Subgroups — C₃×C₄×C₅×C₁₃×C₃₁ #37563702

Order 24180.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₃₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₄×C₁₃×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₄×C₅×C₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₁₃×C₃₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₃×C₃₁	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₅×C₃₁	C₂×C₁₃	1	1	yes	characteristic
12	C₂×C₁₃×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₃×C₄×C₅×C₁₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₄×C₅×C₃₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₃₁	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₁₃×C₃₁	C₃×C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₅×C₁₃	C₂×C₃₁	1	1	yes	characteristic
18	C₃×C₄×C₃₁	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅×C₃₁	C₂×C₃×C₁₃	1	1	yes	characteristic
20	C₄×C₅×C₁₃	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅×C₁₃	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₃₁	C₂×C₅×C₁₃	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₃₁	C₃×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅×C₁₃	C₂×C₃×C₃₁	1	1	yes	characteristic
26	C₄×C₃₁	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₃₁	C₄×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₁₃	C₂×C₅×C₃₁	1	1	yes	characteristic
29	C₅×C₁₃	C₃×C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃₁	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
31	C₃×C₄×C₅	C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
32	C₄×C₁₃	C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₁₃	C₄×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
34	C₃₁	C₃×C₄×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃×C₅	C₂×C₁₃×C₃₁	1	1	yes	characteristic
36	C₂×C₁₃	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic
37	C₄×C₅	C₃×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	C₄×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
39	C₁₃	C₃×C₄×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₄	C₅×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₅	C₂×C₃×C₁₃×C₃₁	1	1	yes	characteristic
42	C₂×C₃	C₂×C₅×C₁₃×C₃₁	1	1	yes	characteristic
43	C₅	C₃×C₄×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	C₃×C₅×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₄×C₅×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₂×C₃×C₅×C₁₃×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₅×C₁₃×C₃₁
socle, prime radical	C₂×C₃×C₅×C₁₃×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×C₁₃×C₃₁	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₃₁	C₄	direct (N × H)
4. C₃×C₄×C₁₃×C₃₁	C₅	direct (N × H)
7. C₅×C₁₃×C₃₁	C₃×C₄	direct (N × H)
8. C₃×C₄×C₅×C₃₁	C₁₃	direct (N × H)
9. C₄×C₁₃×C₃₁	C₃×C₅	direct (N × H)
10. C₃×C₁₃×C₃₁	C₄×C₅	direct (N × H)
13. C₃×C₄×C₅×C₁₃	C₃₁	direct (N × H)
14. C₄×C₅×C₃₁	C₃×C₁₃	direct (N × H)
15. C₃×C₅×C₃₁	C₄×C₁₃	direct (N × H)
16. C₁₃×C₃₁	C₃×C₄×C₅	direct (N × H)
18. C₃×C₄×C₃₁	C₅×C₁₃	direct (N × H)
20. C₄×C₅×C₁₃	C₃×C₃₁	direct (N × H)
21. C₃×C₅×C₁₃	C₄×C₃₁	direct (N × H)
23. C₃×C₄×C₁₃	C₅×C₃₁	direct (N × H)
24. C₅×C₃₁	C₃×C₄×C₁₃	direct (N × H)
26. C₄×C₃₁	C₃×C₅×C₁₃	direct (N × H)
27. C₃×C₃₁	C₄×C₅×C₁₃	direct (N × H)
29. C₅×C₁₃	C₃×C₄×C₃₁	direct (N × H)
31. C₃×C₄×C₅	C₁₃×C₃₁	direct (N × H)
32. C₄×C₁₃	C₃×C₅×C₃₁	direct (N × H)
33. C₃×C₁₃	C₄×C₅×C₃₁	direct (N × H)
34. C₃₁	C₃×C₄×C₅×C₁₃	direct (N × H)
37. C₄×C₅	C₃×C₁₃×C₃₁	direct (N × H)
38. C₃×C₅	C₄×C₁₃×C₃₁	direct (N × H)
39. C₁₃	C₃×C₄×C₅×C₃₁	direct (N × H)
40. C₃×C₄	C₅×C₁₃×C₃₁	direct (N × H)
43. C₅	C₃×C₄×C₁₃×C₃₁	direct (N × H)
44. C₄	C₃×C₅×C₁₃×C₃₁	direct (N × H)
45. C₃	C₄×C₅×C₁₃×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×C₃×C₅×C₁₃×C₃₁	2
C₄×C₅×C₁₃×C₃₁	3
C₃×C₄×C₁₃×C₃₁	5
C₃×C₄×C₅×C₃₁	13
C₃×C₄×C₅×C₁₃	31

Subgroups — C3×C4×C5×C13×C31 #37563702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×C₁₃×C₃₁ #37563702