Subgroups — C₃×C₃⋊(C₅⋊(C₁₉⋊D₁₉)) #44570631

Order 32490.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊(C₁₉⋊D₁₉)	—	3	1	no	maximal
3	C₃⋊(C₅⋊(C₁₉⋊D₁₉))	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₃⋊(C₁₉⋊D₁₉)	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₉²	—	2	1	no	—
6	C₃×C₅×C₁₉²	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅⋊(C₁₉⋊D₁₉)	—	3	1	no	Hall
9	C₃²×C₁₉²	D₅	1	1	yes	characteristic, complemented, Hall
10	C₃⋊(C₁₉⋊D₁₉)	—	5	1	no	—
11	C₃×C₁₉⋊D₁₉	—	15	1	no	—
12	C₅×C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₂₈₅	—	19	20	no	maximal
14	C₃×C₁₉²	—	2	1	no	—
15	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented
16	C₃×C₁₉²	D₁₅	1	1	yes	characteristic, complemented
17	C₃²×C₅×C₁₉	D₁₉	1	20	yes	complemented
18	C₁₉⋊D₁₉	—	15	1	no	Hall
19	D₂₈₅	—	19	20	no	—
20	C₃×D₉₅	—	57	20	no	—
21	C₁₉²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
22	C₃×D₅₇	—	95	20	no	—
23	C₃×C₅×C₁₉	—	2	20	no	—
24	C₃×C₅×C₁₉	C₃×D₁₉	1	20	yes	complemented
25	C₃×C₅×C₁₉	D₅₇	1	20	yes	complemented
26	D₉₅	—	57	20	no	—
27	C₃²×C₁₉	D₉₅	1	20	yes	complemented
28	D₅₇	—	95	20	no	—
29	C₃×D₁₉	—	285	20	no	—
30	C₅×C₁₉	C₃×D₅₇	1	20	yes	complemented
31	C₃×D₁₅	—	361	1	no	Hall
32	C₃×C₁₉	—	2	20	no	—
33	C₃×C₁₉	C₃×D₉₅	1	20	yes	complemented
34	C₃×C₁₉	D₂₈₅	1	20	yes	complemented
35	C₃²×C₅	C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Hall
36	D₁₉	—	285	20	no	—
37	D₁₅	—	361	1	no	—
38	C₃×D₅	—	1083	1	no	—
39	C₁₉	C₃×D₂₈₅	1	20	yes	complemented
40	C₃×D₃	—	1805	1	no	Hall
41	C₃×C₅	—	2	1	no	—
42	C₃×C₅	C₃×C₁₉⋊D₁₉	1	1	yes	characteristic, complemented
43	C₃×C₅	C₃⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented
44	D₅	—	1083	1	no	Hall
45	C₃²	C₅⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	5415	1	no	—
47	D₃	—	1805	1	no	—
48	C₅	C₃×C₃⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
49	C₃	—	2	1	no	—
50	C₃	C₃⋊(C₅⋊(C₁₉⋊D₁₉))	1	1	yes	characteristic, direct product factor
51	C₃	C₃×C₅⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented
52	C₂	—	5415	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
3. C₃⋊(C₅⋊(C₁₉⋊D₁₉))	C₃	direct (N × H)
6. C₃×C₅×C₁₉²	D₃	semidirect
7. C₃×C₅×C₁₉²	C₂×C₃	semidirect
9. C₃²×C₁₉²	D₅	semidirect
12. C₅×C₁₉²	C₃×D₃	semidirect
15. C₃×C₁₉²	C₃×D₅	semidirect
16. C₃×C₁₉²	D₁₅	semidirect
17. C₃²×C₅×C₁₉	D₁₉	semidirect
21. C₁₉²	C₃×D₁₅	semidirect
24. C₃×C₅×C₁₉	C₃×D₁₉	semidirect
25. C₃×C₅×C₁₉	D₅₇	semidirect
27. C₃²×C₁₉	D₉₅	semidirect
30. C₅×C₁₉	C₃×D₅₇	semidirect
33. C₃×C₁₉	C₃×D₉₅	semidirect
34. C₃×C₁₉	D₂₈₅	semidirect
35. C₃²×C₅	C₁₉⋊D₁₉	semidirect
39. C₁₉	C₃×D₂₈₅	semidirect
42. C₃×C₅	C₃×C₁₉⋊D₁₉	semidirect
43. C₃×C₅	C₃⋊(C₁₉⋊D₁₉)	semidirect
45. C₃²	C₅⋊(C₁₉⋊D₁₉)	semidirect
48. C₅	C₃×C₃⋊(C₁₉⋊D₁₉)	semidirect
50. C₃	C₃⋊(C₅⋊(C₁₉⋊D₁₉))	direct (N × H)
51. C₃	C₃×C₅⋊(C₁₉⋊D₁₉)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₉²	2
C₃×C₅⋊(C₁₉⋊D₁₉)	3
C₃⋊(C₅⋊(C₁₉⋊D₁₉))	3
C₃×C₃⋊(C₁₉⋊D₁₉)	5
C₃×D₂₈₅	19

Subgroups — C3×C3⋊(C5⋊(C19⋊D19)) #44570631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊(C₅⋊(C₁₉⋊D₁₉)) #44570631