Subgroups — C₃×C₅⋊((C₁₉⋊C₃)⋊D₁₉) #44570587

Order 32490.

144 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	C₃×C₅⋊(C₁₉⋊D₁₉)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊((C₁₉⋊C₃)⋊D₁₉)	C₃	1	3	yes	maximal, direct product factor
4	C₃×(C₁₉⋊C₃)⋊D₁₉	—	5	1	no	maximal, Hall
5	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊(C₁₉⋊D₁₉)	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₉⋊D₁₉	—	5	1	no	—
10	(C₁₉⋊C₃)⋊D₁₉	—	5	3	no	—
11	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃²×D₉₅	—	19	1	no	maximal
13	C₃×C₅⋊(D₁₉⋊C₃)	—	19	1	no	maximal
14	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
15	C₁₉×C₁₉⋊C₃	C₃×D₅	1	3	yes	complemented
16	C₃²×C₅×C₁₉	—	19	1	no	—
17	C₃×C₅×C₁₉⋊C₃	D₁₉	1	1	yes	characteristic, complemented
18	C₁₉⋊D₁₉	—	5	1	no	Hall
19	C₃×D₉₅	—	19	3	no	—
20	C₃×D₉₅	—	19	1	no	—
21	C₃×D₉₅	—	19	1	no	—
22	C₃×D₉₅	—	57	6	no	—
23	C₅⋊(D₁₉⋊C₃)	—	19	3	no	—
24	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
25	C₃²×D₁₉	—	95	1	no	—
26	C₃×D₁₉⋊C₃	—	95	1	no	—
27	C₃×C₅×C₁₉	—	3	6	no	—
28	C₃×C₅×C₁₉	—	19	3	no	—
29	C₃×C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
30	C₃×C₅×C₁₉	C₃×D₁₉	1	1	yes	characteristic, complemented
31	C₅×C₁₉⋊C₃	C₃×D₁₉	1	3	yes	complemented
32	D₉₅	—	19	1	no	—
33	D₉₅	—	19	1	no	—
34	D₉₅	—	57	6	no	—
35	C₃²×C₁₉	—	19	1	no	—
36	C₃×C₁₉⋊C₃	D₉₅	1	1	yes	characteristic, complemented
37	C₃×D₁₉	—	285	6	no	—
38	C₃×D₁₉	—	95	3	no	—
39	C₃×D₁₉	—	95	1	no	—
40	C₃×D₁₉	—	95	1	no	—
41	D₁₉⋊C₃	—	95	3	no	—
42	C₅×C₁₉	—	3	6	no	—
43	C₅×C₁₉	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
44	C₅×C₁₉	C₃²×D₁₉	1	1	yes	characteristic, complemented
45	C₃²×D₅	—	361	1	no	Hall
46	C₃×C₁₉	—	3	6	no	—
47	C₃×C₁₉	—	19	3	no	—
48	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
49	C₃×C₁₉	C₃×D₉₅	1	1	yes	characteristic, complemented
50	C₁₉⋊C₃	C₃×D₉₅	1	3	yes	complemented
51	C₃²×C₅	—	19	1	no	Hall
52	D₁₉	—	285	6	no	—
53	D₁₉	—	95	1	no	—
54	D₁₉	—	95	1	no	—
55	C₃×D₅	—	361	3	no	—
56	C₃×D₅	—	361	1	no	—
57	C₁₉	—	3	6	no	—
58	C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
59	C₁₉	C₃²×D₉₅	1	1	yes	characteristic, complemented
60	C₂×C₃²	—	1805	1	no	Hall
61	C₃×C₅	—	19	3	no	—
62	C₃×C₅	(C₁₉⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented
63	D₅	—	361	1	no	Hall
64	C₃²	—	19	1	no	Sylow
65	C₂×C₃	—	1805	3	no	—
66	C₂×C₃	—	1805	1	no	—
67	C₅	C₃×(C₁₉⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
68	C₃	—	19	3	no	—
69	C₃	C₅⋊((C₁₉⋊C₃)⋊D₁₉)	1	1	yes	characteristic, direct product factor
70	C₂	—	1805	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₅⋊((C₁₉⋊C₃)⋊D₁₉)
commutator, cosocle, hypocenter	C₅×C₁₉²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₅×C₁₉²
UCS	C₁ ◁ C₃

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. C₃×C₅⋊(C₁₉⋊D₁₉)	C₃	semidirect
3. C₅⋊((C₁₉⋊C₃)⋊D₁₉)	C₃	direct (N × H)
5. C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	semidirect
6. C₃×C₅×C₁₉²	C₂×C₃	semidirect
7. C₅⋊(C₁₉⋊D₁₉)	C₃²	semidirect
8. C₃×C₁₉×C₁₉⋊C₃	D₅	semidirect
11. C₅×C₁₉²	C₂×C₃²	semidirect
14. C₃×C₁₉²	C₃×D₅	semidirect
15. C₁₉×C₁₉⋊C₃	C₃×D₅	semidirect
17. C₃×C₅×C₁₉⋊C₃	D₁₉	semidirect
24. C₁₉²	C₃²×D₅	semidirect
29. C₃×C₅×C₁₉	D₁₉⋊C₃	semidirect
30. C₃×C₅×C₁₉	C₃×D₁₉	semidirect
31. C₅×C₁₉⋊C₃	C₃×D₁₉	semidirect
36. C₃×C₁₉⋊C₃	D₉₅	semidirect
43. C₅×C₁₉	C₃×D₁₉⋊C₃	semidirect
44. C₅×C₁₉	C₃²×D₁₉	semidirect
48. C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	semidirect
49. C₃×C₁₉	C₃×D₉₅	semidirect
50. C₁₉⋊C₃	C₃×D₉₅	semidirect
58. C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	semidirect
59. C₁₉	C₃²×D₉₅	semidirect
62. C₃×C₅	(C₁₉⋊C₃)⋊D₁₉	semidirect
67. C₅	C₃×(C₁₉⋊C₃)⋊D₁₉	semidirect
69. C₃	C₅⋊((C₁₉⋊C₃)⋊D₁₉)	direct (N × H)

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
C₃×C₅⋊(C₁₉⋊D₁₉)	3
C₅⋊((C₁₉⋊C₃)⋊D₁₉)	3
C₃×(C₁₉⋊C₃)⋊D₁₉	5
C₃²×D₉₅	19
C₃×C₅⋊(D₁₉⋊C₃)	19

Subgroups — C3×C5⋊((C19⋊C3)⋊D19) #44570587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊((C₁₉⋊C₃)⋊D₁₉) #44570587