Subgroups — C₂×C₄×C₅×C₉×C₃₁ #72189656

Order 11160.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×C₃₁	C₃	1	1	yes	maximal, characteristic
2	C₂×C₄×C₉×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂²×C₅×C₉×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×C₉×C₃₁	C₂	1	2	yes	maximal, direct product factor
5	C₂×C₅×C₉×C₃₁	C₄	1	2	yes	direct product factor
6	C₂×C₅×C₉×C₃₁	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₅×C₃₁	C₂×C₃	1	1	yes	characteristic
8	C₃×C₄×C₅×C₃₁	C₂×C₃	1	2	yes	—
9	C₅×C₉×C₃₁	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₄×C₅×C₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₉×C₃₁	C₂×C₅	1	1	yes	characteristic
12	C₄×C₉×C₃₁	C₂×C₅	1	2	yes	direct product factor
13	C₂×C₃×C₅×C₃₁	C₃×C₄	1	2	yes	—
14	C₂×C₃×C₅×C₃₁	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₄×C₃₁	C₃×C₅	1	1	yes	characteristic
16	C₂²×C₅×C₃₁	C₂×C₉	1	1	yes	characteristic
17	C₄×C₅×C₃₁	C₂×C₉	1	2	yes	direct product factor
18	C₂×C₉×C₃₁	C₄×C₅	1	2	yes	direct product factor
19	C₂×C₉×C₃₁	C₂²×C₅	1	1	yes	characteristic
20	C₃×C₅×C₃₁	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
22	C₃×C₄×C₃₁	C₂×C₃×C₅	1	2	yes	—
23	C₂×C₄×C₅×C₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×C₃₁	C₄×C₉	1	2	yes	direct product factor
25	C₂×C₅×C₃₁	C₂²×C₉	1	1	yes	characteristic
26	C₉×C₃₁	C₂×C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₄×C₃₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₃₁	C₃×C₄×C₅	1	2	yes	—
29	C₂×C₃×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic
30	C₂²×C₅×C₉	C₂×C₃₁	1	1	yes	characteristic
31	C₄×C₅×C₉	C₂×C₃₁	1	2	yes	direct product factor
32	C₅×C₃₁	C₂×C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
33	C₂²×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic
34	C₄×C₃₁	C₂×C₅×C₉	1	2	yes	direct product factor
35	C₂×C₃×C₄×C₅	C₃×C₃₁	1	1	yes	characteristic
36	C₃×C₃₁	C₂×C₃×C₄×C₅	1	1	yes	characteristic
37	C₂×C₅×C₉	C₄×C₃₁	1	2	yes	direct product factor
38	C₂×C₅×C₉	C₂²×C₃₁	1	1	yes	characteristic
39	C₂×C₄×C₉	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₃₁	C₄×C₅×C₉	1	2	yes	direct product factor
41	C₂×C₃₁	C₂²×C₅×C₉	1	1	yes	characteristic
42	C₂²×C₃×C₅	C₂×C₃×C₃₁	1	1	yes	characteristic
43	C₃×C₄×C₅	C₂×C₃×C₃₁	1	2	yes	—
44	C₅×C₉	C₂×C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₄×C₅	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
46	C₂²×C₉	C₂×C₅×C₃₁	1	1	yes	characteristic
47	C₄×C₉	C₂×C₅×C₃₁	1	2	yes	direct product factor
