Subgroups — C₁₉×D₁₅×C₁₉⋊C₃ #44570607

Order 32490.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉²×D₁₅	C₃	1	1	yes	maximal, characteristic, complemented
3	D₅×C₁₉×C₁₉⋊C₃	—	3	1	no	maximal
4	D₃×C₁₉×C₁₉⋊C₃	—	5	1	no	maximal, Hall
5	C₅×C₁₉×C₁₉⋊C₃	—	2	1	no	—
6	C₅×C₁₉×C₁₉⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₉²	—	3	1	no	Hall
9	C₃×C₁₉×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₉²	—	5	1	no	—
11	C₂×C₁₉×C₁₉⋊C₃	—	15	1	no	—
12	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₉×D₁₅	—	19	1	no	maximal
14	D₁₅×C₁₉⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor
15	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
16	C₁₉×C₁₉⋊C₃	—	2	1	no	—
17	C₁₉×C₁₉⋊C₃	D₁₅	1	1	yes	characteristic, direct product factor
18	C₃²×C₅×C₁₉	—	19	1	no	—
19	C₃×C₅×C₁₉⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented
20	C₂×C₁₉²	—	15	1	no	Hall
21	C₁₉×D₁₅	—	3	6	no	—
22	C₁₉×D₁₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
23	C₁₉×D₁₅	C₃×C₁₉	1	1	yes	characteristic, complemented
24	C₃×D₅×C₁₉	—	57	1	no	—
25	D₅×C₁₉⋊C₃	—	3	1	no	—
26	C₁₉²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃×C₁₉	—	95	1	no	—
28	D₃×C₁₉⋊C₃	—	5	1	no	—
29	C₃×C₅×C₁₉	—	3	6	no	—
30	C₃×C₅×C₁₉	—	19	1	no	—
31	C₃×C₅×C₁₉	—	38	1	no	—
32	C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
33	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
34	C₅×C₁₉⋊C₃	—	2	1	no	—
35	C₅×C₁₉⋊C₃	D₃×C₁₉	1	1	yes	characteristic, complemented
36	D₅×C₁₉	—	3	1	no	—
37	D₅×C₁₉	—	3	1	no	—
38	D₅×C₁₉	—	9	6	no	—
39	C₃²×C₁₉	—	19	1	no	—
40	C₃×C₁₉⋊C₃	D₅×C₁₉	1	1	yes	characteristic, complemented
41	C₂×C₃×C₁₉	—	285	1	no	—
42	D₃×C₁₉	—	5	1	no	—
43	D₃×C₁₉	—	5	1	no	—
44	D₃×C₁₉	—	15	6	no	—
45	C₂×C₁₉⋊C₃	—	15	1	no	—
46	C₅×C₁₉	—	3	6	no	—
47	C₅×C₁₉	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
48	C₅×C₁₉	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented
49	C₃×D₁₅	—	19	1	no	Hall
50	C₃×C₁₉	—	3	6	no	—
51	C₃×C₁₉	—	19	1	no	—
52	C₃×C₁₉	—	38	1	no	—
53	C₃×C₁₉	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
54	C₃×C₁₉	C₃×D₅×C₁₉	1	1	yes	characteristic, complemented
55	C₁₉⋊C₃	—	2	1	no	—
56	C₁₉⋊C₃	C₁₉×D₁₅	1	1	yes	characteristic, direct product factor
57	C₃²×C₅	—	19	1	no	Hall
58	C₂×C₁₉	—	15	1	no	—
59	C₂×C₁₉	—	15	1	no	—
60	C₂×C₁₉	—	45	6	no	—
61	D₁₅	C₁₉×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
62	C₃×D₅	—	57	1	no	—
63	C₁₉	—	3	6	no	—
64	C₁₉	D₁₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
65	C₁₉	C₃×C₁₉×D₁₅	1	1	yes	characteristic, complemented
66	C₃×D₃	—	95	1	no	Hall
67	C₃×C₅	—	19	1	no	—
68	C₃×C₅	—	38	1	no	—
69	C₃×C₅	C₂×C₁₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented
70	D₅	—	3	1	no	Hall
71	C₃²	—	19	1	no	Sylow
72	C₂×C₃	—	285	1	no	—
73	D₃	—	5	1	no	—
74	C₅	D₃×C₁₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
75	C₃	—	19	1	no	—
76	C₃	—	38	1	no	—
77	C₃	D₅×C₁₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented
78	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₁₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₅×C₁₉	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₉×C₁₉⋊C₃	C₂	semidirect
2. C₁₉²×D₁₅	C₃	semidirect
6. C₅×C₁₉×C₁₉⋊C₃	D₃	semidirect
7. C₃×C₅×C₁₉²	C₂×C₃	semidirect
9. C₃×C₁₉×C₁₉⋊C₃	D₅	semidirect
12. C₅×C₁₉²	C₃×D₃	semidirect
14. D₁₅×C₁₉⋊C₃	C₁₉	direct (N × H)
15. C₃×C₁₉²	C₃×D₅	semidirect
17. C₁₉×C₁₉⋊C₃	D₁₅	direct (N × H)
19. C₃×C₅×C₁₉⋊C₃	C₂×C₁₉	semidirect
22. C₁₉×D₁₅	C₁₉⋊C₃	direct (N × H)
23. C₁₉×D₁₅	C₃×C₁₉	semidirect
26. C₁₉²	C₃×D₁₅	semidirect
32. C₃×C₅×C₁₉	C₂×C₁₉⋊C₃	semidirect
33. C₃×C₅×C₁₉	C₂×C₃×C₁₉	semidirect
35. C₅×C₁₉⋊C₃	D₃×C₁₉	semidirect
40. C₃×C₁₉⋊C₃	D₅×C₁₉	semidirect
47. C₅×C₁₉	D₃×C₁₉⋊C₃	semidirect
48. C₅×C₁₉	C₃×D₃×C₁₉	semidirect
53. C₃×C₁₉	D₅×C₁₉⋊C₃	semidirect
54. C₃×C₁₉	C₃×D₅×C₁₉	semidirect
56. C₁₉⋊C₃	C₁₉×D₁₅	direct (N × H)
61. D₁₅	C₁₉×C₁₉⋊C₃	direct (N × H)
64. C₁₉	D₁₅×C₁₉⋊C₃	direct (N × H)
65. C₁₉	C₃×C₁₉×D₁₅	semidirect
69. C₃×C₅	C₂×C₁₉×C₁₉⋊C₃	semidirect
74. C₅	D₃×C₁₉×C₁₉⋊C₃	semidirect
77. C₃	D₅×C₁₉×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₉×C₁₉⋊C₃	2
C₁₉²×D₁₅	3
D₅×C₁₉×C₁₉⋊C₃	3
D₃×C₁₉×C₁₉⋊C₃	5
C₃×C₁₉×D₁₅	19
D₁₅×C₁₉⋊C₃	19

Subgroups — C19×D15×C19⋊C3 #44570607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₁₅×C₁₉⋊C₃ #44570607