Subgroups — C₂×C₅×C₇×C₉×C₃₁ #34086096

Order 19530.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×C₃₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅×C₇×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₉×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×C₉×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₃₁	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₉×C₃₁	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₃₁	C₃×C₅	1	1	yes	characteristic
10	C₅×C₇×C₃₁	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₅×C₃₁	C₃×C₇	1	1	yes	characteristic
12	C₃×C₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₂×C₅×C₇×C₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₉×C₃₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic
16	C₂×C₇×C₃₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₅×C₇×C₉	C₂×C₃₁	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₃₁	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
19	C₉×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
20	C₇×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₅×C₇	C₃×C₃₁	1	1	yes	characteristic
22	C₂×C₃×C₃₁	C₃×C₅×C₇	1	1	yes	characteristic
23	C₅×C₃₁	C₂×C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₇×C₉	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₅×C₇	C₂×C₃×C₃₁	1	1	yes	characteristic
26	C₃×C₃₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic
27	C₂×C₅×C₉	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₅×C₇	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
29	C₇×C₉	C₂×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃₁	C₅×C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₉	C₂×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₃×C₇	C₃×C₅×C₃₁	1	1	yes	characteristic
33	C₅×C₇	C₂×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
34	C₃₁	C₂×C₅×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃×C₅	C₃×C₇×C₃₁	1	1	yes	characteristic
36	C₃×C₇	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic
37	C₂×C₉	C₅×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	C₂×C₃×C₇×C₃₁	1	1	yes	characteristic
39	C₂×C₇	C₅×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	C₇×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
41	C₉	C₂×C₅×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₅×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₃×C₅×C₇×C₃₁	1	1	yes	characteristic
44	C₅	C₂×C₇×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₂×C₃×C₅×C₇×C₃₁	1	1	yes	characteristic
46	C₂	C₅×C₇×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅×C₇×C₃₁
socle, prime radical	C₂×C₃×C₅×C₇×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. C₅×C₇×C₉×C₃₁	C₂	direct (N × H)
3. C₂×C₇×C₉×C₃₁	C₅	direct (N × H)
5. C₂×C₅×C₉×C₃₁	C₇	direct (N × H)
6. C₂×C₅×C₇×C₃₁	C₉	direct (N × H)
7. C₇×C₉×C₃₁	C₂×C₅	direct (N × H)
8. C₅×C₉×C₃₁	C₂×C₇	direct (N × H)
10. C₅×C₇×C₃₁	C₂×C₉	direct (N × H)
13. C₂×C₅×C₇×C₉	C₃₁	direct (N × H)
14. C₂×C₉×C₃₁	C₅×C₇	direct (N × H)
16. C₂×C₇×C₃₁	C₅×C₉	direct (N × H)
17. C₅×C₇×C₉	C₂×C₃₁	direct (N × H)
18. C₂×C₅×C₃₁	C₇×C₉	direct (N × H)
19. C₉×C₃₁	C₂×C₅×C₇	direct (N × H)
20. C₇×C₃₁	C₂×C₅×C₉	direct (N × H)
23. C₅×C₃₁	C₂×C₇×C₉	direct (N × H)
24. C₂×C₇×C₉	C₅×C₃₁	direct (N × H)
27. C₂×C₅×C₉	C₇×C₃₁	direct (N × H)
28. C₂×C₅×C₇	C₉×C₃₁	direct (N × H)
29. C₇×C₉	C₂×C₅×C₃₁	direct (N × H)
30. C₂×C₃₁	C₅×C₇×C₉	direct (N × H)
31. C₅×C₉	C₂×C₇×C₃₁	direct (N × H)
33. C₅×C₇	C₂×C₉×C₃₁	direct (N × H)
34. C₃₁	C₂×C₅×C₇×C₉	direct (N × H)
37. C₂×C₉	C₅×C₇×C₃₁	direct (N × H)
39. C₂×C₇	C₅×C₉×C₃₁	direct (N × H)
40. C₂×C₅	C₇×C₉×C₃₁	direct (N × H)
41. C₉	C₂×C₅×C₇×C₃₁	direct (N × H)
42. C₇	C₂×C₅×C₉×C₃₁	direct (N × H)
44. C₅	C₂×C₇×C₉×C₃₁	direct (N × H)
46. C₂	C₅×C₇×C₉×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
C₅×C₇×C₉×C₃₁	2
C₂×C₃×C₅×C₇×C₃₁	3
C₂×C₇×C₉×C₃₁	5
C₂×C₅×C₉×C₃₁	7
C₂×C₅×C₇×C₉	31

Subgroups — C2×C5×C7×C9×C31 #34086096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×C₉×C₃₁ #34086096