C₂₃×C₃₁	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×C₂₃×C₃₁	3
C₉×C₂₃×C₃₁	5
C₅×C₉×C₃₁	23
C₅×C₉×C₂₃	31

Subgroups — C5×C9×C23×C31 #44545539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₂₃×C₃₁ #44545539