Subgroups — C₂×C₁₃×C₁₉×D₃₉ #50310539

Order 38532.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×D₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×C₁₉×D₁₃	—	3	1	no	maximal, Hall
4	C₃×C₁₃²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₁₉×D₁₃	—	3	2	no	—
6	C₂×C₁₃²×C₁₉	D₃	1	1	yes	characteristic, complemented
7	C₁₃²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₉×D₃₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×D₃×C₁₃×C₁₉	—	13	1	no	maximal
10	C₂×C₁₃×D₃₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₁₃×C₁₉	—	2	6	no	—
12	C₂×C₃×C₁₃×C₁₉	D₁₃	1	1	yes	characteristic, complemented
13	C₂×C₃×C₁₃×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
14	C₁₉×D₃₉	C₂×C₁₃	1	2	yes	direct product factor
15	D₃×C₁₃×C₁₉	—	13	2	no	—
16	C₂×C₃×C₁₃²	C₂×C₁₉	1	1	yes	characteristic, complemented
17	C₁₃×D₃₉	C₂×C₁₉	1	2	yes	direct product factor
18	C₂²×C₁₃×C₁₉	—	39	1	no	—
19	C₂×C₁₉×D₁₃	—	3	1	no	—
20	C₃×C₁₃×C₁₉	—	2	6	no	—
21	C₃×C₁₃×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented
22	C₃×C₁₃×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented
23	C₂×C₁₃×D₁₃	—	3	1	no	Hall
24	C₃×C₁₃²	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₃×C₁₉	—	2	6	no	—
26	C₂×C₁₃×C₁₉	—	39	2	no	—
27	C₂×C₁₃×C₁₉	D₃×C₁₃	1	1	yes	characteristic, complemented
28	C₂×C₁₃×C₁₉	D₃₉	1	1	yes	characteristic, direct product factor
29	C₁₉×D₁₃	—	3	2	no	—
30	C₂×C₁₃²	D₃×C₁₉	1	1	yes	characteristic, complemented
31	C₁₃×D₁₃	—	3	2	no	—
32	C₁₃×C₁₉	—	2	6	no	—
33	C₁₃×C₁₉	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
34	C₁₃×C₁₉	C₂×D₃₉	1	1	yes	characteristic, direct product factor
35	C₂×D₃×C₁₉	—	13	1	no	Hall
36	C₁₃²	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₃₉	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor
38	C₂×D₃×C₁₃	—	13	1	no	—
39	C₂×C₃×C₁₉	C₁₃×D₁₃	1	1	yes	characteristic, complemented
40	D₃×C₁₉	—	13	2	no	—
41	C₂×C₃×C₁₃	—	2	6	no	—
42	C₂×C₃×C₁₃	C₁₉×D₁₃	1	1	yes	characteristic, complemented
43	C₂×C₃×C₁₃	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented
44	D₃₉	C₂×C₁₃×C₁₉	1	2	yes	direct product factor
45	D₃×C₁₃	—	13	2	no	—
46	C₂²×C₁₉	—	39	1	no	Hall
47	C₃×C₁₉	C₂×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₁₃	—	39	1	no	—
49	C₂×D₁₃	—	3	1	no	—
50	C₃×C₁₃	—	2	6	no	—
51	C₃×C₁₃	C₂×C₁₉×D₁₃	1	1	yes	characteristic, complemented
52	C₃×C₁₃	C₂²×C₁₃×C₁₉	1	1	yes	characteristic, complemented
