Subgroups — C₁₉×C₃⋊(C₅⋊(D₁₉⋊C₃)) #44570608

Order 32490.

84 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	C₁₉×D₂₈₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×C₅⋊(D₁₉⋊C₃)	—	3	1	no	maximal
4	C₁₉×C₃⋊(D₁₉⋊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	C₁₉×D₉₅	—	3	1	no	Hall
9	C₃×C₁₉×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
10	C₁₉×D₅₇	—	5	1	no	—
11	C₁₉×D₁₉⋊C₃	—	15	1	no	—
12	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₉×D₁₅	—	19	1	no	maximal
14	C₃⋊(C₅⋊(D₁₉⋊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, complemented
18	C₃²×C₅×C₁₉	—	19	1	no	—
19	C₃×C₅×C₁₉⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented
20	C₁₉×D₁₉	—	15	1	no	Hall
21	D₂₈₅	C₃×C₁₉	1	1	yes	characteristic, complemented
22	C₁₉×D₁₅	—	19	1	no	—
23	C₃×D₅×C₁₉	—	57	1	no	—
24	C₅⋊(D₁₉⋊C₃)	—	3	1	no	—
25	C₁₉²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
26	C₃×D₃×C₁₉	—	95	1	no	—
27	C₃⋊(D₁₉⋊C₃)	—	5	1	no	—
28	C₃×C₅×C₁₉	—	6	3	no	—
29	C₃×C₅×C₁₉	—	19	1	no	—
30	C₃×C₅×C₁₉	—	38	1	no	—
31	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
32	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
33	C₅×C₁₉⋊C₃	—	2	1	no	—
34	C₅×C₁₉⋊C₃	D₃×C₁₉	1	1	yes	characteristic, complemented
35	D₉₅	—	3	1	no	—
36	D₅×C₁₉	—	57	1	no	—
37	C₃²×C₁₉	—	19	1	no	—
38	C₃×C₁₉⋊C₃	D₅×C₁₉	1	1	yes	characteristic, complemented
39	C₂×C₃×C₁₉	—	285	1	no	—
40	D₅₇	—	5	1	no	—
41	D₃×C₁₉	—	95	1	no	—
42	D₁₉⋊C₃	—	15	1	no	—
43	C₅×C₁₉	—	6	3	no	—
44	C₅×C₁₉	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
45	C₅×C₁₉	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented
46	C₃×D₁₅	—	19	1	no	Hall
47	C₃×C₁₉	—	6	3	no	—
48	C₃×C₁₉	—	19	1	no	—
49	C₃×C₁₉	—	38	1	no	—
50	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
51	C₃×C₁₉	C₃×D₅×C₁₉	1	1	yes	characteristic, complemented
52	C₁₉⋊C₃	—	2	1	no	—
53	C₁₉⋊C₃	C₁₉×D₁₅	1	1	yes	characteristic, complemented
54	C₃²×C₅	—	19	1	no	Hall
55	C₂×C₁₉	—	285	1	no	—
56	D₁₉	—	15	1	no	—
57	D₁₅	—	19	1	no	—
58	C₃×D₅	—	57	1	no	—
59	C₁₉	—	6	3	no	—
60	C₁₉	C₃⋊(C₅⋊(D₁₉⋊C₃))	1	1	yes	characteristic, direct product factor
61	C₁₉	C₃×C₁₉×D₁₅	1	1	yes	characteristic, complemented
62	C₃×D₃	—	95	1	no	Hall
63	C₃×C₅	—	19	1	no	—
64	C₃×C₅	—	38	1	no	—
65	C₃×C₅	C₁₉×D₁₉⋊C₃	1	1	yes	characteristic, complemented
66	D₅	—	57	1	no	Hall
67	C₃²	—	19	1	no	Sylow
68	C₂×C₃	—	285	1	no	—
69	D₃	—	95	1	no	—
70	C₅	C₁₉×C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
71	C₃	—	19	1	no	—
72	C₃	—	38	1	no	—
73	C₃	C₁₉×C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
74	C₂	—	285	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊(C₅⋊(D₁₉⋊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. C₁₉×D₂₈₅	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. C₃⋊(C₅⋊(D₁₉⋊C₃))	C₁₉	direct (N × H)
15. C₃×C₁₉²	C₃×D₅	semidirect
17. C₁₉×C₁₉⋊C₃	D₁₅	semidirect
19. C₃×C₅×C₁₉⋊C₃	C₂×C₁₉	semidirect
21. D₂₈₅	C₃×C₁₉	semidirect
25. C₁₉²	C₃×D₁₅	semidirect
31. C₃×C₅×C₁₉	D₁₉⋊C₃	semidirect
32. C₃×C₅×C₁₉	C₂×C₃×C₁₉	semidirect
34. C₅×C₁₉⋊C₃	D₃×C₁₉	semidirect
38. C₃×C₁₉⋊C₃	D₅×C₁₉	semidirect
44. C₅×C₁₉	C₃⋊(D₁₉⋊C₃)	semidirect
45. C₅×C₁₉	C₃×D₃×C₁₉	semidirect
50. C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	semidirect
51. C₃×C₁₉	C₃×D₅×C₁₉	semidirect
53. C₁₉⋊C₃	C₁₉×D₁₅	semidirect
60. C₁₉	C₃⋊(C₅⋊(D₁₉⋊C₃))	direct (N × H)
61. C₁₉	C₃×C₁₉×D₁₅	semidirect
65. C₃×C₅	C₁₉×D₁₉⋊C₃	semidirect
70. C₅	C₁₉×C₃⋊(D₁₉⋊C₃)	semidirect
73. C₃	C₁₉×C₅⋊(D₁₉⋊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
C₁₉×D₂₈₅	3
C₁₉×C₅⋊(D₁₉⋊C₃)	3
C₁₉×C₃⋊(D₁₉⋊C₃)	5
C₃×C₁₉×D₁₅	19
C₃⋊(C₅⋊(D₁₉⋊C₃))	19

Subgroups — C19×C3⋊(C5⋊(D19⋊C3)) #44570608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊(C₅⋊(D₁₉⋊C₃)) #44570608