Subgroups — C₃×C₇×C₁₃×D₅₇ #44528031

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₃×D₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×C₁₃×D₁₉	—	3	1	no	maximal
4	C₃×C₇×C₁₃×C₁₉	—	2	1	no	—
5	C₃×C₇×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₁₃×D₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₃×D₁₉	—	3	1	no	Hall
9	C₃×C₇×D₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₁₃×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃×D₃×C₇×C₁₃	—	19	1	no	maximal, Hall
13	C₁₃×D₅₇	C₃×C₇	1	1	yes	characteristic, direct product factor
14	C₃×C₁₃×D₁₉	—	3	1	no	—
15	C₃²×C₇×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
17	C₇×D₅₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor
18	C₃×C₇×D₁₉	—	3	1	no	—
19	C₃×C₁₃×C₁₉	—	2	1	no	—
20	C₃×C₁₃×C₁₉	D₃×C₇	1	1	yes	characteristic, complemented
21	C₃×C₁₃×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
22	C₂×C₃×C₇×C₁₃	—	57	1	no	—
23	D₃×C₇×C₁₃	—	19	1	no	—
24	C₁₃×D₁₉	—	3	1	no	Hall
25	C₃×C₇×C₁₉	—	2	1	no	—
26	C₃×C₇×C₁₉	D₃×C₁₃	1	1	yes	characteristic, complemented
27	C₃×C₇×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
28	C₃×D₅₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₇×C₁₃	—	2	1	no	—
30	C₃×C₇×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
31	C₃×C₇×C₁₃	D₅₇	1	1	yes	characteristic, direct product factor
32	C₇×D₁₉	—	3	1	no	Hall
33	C₁₃×C₁₉	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Hall
34	C₃×D₃×C₁₃	—	19	1	no	Hall
35	C₂×C₇×C₁₃	—	57	1	no	Hall
36	C₃²×C₁₉	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
37	C₇×C₁₉	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
38	C₃×D₃×C₇	—	19	1	no	Hall
39	C₃²×C₁₃	C₇×D₁₉	1	1	yes	characteristic, complemented, Hall
40	D₅₇	C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor
41	C₃×D₁₉	—	3	1	no	—
42	C₇×C₁₃	C₃×D₅₇	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₁₃	—	57	1	no	—
44	D₃×C₁₃	—	19	1	no	—
45	C₃²×C₇	C₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
46	C₃×C₁₉	—	2	1	no	—
47	C₃×C₁₉	D₃×C₇×C₁₃	1	1	yes	characteristic, complemented
48	C₃×C₁₉	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic, complemented
49	C₂×C₃×C₇	—	57	1	no	—
50	D₃×C₇	—	19	1	no	—
51	C₃×C₁₃	—	2	1	no	—
52	C₃×C₁₃	C₃×C₇×D₁₉	1	1	yes	characteristic, complemented
53	C₃×C₁₃	C₇×D₅₇	1	1	yes	characteristic, direct product factor
54	D₁₉	—	3	1	no	Hall
55	C₂×C₁₃	—	57	1	no	Hall
56	C₃×C₇	—	2	1	no	—
57	C₃×C₇	C₃×C₁₃×D₁₉	1	1	yes	characteristic, complemented
58	C₃×C₇	C₁₃×D₅₇	1	1	yes	characteristic, direct product factor
59	C₁₉	C₃×D₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
60	C₃×D₃	—	19	1	no	Hall
61	C₂×C₇	—	57	1	no	Hall
62	C₁₃	C₃×C₇×D₅₇	1	1	yes	characteristic, direct product factor, Sylow
63	C₃²	C₇×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₃×C₁₃×D₅₇	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₃	—	57	1	no	—
66	D₃	—	19	1	no	—
67	C₃	—	2	1	no	—
68	C₃	C₃×C₇×C₁₃×D₁₉	1	1	yes	characteristic, complemented
69	C₃	C₇×C₁₃×D₅₇	1	1	yes	characteristic, direct product factor
70	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₃	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₃×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₃×C₁₉	C₂	semidirect
2. C₇×C₁₃×D₅₇	C₃	direct (N × H)
5. C₃×C₇×C₁₃×C₁₉	D₃	semidirect
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₃×C₁₃×D₅₇	C₇	direct (N × H)
9. C₃×C₇×D₅₇	C₁₃	direct (N × H)
10. C₃²×C₁₃×C₁₉	C₂×C₇	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
13. C₁₃×D₅₇	C₃×C₇	direct (N × H)
15. C₃²×C₇×C₁₉	C₂×C₁₃	semidirect
16. C₃²×C₇×C₁₃	D₁₉	semidirect
17. C₇×D₅₇	C₃×C₁₃	direct (N × H)
20. C₃×C₁₃×C₁₉	D₃×C₇	semidirect
21. C₃×C₁₃×C₁₉	C₂×C₃×C₇	semidirect
26. C₃×C₇×C₁₉	D₃×C₁₃	semidirect
27. C₃×C₇×C₁₉	C₂×C₃×C₁₃	semidirect
28. C₃×D₅₇	C₇×C₁₃	direct (N × H)
30. C₃×C₇×C₁₃	C₃×D₁₉	semidirect
31. C₃×C₇×C₁₃	D₅₇	direct (N × H)
33. C₁₃×C₁₉	C₃×D₃×C₇	semidirect
36. C₃²×C₁₉	C₂×C₇×C₁₃	semidirect
37. C₇×C₁₉	C₃×D₃×C₁₃	semidirect
39. C₃²×C₁₃	C₇×D₁₉	semidirect
40. D₅₇	C₃×C₇×C₁₃	direct (N × H)
42. C₇×C₁₃	C₃×D₅₇	direct (N × H)
45. C₃²×C₇	C₁₃×D₁₉	semidirect
47. C₃×C₁₉	D₃×C₇×C₁₃	semidirect
48. C₃×C₁₉	C₂×C₃×C₇×C₁₃	semidirect
52. C₃×C₁₃	C₃×C₇×D₁₉	semidirect
53. C₃×C₁₃	C₇×D₅₇	direct (N × H)
57. C₃×C₇	C₃×C₁₃×D₁₉	semidirect
58. C₃×C₇	C₁₃×D₅₇	direct (N × H)
59. C₁₉	C₃×D₃×C₇×C₁₃	semidirect
62. C₁₃	C₃×C₇×D₅₇	direct (N × H)
63. C₃²	C₇×C₁₃×D₁₉	semidirect
64. C₇	C₃×C₁₃×D₅₇	direct (N × H)
68. C₃	C₃×C₇×C₁₃×D₁₉	semidirect
69. C₃	C₇×C₁₃×D₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₃×C₁₉	2
C₇×C₁₃×D₅₇	3
C₃×C₇×C₁₃×D₁₉	3
C₃×C₁₃×D₅₇	7
C₃×C₇×D₅₇	13
C₃×D₃×C₇×C₁₃	19

Subgroups — C3×C7×C13×D57 #44528031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₃×D₅₇ #44528031