Subgroups — C₃×C₁₃×C₁₉×D₂₁ #44528034

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	C₁₃×C₁₉×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₃×D₇×C₁₉	—	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×D₃×C₁₃×C₁₉	—	7	1	no	maximal, Hall
8	C₁₃×D₇×C₁₉	—	3	1	no	Hall
9	C₃×C₁₉×D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₁₃×C₁₉	D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×D₂₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₁₃×C₁₉	—	21	1	no	—
14	D₃×C₁₃×C₁₉	—	7	1	no	—
15	C₃²×C₇×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₁₉×D₂₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor
18	C₃×D₇×C₁₉	—	3	1	no	—
19	C₃×C₁₃×C₁₉	—	2	1	no	—
20	C₃×C₁₃×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
21	C₃×C₁₃×C₁₉	D₂₁	1	1	yes	characteristic, direct product factor
22	C₁₃×D₂₁	C₃×C₁₉	1	1	yes	characteristic, direct product factor
23	C₃×C₁₃×D₇	—	3	1	no	—
24	C₂×C₁₃×C₁₉	—	21	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×D₃×C₁₉	—	7	1	no	Hall
29	C₃×C₇×C₁₃	—	2	1	no	—
30	C₃×C₇×C₁₃	D₃×C₁₉	1	1	yes	characteristic, complemented
31	C₃×C₇×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
32	D₇×C₁₉	—	3	1	no	Hall
33	C₁₃×C₁₉	C₃×D₂₁	1	1	yes	characteristic, direct product factor, Hall
34	C₃×D₃×C₁₃	—	7	1	no	Hall
35	C₁₃×D₇	—	3	1	no	Hall
36	C₃²×C₁₉	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
37	C₇×C₁₉	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
38	C₃×D₂₁	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
39	C₃²×C₁₃	D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₁₉	—	21	1	no	—
41	D₃×C₁₉	—	7	1	no	—
42	C₇×C₁₃	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₁₃	—	21	1	no	—
44	D₃×C₁₃	—	7	1	no	—
45	C₃²×C₇	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Hall
46	C₃×C₁₉	—	2	1	no	—
47	C₃×C₁₉	C₃×C₁₃×D₇	1	1	yes	characteristic, complemented
48	C₃×C₁₉	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
49	D₂₁	C₃×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor
50	C₃×D₇	—	3	1	no	—
51	C₃×C₁₃	—	2	1	no	—
52	C₃×C₁₃	C₃×D₇×C₁₉	1	1	yes	characteristic, complemented
53	C₃×C₁₃	C₁₉×D₂₁	1	1	yes	characteristic, direct product factor
54	C₂×C₁₉	—	21	1	no	Hall
55	C₂×C₁₃	—	21	1	no	Hall
56	C₃×C₇	—	2	1	no	—
57	C₃×C₇	D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
58	C₃×C₇	C₂×C₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
59	C₁₉	C₃×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
60	C₃×D₃	—	7	1	no	Hall
61	D₇	—	3	1	no	Hall
62	C₁₃	C₃×C₁₉×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
63	C₃²	C₁₃×D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₃×D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	21	1	no	—
66	D₃	—	7	1	no	—
67	C₃	—	2	1	no	—
68	C₃	C₃×C₁₃×D₇×C₁₉	1	1	yes	characteristic, complemented
69	C₃	C₁₃×C₁₉×D₂₁	1	1	yes	characteristic, direct product factor
70	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₉	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₃×C₁₉	C₂	semidirect
2. C₁₃×C₁₉×D₂₁	C₃	direct (N × H)
5. C₃×C₇×C₁₃×C₁₉	D₃	semidirect
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
9. C₃×C₁₉×D₂₁	C₁₃	direct (N × H)
10. C₃²×C₁₃×C₁₉	D₇	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
12. C₃×C₁₃×D₂₁	C₁₉	direct (N × H)
15. C₃²×C₇×C₁₉	C₂×C₁₃	semidirect
16. C₃²×C₇×C₁₃	C₂×C₁₉	semidirect
17. C₁₉×D₂₁	C₃×C₁₃	direct (N × H)
20. C₃×C₁₃×C₁₉	C₃×D₇	semidirect
21. C₃×C₁₃×C₁₉	D₂₁	direct (N × H)
22. C₁₃×D₂₁	C₃×C₁₉	direct (N × H)
26. C₃×C₇×C₁₉	D₃×C₁₃	semidirect
27. C₃×C₇×C₁₉	C₂×C₃×C₁₃	semidirect
30. C₃×C₇×C₁₃	D₃×C₁₉	semidirect
31. C₃×C₇×C₁₃	C₂×C₃×C₁₉	semidirect
33. C₁₃×C₁₉	C₃×D₂₁	direct (N × H)
36. C₃²×C₁₉	C₁₃×D₇	semidirect
37. C₇×C₁₉	C₃×D₃×C₁₃	semidirect
38. C₃×D₂₁	C₁₃×C₁₉	direct (N × H)
39. C₃²×C₁₃	D₇×C₁₉	semidirect
42. C₇×C₁₃	C₃×D₃×C₁₉	semidirect
45. C₃²×C₇	C₂×C₁₃×C₁₉	semidirect
47. C₃×C₁₉	C₃×C₁₃×D₇	semidirect
48. C₃×C₁₉	C₁₃×D₂₁	direct (N × H)
49. D₂₁	C₃×C₁₃×C₁₉	direct (N × H)
52. C₃×C₁₃	C₃×D₇×C₁₉	semidirect
53. C₃×C₁₃	C₁₉×D₂₁	direct (N × H)
57. C₃×C₇	D₃×C₁₃×C₁₉	semidirect
58. C₃×C₇	C₂×C₃×C₁₃×C₁₉	semidirect
59. C₁₉	C₃×C₁₃×D₂₁	direct (N × H)
62. C₁₃	C₃×C₁₉×D₂₁	direct (N × H)
63. C₃²	C₁₃×D₇×C₁₉	semidirect
64. C₇	C₃×D₃×C₁₃×C₁₉	semidirect
68. C₃	C₃×C₁₃×D₇×C₁₉	semidirect
69. C₃	C₁₃×C₁₉×D₂₁	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
C₁₃×C₁₉×D₂₁	3
C₃×C₁₃×D₇×C₁₉	3
C₃×D₃×C₁₃×C₁₉	7
C₃×C₁₉×D₂₁	13
C₃×C₁₃×D₂₁	19

Subgroups — C3×C13×C19×D21 #44528034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₁₉×D₂₁ #44528034