48	C₃₁	C₂×C₄×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃×C₅	C₃×C₄×C₃₁	1	2	yes	—
50	C₂×C₃×C₅	C₂²×C₃×C₃₁	1	1	yes	characteristic
51	C₂×C₃×C₄	C₃×C₅×C₃₁	1	1	yes	characteristic
52	C₂²×C₅	C₂×C₉×C₃₁	1	1	yes	characteristic
53	C₄×C₅	C₂×C₉×C₃₁	1	2	yes	direct product factor
54	C₂×C₉	C₄×C₅×C₃₁	1	2	yes	direct product factor
55	C₂×C₉	C₂²×C₅×C₃₁	1	1	yes	characteristic
56	C₃×C₅	C₂×C₃×C₄×C₃₁	1	1	yes	characteristic
57	C₂²×C₃	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic
58	C₃×C₄	C₂×C₃×C₅×C₃₁	1	2	yes	—
59	C₂×C₅	C₄×C₉×C₃₁	1	2	yes	direct product factor
60	C₂×C₅	C₂²×C₉×C₃₁	1	1	yes	characteristic
61	C₉	C₂×C₄×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₄	C₅×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₃	C₃×C₄×C₅×C₃₁	1	2	yes	—
64	C₂×C₃	C₂²×C₃×C₅×C₃₁	1	1	yes	characteristic
65	C₅	C₂×C₄×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²	C₂×C₅×C₉×C₃₁	1	1	yes	characteristic
67	C₄	C₂×C₅×C₉×C₃₁	1	2	yes	direct product factor
68	C₃	C₂×C₃×C₄×C₅×C₃₁	1	1	yes	characteristic
69	C₂	C₄×C₅×C₉×C₃₁	1	2	yes	direct product factor
70	C₂	C₂²×C₅×C₉×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₅×C₃₁
socle, prime radical	C₂²×C₃×C₅×C₃₁	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₉×C₃₁	C₅	direct (N × H)
4. C₄×C₅×C₉×C₃₁	C₂	direct (N × H)
5. C₂×C₅×C₉×C₃₁	C₄	direct (N × H)
9. C₅×C₉×C₃₁	C₂×C₄	direct (N × H)
10. C₂×C₄×C₅×C₃₁	C₉	direct (N × H)
12. C₄×C₉×C₃₁	C₂×C₅	direct (N × H)
17. C₄×C₅×C₃₁	C₂×C₉	direct (N × H)
18. C₂×C₉×C₃₁	C₄×C₅	direct (N × H)
23. C₂×C₄×C₅×C₉	C₃₁	direct (N × H)
24. C₂×C₅×C₃₁	C₄×C₉	direct (N × H)
26. C₉×C₃₁	C₂×C₄×C₅	direct (N × H)
27. C₂×C₄×C₃₁	C₅×C₉	direct (N × H)
31. C₄×C₅×C₉	C₂×C₃₁	direct (N × H)
32. C₅×C₃₁	C₂×C₄×C₉	direct (N × H)
34. C₄×C₃₁	C₂×C₅×C₉	direct (N × H)
37. C₂×C₅×C₉	C₄×C₃₁	direct (N × H)
39. C₂×C₄×C₉	C₅×C₃₁	direct (N × H)
40. C₂×C₃₁	C₄×C₅×C₉	direct (N × H)
44. C₅×C₉	C₂×C₄×C₃₁	direct (N × H)
45. C₂×C₄×C₅	C₉×C₃₁	direct (N × H)
47. C₄×C₉	C₂×C₅×C₃₁	direct (N × H)
48. C₃₁	C₂×C₄×C₅×C₉	direct (N × H)
53. C₄×C₅	C₂×C₉×C₃₁	direct (N × H)
54. C₂×C₉	C₄×C₅×C₃₁	direct (N × H)
59. C₂×C₅	C₄×C₉×C₃₁	direct (N × H)
61. C₉	C₂×C₄×C₅×C₃₁	direct (N × H)
62. C₂×C₄	C₅×C₉×C₃₁	direct (N × H)
65. C₅	C₂×C₄×C₉×C₃₁	direct (N × H)
67. C₄	C₂×C₅×C₉×C₃₁	direct (N × H)
69. C₂	C₄×C₅×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
C₂×C₃×C₄×C₅×C₃₁	3
C₂×C₄×C₉×C₃₁	5
C₂²×C₅×C₉×C₃₁	2
C₄×C₅×C₉×C₃₁	2
C₂×C₄×C₅×C₉	31

Subgroups — C2×C4×C5×C9×C31 #72189656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅×C₉×C₃₁ #72189656