Subgroups — C₁₃×D₁₅×D₁₉ #28414903

Order 14820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₂₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₁₉×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₃×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₃×D₁₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₃×D₁₉	—	5	1	no	maximal, Hall
7	C₁₃×D₉₅	—	3	1	no	—
8	D₅×C₁₃×C₁₉	—	3	1	no	—
9	C₅×C₁₃×D₁₉	D₃	1	1	yes	characteristic, complemented
10	C₁₃×D₅₇	—	5	1	no	—
11	D₃×C₁₃×C₁₉	—	5	1	no	—
12	C₃×C₁₃×D₁₉	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅×D₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₁₃×D₁₉	—	15	1	no	Hall
16	C₂×C₁₃×D₁₅	—	19	1	no	maximal, Hall
17	C₃×C₁₃×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	D₂₈₅	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₁₉×D₁₅	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₃×C₅×D₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
21	C₂×C₁₃×C₁₉	—	15	1	no	—
22	C₁₃×D₁₉	—	15	1	no	—
23	C₁₃×D₁₉	D₁₅	1	1	yes	characteristic, direct product factor
24	C₂×C₃×C₅×C₁₃	—	19	1	no	—
25	C₁₃×D₁₅	—	19	1	no	—
26	C₁₃×D₁₅	D₁₉	1	1	yes	characteristic, direct product factor
27	D₅×D₁₉	—	3	1	no	Hall
28	C₃×C₅×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×D₅×C₁₃	—	57	1	no	Hall
30	C₁₃×C₁₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
31	D₃×D₁₉	—	5	1	no	Hall
32	C₃×C₅×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
33	D₉₅	—	3	1	no	—
34	C₅×D₁₉	D₃×C₁₃	1	1	yes	characteristic, complemented
35	D₅×C₁₉	—	3	1	no	—
36	C₂×D₃×C₁₃	—	95	1	no	Hall
37	C₂×C₅×C₁₃	—	19	1	no	—
38	D₅×C₁₃	—	3	1	no	—
39	D₅×C₁₃	—	57	1	no	—
40	D₅₇	—	5	1	no	—
41	C₃×D₁₉	D₅×C₁₃	1	1	yes	characteristic, complemented
42	D₃×C₁₉	—	5	1	no	—
43	C₅×C₁₉	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₁₃	—	19	1	no	—
45	D₃×C₁₃	—	5	1	no	—
46	D₃×C₁₃	—	95	1	no	—
47	C₂×D₁₉	—	15	1	no	Hall
48	C₅×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented, Hall
49	C₂×D₁₅	—	19	1	no	Hall
50	C₃×C₁₉	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂²×C₁₃	—	285	1	no	Hall
52	C₃×C₁₃	D₅×D₁₉	1	1	yes	characteristic, complemented, Hall
53	C₂×C₁₉	—	15	1	no	—
54	D₁₉	—	15	1	no	—
55	D₁₉	C₁₃×D₁₅	1	1	yes	characteristic, direct product factor
56	C₂×C₃×C₅	—	19	1	no	—
57	D₁₅	—	19	1	no	—
58	D₁₅	C₁₃×D₁₉	1	1	yes	characteristic, direct product factor
59	C₂×C₁₃	—	15	1	no	—
60	C₂×C₁₃	—	19	1	no	—
61	C₂×C₁₃	—	285	1	no	—
62	C₂×D₅	—	57	1	no	Hall
63	C₁₉	C₂×C₁₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₅	C₂×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
65	C₁₃	D₁₅×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×D₃	—	95	1	no	Hall
67	C₂×C₅	—	19	1	no	—
68	D₅	—	3	1	no	—
69	D₅	—	57	1	no	—
70	C₂×C₃	—	19	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	95	1	no	—
73	C₅	D₃×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	285	1	no	Sylow
75	C₃	D₅×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	15	1	no	—
77	C₂	—	19	1	no	—
78	C₂	—	285	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₁₅×D₁₉
commutator, cosocle, hypocenter	C₃×C₅×C₁₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₂₈₅	C₂	semidirect
2. C₁₃×C₁₉×D₁₅	C₂	semidirect
3. C₃×C₅×C₁₃×D₁₉	C₂	semidirect
5. C₃×C₅×C₁₃×C₁₉	C₂²	semidirect
9. C₅×C₁₃×D₁₉	D₃	semidirect
12. C₃×C₁₃×D₁₉	D₅	semidirect
13. C₅×C₁₃×C₁₉	C₂×D₃	semidirect
14. D₁₅×D₁₉	C₁₃	direct (N × H)
17. C₃×C₁₃×C₁₉	C₂×D₅	semidirect
18. D₂₈₅	C₂×C₁₃	semidirect
19. C₁₉×D₁₅	C₂×C₁₃	semidirect
20. C₃×C₅×D₁₉	C₂×C₁₃	semidirect
23. C₁₃×D₁₉	D₁₅	direct (N × H)
26. C₁₃×D₁₅	D₁₉	direct (N × H)
28. C₃×C₅×C₁₉	C₂²×C₁₃	semidirect
30. C₁₃×C₁₉	C₂×D₁₅	semidirect
32. C₃×C₅×C₁₃	C₂×D₁₉	semidirect
34. C₅×D₁₉	D₃×C₁₃	semidirect
41. C₃×D₁₉	D₅×C₁₃	semidirect
43. C₅×C₁₉	C₂×D₃×C₁₃	semidirect
48. C₅×C₁₃	D₃×D₁₉	semidirect
50. C₃×C₁₉	C₂×D₅×C₁₃	semidirect
52. C₃×C₁₃	D₅×D₁₉	semidirect
55. D₁₉	C₁₃×D₁₅	direct (N × H)
58. D₁₅	C₁₃×D₁₉	direct (N × H)
63. C₁₉	C₂×C₁₃×D₁₅	semidirect
64. C₃×C₅	C₂×C₁₃×D₁₉	semidirect
65. C₁₃	D₁₅×D₁₉	direct (N × H)
73. C₅	D₃×C₁₃×D₁₉	semidirect
75. C₃	D₅×C₁₃×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₂₈₅	2
C₁₃×C₁₉×D₁₅	2
C₃×C₅×C₁₃×D₁₉	2
D₅×C₁₃×D₁₉	3
D₃×C₁₃×D₁₉	5
D₁₅×D₁₉	13
C₂×C₁₃×D₁₅	19

Subgroups — C13×D15×D19 #28414903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₁₅×D₁₉ #28414903