Subgroups — C₂²×C₉×C₂₉×C₃₁ #44569027

Order 32364.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂₉×C₃₁	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₂₉×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₉×C₃₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₂₉×C₃₁	C₂×C₃	1	3	yes	—
5	C₂²×C₂₉×C₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₉×C₃₁	C₂²×C₃	1	1	yes	characteristic
7	C₂×C₂₉×C₃₁	C₂×C₉	1	3	yes	direct product factor
8	C₂²×C₉×C₃₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₉×C₂₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂₉×C₃₁	C₂²×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₉×C₃₁	C₂×C₂₉	1	3	yes	direct product factor
12	C₂×C₉×C₂₉	C₂×C₃₁	1	3	yes	direct product factor
13	C₂²×C₃×C₃₁	C₃×C₂₉	1	1	yes	characteristic
14	C₂²×C₃×C₂₉	C₃×C₃₁	1	1	yes	characteristic
15	C₉×C₃₁	C₂²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₉×C₂₉	C₂²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₃₁	C₂×C₃×C₂₉	1	3	yes	—
18	C₂×C₃×C₂₉	C₂×C₃×C₃₁	1	3	yes	—
19	C₂²×C₃₁	C₉×C₂₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₂₉	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₃₁	C₂²×C₃×C₂₉	1	1	yes	characteristic
22	C₃×C₂₉	C₂²×C₃×C₃₁	1	1	yes	characteristic
23	C₂×C₃₁	C₂×C₉×C₂₉	1	3	yes	direct product factor
24	C₂×C₂₉	C₂×C₉×C₃₁	1	3	yes	direct product factor
25	C₂²×C₉	C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
26	C₃₁	C₂²×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂₉	C₂²×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	C₂×C₂₉×C₃₁	1	3	yes	direct product factor
29	C₂²×C₃	C₃×C₂₉×C₃₁	1	1	yes	characteristic
30	C₉	C₂²×C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₂₉×C₃₁	1	3	yes	—
32	C₂²	C₉×C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₂₉×C₃₁	1	1	yes	characteristic
34	C₂	C₂×C₉×C₂₉×C₃₁	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₂₉×C₃₁
socle, prime radical	C₂²×C₃×C₂₉×C₃₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×C₂₉×C₃₁	C₂	direct (N × H)
3. C₉×C₂₉×C₃₁	C₂²	direct (N × H)
5. C₂²×C₂₉×C₃₁	C₉	direct (N × H)
7. C₂×C₂₉×C₃₁	C₂×C₉	direct (N × H)
8. C₂²×C₉×C₃₁	C₂₉	direct (N × H)
9. C₂²×C₉×C₂₉	C₃₁	direct (N × H)
10. C₂₉×C₃₁	C₂²×C₉	direct (N × H)
11. C₂×C₉×C₃₁	C₂×C₂₉	direct (N × H)
12. C₂×C₉×C₂₉	C₂×C₃₁	direct (N × H)
15. C₉×C₃₁	C₂²×C₂₉	direct (N × H)
16. C₉×C₂₉	C₂²×C₃₁	direct (N × H)
19. C₂²×C₃₁	C₉×C₂₉	direct (N × H)
20. C₂²×C₂₉	C₉×C₃₁	direct (N × H)
23. C₂×C₃₁	C₂×C₉×C₂₉	direct (N × H)
24. C₂×C₂₉	C₂×C₉×C₃₁	direct (N × H)
25. C₂²×C₉	C₂₉×C₃₁	direct (N × H)
26. C₃₁	C₂²×C₉×C₂₉	direct (N × H)
27. C₂₉	C₂²×C₉×C₃₁	direct (N × H)
28. C₂×C₉	C₂×C₂₉×C₃₁	direct (N × H)
30. C₉	C₂²×C₂₉×C₃₁	direct (N × H)
32. C₂²	C₉×C₂₉×C₃₁	direct (N × H)
34. C₂	C₂×C₉×C₂₉×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
C₂×C₉×C₂₉×C₃₁	2
C₂²×C₃×C₂₉×C₃₁	3
C₂²×C₉×C₃₁	29
C₂²×C₉×C₂₉	31

Subgroups — C22×C9×C29×C31 #44569027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉×C₂₉×C₃₁ #44569027