Subgroups — C₂×C₃×C₅×D₅×C₃₁ #22604944

Order 9300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₅×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃×C₅×C₃₁	—	5	1	no	maximal
6	C₂×C₃×D₅×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₅×C₃₁	C₂×C₃	1	2	yes	direct product factor
9	C₂×C₃×C₅×C₃₁	—	2	2	no	—
10	C₂×C₃×C₅×C₃₁	—	5	2	no	—
11	C₂×C₃×C₅×C₃₁	D₅	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₅×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×D₅×C₃₁	C₂×C₅	1	2	yes	direct product factor
14	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₅×C₃₁	—	5	1	no	—
16	C₂×D₅×C₃₁	C₃×C₅	1	1	yes	characteristic, direct product factor
17	C₃×C₅×C₃₁	—	2	2	no	—
18	C₃×C₅×C₃₁	C₂×D₅	1	1	yes	characteristic, direct product factor
19	C₃×C₅×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₃₁	—	5	1	no	Hall
21	C₂×C₅×C₃₁	—	2	2	no	—
22	C₂×C₅×C₃₁	—	5	2	no	—
23	C₂×C₅×C₃₁	C₃×D₅	1	1	yes	characteristic, direct product factor
24	C₂×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
25	D₅×C₃₁	C₂×C₃×C₅	1	2	yes	direct product factor
26	C₂×C₃×C₅×D₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₃×C₃₁	—	5	2	no	—
28	C₂×C₃×C₃₁	C₅×D₅	1	1	yes	characteristic, direct product factor
29	C₅×C₃₁	—	2	2	no	—
30	C₅×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, direct product factor
31	C₅×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅²	C₂×C₃₁	1	1	yes	characteristic, complemented
33	C₃×C₅×D₅	C₂×C₃₁	1	2	yes	direct product factor
34	C₂²×C₃₁	—	5	1	no	Hall
35	C₂×C₅×D₅	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
36	C₃×C₃₁	C₂×C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅²	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₃₁	—	5	2	no	—
39	C₂×C₃₁	C₃×C₅×D₅	1	1	yes	characteristic, direct product factor
40	C₂²×C₃×C₅	—	5	1	no	—
41	C₂×C₃×D₅	C₅×C₃₁	1	1	yes	characteristic, direct product factor
42	C₂×C₅²	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
43	C₅×D₅	C₂×C₃×C₃₁	1	2	yes	direct product factor
44	C₃₁	C₂×C₃×C₅×D₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₃×C₅	—	2	2	no	—
46	C₂×C₃×C₅	—	5	2	no	—
47	C₂×C₃×C₅	D₅×C₃₁	1	1	yes	characteristic, direct product factor
48	C₂×C₃×C₅	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
49	C₃×D₅	C₂×C₅×C₃₁	1	2	yes	direct product factor
50	C₅²	C₂²×C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	—	5	1	no	—
52	C₂×D₅	C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₂×D₅×C₃₁	1	1	yes	characteristic, direct product factor
55	C₃×C₅	C₂²×C₅×C₃₁	1	1	yes	characteristic, complemented
56	C₂²×C₃	—	5	1	no	Hall
