Subgroups — C₂×C₁₃×C₁₉×D₁₅ #28414939

Order 14820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×D₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₃×C₁₉	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₁₃×C₁₉	—	5	1	no	maximal, Hall
6	D₅×C₁₃×C₁₉	—	3	2	no	—
7	C₂×C₅×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₃×C₁₉	D₅	1	1	yes	characteristic, complemented
9	D₃×C₁₃×C₁₉	—	5	2	no	—
10	C₅×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₉×D₁₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₁₃×C₁₉	—	15	1	no	Hall
13	C₂×C₁₃×D₁₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₁₃×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
16	C₁₉×D₁₅	C₂×C₁₃	1	2	yes	direct product factor
17	C₂×C₁₃×C₁₉	—	15	2	no	—
18	C₂×C₁₃×C₁₉	D₁₅	1	1	yes	characteristic, direct product factor
19	C₂×C₃×C₅×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented
20	C₁₃×D₁₅	C₂×C₁₉	1	2	yes	direct product factor
21	C₂×D₅×C₁₉	—	3	1	no	Hall
22	C₃×C₅×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅×C₁₃	—	3	1	no	Hall
24	C₁₃×C₁₉	C₂×D₁₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂×D₃×C₁₉	—	5	1	no	Hall
26	C₃×C₅×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₉	D₃×C₁₃	1	1	yes	characteristic, complemented
28	D₅×C₁₉	—	3	2	no	—
29	C₂×D₃×C₁₃	—	5	1	no	Hall
30	C₂×C₅×C₁₃	D₃×C₁₉	1	1	yes	characteristic, complemented
31	D₅×C₁₃	—	3	2	no	—
32	C₂×C₃×C₁₉	D₅×C₁₃	1	1	yes	characteristic, complemented
33	D₃×C₁₉	—	5	2	no	—
34	C₅×C₁₉	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₁₃	D₅×C₁₉	1	1	yes	characteristic, complemented
36	D₃×C₁₃	—	5	2	no	—
37	C₂²×C₁₉	—	15	1	no	Hall
38	C₅×C₁₃	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
39	C₂×D₁₅	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
40	C₃×C₁₉	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₃	—	15	1	no	Hall
42	C₃×C₁₃	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₁₉	—	15	2	no	—
44	C₂×C₁₉	C₁₃×D₁₅	1	1	yes	characteristic, direct product factor
45	C₂×C₃×C₅	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented
46	D₁₅	C₂×C₁₃×C₁₉	1	2	yes	direct product factor
47	C₂×C₁₃	—	15	2	no	—
48	C₂×C₁₃	C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
49	C₂×D₅	—	3	1	no	Hall
50	C₁₉	C₂×C₁₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
51	C₃×C₅	C₂²×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Hall
52	C₁₃	C₂×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×D₃	—	5	1	no	Hall
54	C₂×C₅	D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented
55	D₅	—	3	2	no	—
56	C₂×C₃	D₅×C₁₃×C₁₉	1	1	yes	characteristic, complemented
57	D₃	—	5	2	no	—
58	C₅	C₂×D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	15	1	no	Sylow
60	C₃	C₂×D₅×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	15	2	no	—
62	C₂	C₁₃×C₁₉×D₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×D₁₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₃×C₁₉	C₂	semidirect
4. C₃×C₅×C₁₃×C₁₉	C₂²	semidirect
7. C₂×C₅×C₁₃×C₁₉	D₃	semidirect
8. C₂×C₃×C₁₃×C₁₉	D₅	semidirect
10. C₅×C₁₃×C₁₉	C₂×D₃	semidirect
11. C₂×C₁₉×D₁₅	C₁₃	direct (N × H)
13. C₂×C₁₃×D₁₅	C₁₉	direct (N × H)
14. C₃×C₁₃×C₁₉	C₂×D₅	semidirect
15. C₂×C₃×C₅×C₁₉	C₂×C₁₃	semidirect
16. C₁₉×D₁₅	C₂×C₁₃	direct (N × H)
18. C₂×C₁₃×C₁₉	D₁₅	direct (N × H)
19. C₂×C₃×C₅×C₁₃	C₂×C₁₉	semidirect
20. C₁₃×D₁₅	C₂×C₁₉	direct (N × H)
22. C₃×C₅×C₁₉	C₂²×C₁₃	semidirect
24. C₁₃×C₁₉	C₂×D₁₅	direct (N × H)
26. C₃×C₅×C₁₃	C₂²×C₁₉	semidirect
27. C₂×C₅×C₁₉	D₃×C₁₃	semidirect
30. C₂×C₅×C₁₃	D₃×C₁₉	semidirect
32. C₂×C₃×C₁₉	D₅×C₁₃	semidirect
34. C₅×C₁₉	C₂×D₃×C₁₃	semidirect
35. C₂×C₃×C₁₃	D₅×C₁₉	semidirect
38. C₅×C₁₃	C₂×D₃×C₁₉	semidirect
39. C₂×D₁₅	C₁₃×C₁₉	direct (N × H)
40. C₃×C₁₉	C₂×D₅×C₁₃	semidirect
42. C₃×C₁₃	C₂×D₅×C₁₉	semidirect
44. C₂×C₁₉	C₁₃×D₁₅	direct (N × H)
45. C₂×C₃×C₅	C₂×C₁₃×C₁₉	semidirect
46. D₁₅	C₂×C₁₃×C₁₉	direct (N × H)
48. C₂×C₁₃	C₁₉×D₁₅	direct (N × H)
50. C₁₉	C₂×C₁₃×D₁₅	direct (N × H)
51. C₃×C₅	C₂²×C₁₃×C₁₉	semidirect
52. C₁₃	C₂×C₁₉×D₁₅	direct (N × H)
54. C₂×C₅	D₃×C₁₃×C₁₉	semidirect
56. C₂×C₃	D₅×C₁₃×C₁₉	semidirect
58. C₅	C₂×D₃×C₁₃×C₁₉	semidirect
60. C₃	C₂×D₅×C₁₃×C₁₉	semidirect
62. C₂	C₁₃×C₁₉×D₁₅	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×D₁₅	2
C₂×C₃×C₅×C₁₃×C₁₉	2
C₂×D₅×C₁₃×C₁₉	3
C₂×D₃×C₁₃×C₁₉	5
C₂×C₁₉×D₁₅	13
C₂×C₁₃×D₁₅	19

Subgroups — C2×C13×C19×D15 #28414939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₁₉×D₁₅ #28414939