53	C₂×C₁₉	—	39	2	no	—
54	C₂×C₁₉	C₁₃×D₃₉	1	1	yes	characteristic, direct product factor
55	C₂×C₁₃	—	2	6	no	—
56	C₂×C₁₃	—	39	2	no	—
57	C₂×C₁₃	D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
58	C₂×C₁₃	C₁₉×D₃₉	1	1	yes	characteristic, direct product factor
59	D₁₃	—	3	2	no	—
60	C₁₉	C₂×C₁₃×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
61	C₁₃	—	2	6	no	—
62	C₁₃	C₂×D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
63	C₁₃	C₂×C₁₉×D₃₉	1	1	yes	characteristic, direct product factor
64	C₂×D₃	—	13	1	no	Hall
65	C₂×C₃	C₁₃×C₁₉×D₁₃	1	1	yes	characteristic, complemented
66	D₃	—	13	2	no	—
67	C₂²	—	39	1	no	Sylow
68	C₃	C₂×C₁₃×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	39	2	no	—
70	C₂	C₁₃×C₁₉×D₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃²×C₁₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×D₃₉	C₂	direct (N × H)
2. C₂×C₃×C₁₃²×C₁₉	C₂	semidirect
4. C₃×C₁₃²×C₁₉	C₂²	semidirect
6. C₂×C₁₃²×C₁₉	D₃	semidirect
7. C₁₃²×C₁₉	C₂×D₃	semidirect
8. C₂×C₁₉×D₃₉	C₁₃	direct (N × H)
10. C₂×C₁₃×D₃₉	C₁₉	direct (N × H)
12. C₂×C₃×C₁₃×C₁₉	D₁₃	semidirect
13. C₂×C₃×C₁₃×C₁₉	C₂×C₁₃	semidirect
14. C₁₉×D₃₉	C₂×C₁₃	direct (N × H)
16. C₂×C₃×C₁₃²	C₂×C₁₉	semidirect
17. C₁₃×D₃₉	C₂×C₁₉	direct (N × H)
21. C₃×C₁₃×C₁₉	C₂×D₁₃	semidirect
22. C₃×C₁₃×C₁₉	C₂²×C₁₃	semidirect
24. C₃×C₁₃²	C₂²×C₁₉	semidirect
27. C₂×C₁₃×C₁₉	D₃×C₁₃	semidirect
28. C₂×C₁₃×C₁₉	D₃₉	direct (N × H)
30. C₂×C₁₃²	D₃×C₁₉	semidirect
33. C₁₃×C₁₉	C₂×D₃×C₁₃	semidirect
34. C₁₃×C₁₉	C₂×D₃₉	direct (N × H)
36. C₁₃²	C₂×D₃×C₁₉	semidirect
37. C₂×D₃₉	C₁₃×C₁₉	direct (N × H)
39. C₂×C₃×C₁₉	C₁₃×D₁₃	semidirect
42. C₂×C₃×C₁₃	C₁₉×D₁₃	semidirect
43. C₂×C₃×C₁₃	C₂×C₁₃×C₁₉	semidirect
44. D₃₉	C₂×C₁₃×C₁₉	direct (N × H)
47. C₃×C₁₉	C₂×C₁₃×D₁₃	semidirect
51. C₃×C₁₃	C₂×C₁₉×D₁₃	semidirect
52. C₃×C₁₃	C₂²×C₁₃×C₁₉	semidirect
54. C₂×C₁₉	C₁₃×D₃₉	direct (N × H)
57. C₂×C₁₃	D₃×C₁₃×C₁₉	semidirect
58. C₂×C₁₃	C₁₉×D₃₉	direct (N × H)
60. C₁₉	C₂×C₁₃×D₃₉	direct (N × H)
62. C₁₃	C₂×D₃×C₁₃×C₁₉	semidirect
63. C₁₃	C₂×C₁₉×D₃₉	direct (N × H)
65. C₂×C₃	C₁₃×C₁₉×D₁₃	semidirect
68. C₃	C₂×C₁₃×C₁₉×D₁₃	semidirect
70. C₂	C₁₃×C₁₉×D₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×D₃₉	2
C₂×C₃×C₁₃²×C₁₉	2
C₂×C₁₃×C₁₉×D₁₃	3
C₂×C₁₉×D₃₉	13
C₂×D₃×C₁₃×C₁₉	13
C₂×C₁₃×D₃₉	19

Subgroups — C2×C13×C19×D39 #50310539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₁₉×D₃₉ #50310539