Subgroups — C₂×C₃×C₅×D₅₁₉ #44528216

Order 31140.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₁₇₃	—	3	1	no	maximal
4	C₂×C₅×D₅₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₅×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₅₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₅₁₉	C₂×C₃	1	2	yes	direct product factor
8	C₃×C₅×D₁₇₃	—	3	2	no	—
9	C₂×C₃×C₅×C₁₇₃	—	2	1	no	—
10	C₂×C₃×C₅×C₁₇₃	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₁₇₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₅×D₁₇₃	—	3	1	no	Hall
13	C₃×D₅₁₉	C₂×C₅	1	2	yes	direct product factor
14	C₂×C₃²×C₁₇₃	C₂×C₅	1	1	yes	characteristic, complemented
15	C₃×C₅×C₁₇₃	—	2	1	no	—
16	C₃×C₅×C₁₇₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅×C₁₇₃	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃×D₁₇₃	—	3	1	no	—
19	C₂×D₅₁₉	C₃×C₅	1	1	yes	characteristic, direct product factor
20	C₂×C₅×C₁₇₃	C₃×D₃	1	1	yes	characteristic, complemented
21	C₅×D₁₇₃	—	3	2	no	—
22	C₃²×C₁₇₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₁₇₃	—	2	1	no	—
24	C₂×C₃×C₁₇₃	C₅×D₃	1	1	yes	characteristic, complemented
25	C₂×C₃×C₁₇₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
26	D₅₁₉	C₂×C₃×C₅	1	2	yes	direct product factor
27	C₃×D₁₇₃	—	3	2	no	—
28	C₅×C₁₇₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	C₂×D₁₇₃	—	3	1	no	Hall
30	C₃×C₁₇₃	—	2	1	no	—
31	C₃×C₁₇₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
32	C₃×C₁₇₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
33	C₂×C₁₇₃	C₃×C₅×D₃	1	1	yes	characteristic, complemented
34	D₁₇₃	—	3	2	no	—
35	C₂×C₃×C₅×D₃	—	173	1	no	maximal, Hall
36	C₁₇₃	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²×C₅	D₁₇₃	1	1	yes	characteristic, complemented
38	C₃×C₅×D₃	—	173	2	no	—
39	C₂²×C₃×C₅	—	519	1	no	—
40	C₂×C₅×D₃	—	173	1	no	—
41	C₃²×C₅	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×D₃	—	173	1	no	Hall
43	C₂×C₃×C₅	—	2	1	no	—
44	C₂×C₃×C₅	—	519	2	no	—
45	C₂×C₃×C₅	C₃×D₁₇₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅	D₅₁₉	1	1	yes	characteristic, direct product factor
47	C₅×D₃	—	173	2	no	—
48	C₂²×C₅	—	519	1	no	Hall
49	C₂×C₃²	C₅×D₁₇₃	1	1	yes	characteristic, complemented
50	C₃×D₃	—	173	2	no	—
51	C₃×C₅	—	2	1	no	—
52	C₃×C₅	C₂×D₅₁₉	1	1	yes	characteristic, direct product factor
53	C₃×C₅	C₂×C₃×D₁₇₃	1	1	yes	characteristic, complemented
54	C₂²×C₃	—	519	1	no	—
55	C₂×D₃	—	173	1	no	—
56	C₂×C₅	—	519	2	no	—
57	C₂×C₅	C₃×D₅₁₉	1	1	yes	characteristic, direct product factor
58	C₃²	C₂×C₅×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	519	2	no	—
61	C₂×C₃	C₃×C₅×D₁₇₃	1	1	yes	characteristic, complemented
62	C₂×C₃	C₅×D₅₁₉	1	1	yes	characteristic, direct product factor
63	D₃	—	173	2	no	—
64	C₅	C₂×C₃×D₅₁₉	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²	—	519	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₅×D₅₁₉	1	1	yes	characteristic, direct product factor
68	C₃	C₂×C₃×C₅×D₁₇₃	1	1	yes	characteristic, complemented
69	C₂	—	519	2	no	—
70	C₂	C₃×C₅×D₅₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₅₁₉
commutator, cosocle, hypocenter	C₃×C₁₇₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₇₃	C₂
LCS	G ▷ C₃×C₁₇₃
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₇₃	C₂	semidirect
4. C₂×C₅×D₅₁₉	C₃	direct (N × H)
5. C₃²×C₅×C₁₇₃	C₂²	semidirect
6. C₂×C₃×D₅₁₉	C₅	direct (N × H)
7. C₅×D₅₁₉	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅×C₁₇₃	D₃	semidirect
11. C₂×C₃×C₅×C₁₇₃	C₂×C₃	semidirect
13. C₃×D₅₁₉	C₂×C₅	direct (N × H)
14. C₂×C₃²×C₁₇₃	C₂×C₅	semidirect
16. C₃×C₅×C₁₇₃	C₂×D₃	semidirect
17. C₃×C₅×C₁₇₃	C₂²×C₃	semidirect
19. C₂×D₅₁₉	C₃×C₅	direct (N × H)
20. C₂×C₅×C₁₇₃	C₃×D₃	semidirect
22. C₃²×C₁₇₃	C₂²×C₅	semidirect
24. C₂×C₃×C₁₇₃	C₅×D₃	semidirect
25. C₂×C₃×C₁₇₃	C₂×C₃×C₅	semidirect
26. D₅₁₉	C₂×C₃×C₅	direct (N × H)
28. C₅×C₁₇₃	C₂×C₃×D₃	semidirect
31. C₃×C₁₇₃	C₂×C₅×D₃	semidirect
32. C₃×C₁₇₃	C₂²×C₃×C₅	semidirect
33. C₂×C₁₇₃	C₃×C₅×D₃	semidirect
36. C₁₇₃	C₂×C₃×C₅×D₃	semidirect
37. C₂×C₃²×C₅	D₁₇₃	semidirect
41. C₃²×C₅	C₂×D₁₇₃	semidirect
45. C₂×C₃×C₅	C₃×D₁₇₃	semidirect
46. C₂×C₃×C₅	D₅₁₉	direct (N × H)
49. C₂×C₃²	C₅×D₁₇₃	semidirect
52. C₃×C₅	C₂×D₅₁₉	direct (N × H)
53. C₃×C₅	C₂×C₃×D₁₇₃	semidirect
57. C₂×C₅	C₃×D₅₁₉	direct (N × H)
58. C₃²	C₂×C₅×D₁₇₃	semidirect
61. C₂×C₃	C₃×C₅×D₁₇₃	semidirect
62. C₂×C₃	C₅×D₅₁₉	direct (N × H)
64. C₅	C₂×C₃×D₅₁₉	direct (N × H)
67. C₃	C₂×C₅×D₅₁₉	direct (N × H)
68. C₃	C₂×C₃×C₅×D₁₇₃	semidirect
70. C₂	C₃×C₅×D₅₁₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×D₅₁₉	2
C₂×C₃²×C₅×C₁₇₃	2
C₂×C₃×C₅×D₁₇₃	3
C₂×C₅×D₅₁₉	3
C₂×C₃×D₅₁₉	5
C₂×C₃×C₅×D₃	173

Subgroups — C2×C3×C5×D519 #44528216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×D₅₁₉ #44528216