Subgroups — C₁₃×C₁₉×Dic₃₉ #50310263

Order 38532.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₉×Dic₁₃	—	3	1	no	maximal, Hall
3	C₃×C₁₃²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃²×C₁₉	D₃	1	1	yes	characteristic
5	C₁₃²×C₁₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₁₉×Dic₃₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor
7	Dic₃×C₁₃×C₁₉	—	13	1	no	maximal
8	C₁₃×Dic₃₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₁₃×C₁₉	—	2	6	no	—
10	C₂×C₃×C₁₃×C₁₉	D₁₃	1	1	yes	characteristic
11	C₂×C₃×C₁₃×C₁₉	C₂×C₁₃	1	1	yes	characteristic
12	C₂×C₃×C₁₃²	C₂×C₁₉	1	1	yes	characteristic
13	C₄×C₁₃×C₁₉	—	39	1	no	—
14	C₁₉×Dic₁₃	—	3	1	no	—
15	C₃×C₁₃×C₁₉	—	2	6	no	—
16	C₃×C₁₃×C₁₉	Dic₁₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₁₉	C₄×C₁₃	1	1	yes	characteristic, complemented
18	C₁₃×Dic₁₃	—	3	1	no	Hall
19	C₃×C₁₃²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₃×C₁₉	—	2	6	no	—
21	C₂×C₁₃×C₁₉	D₃×C₁₃	1	1	yes	characteristic
22	C₂×C₁₃×C₁₉	D₃₉	1	1	yes	characteristic
23	C₂×C₁₃²	D₃×C₁₉	1	1	yes	characteristic
24	C₁₃×C₁₉	—	2	6	no	—
25	C₁₃×C₁₉	Dic₃×C₁₃	1	1	yes	characteristic, complemented
26	C₁₃×C₁₉	Dic₃₉	1	1	yes	characteristic, direct product factor
27	Dic₃×C₁₉	—	13	1	no	Hall
28	C₁₃²	Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
29	Dic₃₉	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor
30	Dic₃×C₁₃	—	13	1	no	—
31	C₂×C₃×C₁₉	C₁₃×D₁₃	1	1	yes	characteristic
32	C₂×C₃×C₁₃	—	2	6	no	—
33	C₂×C₃×C₁₃	C₁₉×D₁₃	1	1	yes	characteristic
34	C₂×C₃×C₁₃	C₂×C₁₃×C₁₉	1	1	yes	characteristic
35	C₄×C₁₉	—	39	1	no	Hall
36	C₃×C₁₉	C₁₃×Dic₁₃	1	1	yes	characteristic, complemented, Hall
37	C₄×C₁₃	—	39	1	no	—
38	Dic₁₃	—	3	1	no	—
39	C₃×C₁₃	—	2	6	no	—
40	C₃×C₁₃	C₁₉×Dic₁₃	1	1	yes	characteristic, complemented
41	C₃×C₁₃	C₄×C₁₃×C₁₉	1	1	yes	characteristic, complemented
42	C₂×C₁₉	C₁₃×D₃₉	1	1	yes	characteristic
43	C₂×C₁₃	—	2	6	no	—
44	C₂×C₁₃	D₃×C₁₃×C₁₉	1	1	yes	characteristic
45	C₂×C₁₃	C₁₉×D₃₉	1	1	yes	characteristic
46	C₁₉	C₁₃×Dic₃₉	1	1	yes	characteristic, direct product factor, Sylow
47	C₁₃	—	2	6	no	—
48	C₁₃	Dic₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
49	C₁₃	C₁₉×Dic₃₉	1	1	yes	characteristic, direct product factor
50	Dic₃	—	13	1	no	Hall
51	C₂×C₃	C₁₃×C₁₉×D₁₃	1	1	yes	characteristic
52	C₄	—	39	1	no	Sylow
53	C₃	C₁₃×C₁₉×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
54	C₂	C₁₃×C₁₉×D₃₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	D₃₉
commutator, hypocenter	C₃×C₁₃	C₄×C₁₃×C₁₉
Frattini	C₂	C₁₃×C₁₉×D₃₉
Fitting, socle, prime radical	C₂×C₃×C₁₃²×C₁₉	C₂
cosocle	C₂×C₃×C₁₃	C₂×C₁₃×C₁₉
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
3. C₃×C₁₃²×C₁₉	C₄	semidirect
5. C₁₃²×C₁₉	Dic₃	semidirect
6. C₁₉×Dic₃₉	C₁₃	direct (N × H)
8. C₁₃×Dic₃₉	C₁₉	direct (N × H)
16. C₃×C₁₃×C₁₉	Dic₁₃	semidirect
17. C₃×C₁₃×C₁₉	C₄×C₁₃	semidirect
19. C₃×C₁₃²	C₄×C₁₉	semidirect
25. C₁₃×C₁₉	Dic₃×C₁₃	semidirect
26. C₁₃×C₁₉	Dic₃₉	direct (N × H)
28. C₁₃²	Dic₃×C₁₉	semidirect
29. Dic₃₉	C₁₃×C₁₉	direct (N × H)
36. C₃×C₁₉	C₁₃×Dic₁₃	semidirect
40. C₃×C₁₃	C₁₉×Dic₁₃	semidirect
41. C₃×C₁₃	C₄×C₁₃×C₁₉	semidirect
46. C₁₉	C₁₃×Dic₃₉	direct (N × H)
48. C₁₃	Dic₃×C₁₃×C₁₉	semidirect
49. C₁₃	C₁₉×Dic₃₉	direct (N × H)
53. C₃	C₁₃×C₁₉×Dic₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₃²×C₁₉	2
C₁₃×C₁₉×Dic₁₃	3
C₁₉×Dic₃₉	13
Dic₃×C₁₃×C₁₉	13
C₁₃×Dic₃₉	19

Subgroups — C13×C19×Dic39 #50310263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₁₉×Dic₃₉ #50310263