57	C₂×C₅	—	2	2	no	—
58	C₂×C₅	—	5	2	no	—
59	C₂×C₅	C₃×D₅×C₃₁	1	1	yes	characteristic, direct product factor
60	C₂×C₅	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic, complemented
61	D₅	C₂×C₃×C₅×C₃₁	1	2	yes	direct product factor
62	C₂×C₃	—	5	2	no	—
63	C₂×C₃	C₅×D₅×C₃₁	1	1	yes	characteristic, direct product factor
64	C₅	—	2	2	no	—
65	C₅	C₂×C₃×D₅×C₃₁	1	1	yes	characteristic, direct product factor
66	C₅	C₂²×C₃×C₅×C₃₁	1	1	yes	characteristic, complemented
67	C₂²	—	5	1	no	Sylow
68	C₃	C₂×C₅×D₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	—	5	2	no	—
70	C₂	C₃×C₅×D₅×C₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₃₁	D₅
commutator, hypocenter	C₅	C₂²×C₃×C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₃₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₅×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅×C₃₁	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₃₁	C₂	semidirect
3. C₂×C₅×D₅×C₃₁	C₃	direct (N × H)
4. C₃×C₅²×C₃₁	C₂²	semidirect
6. C₂×C₃×D₅×C₃₁	C₅	direct (N × H)
7. C₂×C₅²×C₃₁	C₂×C₃	semidirect
8. C₅×D₅×C₃₁	C₂×C₃	direct (N × H)
11. C₂×C₃×C₅×C₃₁	D₅	direct (N × H)
12. C₂×C₃×C₅×C₃₁	C₂×C₅	semidirect
13. C₃×D₅×C₃₁	C₂×C₅	direct (N × H)
14. C₅²×C₃₁	C₂²×C₃	semidirect
16. C₂×D₅×C₃₁	C₃×C₅	direct (N × H)
18. C₃×C₅×C₃₁	C₂×D₅	direct (N × H)
19. C₃×C₅×C₃₁	C₂²×C₅	semidirect
23. C₂×C₅×C₃₁	C₃×D₅	direct (N × H)
24. C₂×C₅×C₃₁	C₂×C₃×C₅	semidirect
25. D₅×C₃₁	C₂×C₃×C₅	direct (N × H)
26. C₂×C₃×C₅×D₅	C₃₁	direct (N × H)
28. C₂×C₃×C₃₁	C₅×D₅	direct (N × H)
30. C₅×C₃₁	C₂×C₃×D₅	direct (N × H)
31. C₅×C₃₁	C₂²×C₃×C₅	semidirect
32. C₂×C₃×C₅²	C₂×C₃₁	semidirect
33. C₃×C₅×D₅	C₂×C₃₁	direct (N × H)
35. C₂×C₅×D₅	C₃×C₃₁	direct (N × H)
36. C₃×C₃₁	C₂×C₅×D₅	direct (N × H)
37. C₃×C₅²	C₂²×C₃₁	semidirect
39. C₂×C₃₁	C₃×C₅×D₅	direct (N × H)
41. C₂×C₃×D₅	C₅×C₃₁	direct (N × H)
42. C₂×C₅²	C₂×C₃×C₃₁	semidirect
43. C₅×D₅	C₂×C₃×C₃₁	direct (N × H)
44. C₃₁	C₂×C₃×C₅×D₅	direct (N × H)
47. C₂×C₃×C₅	D₅×C₃₁	direct (N × H)
48. C₂×C₃×C₅	C₂×C₅×C₃₁	semidirect
49. C₃×D₅	C₂×C₅×C₃₁	direct (N × H)
50. C₅²	C₂²×C₃×C₃₁	semidirect
52. C₂×D₅	C₃×C₅×C₃₁	direct (N × H)
54. C₃×C₅	C₂×D₅×C₃₁	direct (N × H)
55. C₃×C₅	C₂²×C₅×C₃₁	semidirect
59. C₂×C₅	C₃×D₅×C₃₁	direct (N × H)
60. C₂×C₅	C₂×C₃×C₅×C₃₁	semidirect
61. D₅	C₂×C₃×C₅×C₃₁	direct (N × H)
63. C₂×C₃	C₅×D₅×C₃₁	direct (N × H)
65. C₅	C₂×C₃×D₅×C₃₁	direct (N × H)
66. C₅	C₂²×C₃×C₅×C₃₁	semidirect
68. C₃	C₂×C₅×D₅×C₃₁	direct (N × H)
70. C₂	C₃×C₅×D₅×C₃₁	direct (N × H)

Subgroups — C2×C3×C5×D5×C31 #22604944

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×D₅×C₃₁ #22604944