Subgroups — C₅×C₃⋊(C₃⋊(C₁₉⋊D₁₉)) #44570634

Order 32490.

528 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	C₅×C₃⋊(C₁₉⋊D₁₉)	—	3	4	no	maximal
3	C₃⋊(C₃⋊(C₁₉⋊D₁₉))	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₉²	D₃	1	4	yes	complemented
5	C₅×C₁₉⋊D₁₉	—	9	1	no	Hall
6	C₃²×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃⋊(C₁₉⋊D₁₉)	—	3	4	no	—
8	C₅×C₁₉²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₅×C₃⋊D₅₇	—	19	20	no	maximal
10	C₃×C₁₉²	C₅×D₃	1	4	yes	complemented
11	C₃²×C₅×C₁₉	D₁₉	1	20	yes	complemented
12	C₁₉⋊D₁₉	—	9	1	no	Hall
13	C₅×D₅₇	—	57	80	no	—
14	C₁₉²	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
15	C₃⋊D₅₇	—	19	20	no	—
16	C₃×C₅×C₁₉	D₅₇	1	80	yes	complemented
17	C₅×D₁₉	—	171	20	no	—
18	C₃²×C₁₉	C₅×D₁₉	1	20	yes	complemented
19	D₅₇	—	57	80	no	—
20	C₅×C₁₉	C₃⋊D₅₇	1	20	yes	complemented
21	C₅×C₃⋊D₃	—	361	1	no	Hall
22	C₃×C₁₉	C₅×D₅₇	1	80	yes	complemented
23	C₃²×C₅	C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Hall
24	D₁₉	—	171	20	no	—
25	C₅×D₃	—	1083	4	no	—
26	C₁₉	C₅×C₃⋊D₅₇	1	20	yes	complemented
27	C₃⋊D₃	—	361	1	no	Hall
28	C₃×C₅	C₃⋊(C₁₉⋊D₁₉)	1	4	yes	complemented
29	C₂×C₅	—	3249	1	no	Hall
30	C₃²	C₅×C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	1083	4	no	—
32	C₅	C₃⋊(C₃⋊(C₁₉⋊D₁₉))	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₅×C₃⋊(C₁₉⋊D₁₉)	1	4	yes	complemented
34	C₂	—	3249	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
3. C₃⋊(C₃⋊(C₁₉⋊D₁₉))	C₅	direct (N × H)
4. C₃×C₅×C₁₉²	D₃	semidirect
6. C₃²×C₁₉²	C₂×C₅	semidirect
8. C₅×C₁₉²	C₃⋊D₃	semidirect
10. C₃×C₁₉²	C₅×D₃	semidirect
11. C₃²×C₅×C₁₉	D₁₉	semidirect
14. C₁₉²	C₅×C₃⋊D₃	semidirect
16. C₃×C₅×C₁₉	D₅₇	semidirect
18. C₃²×C₁₉	C₅×D₁₉	semidirect
20. C₅×C₁₉	C₃⋊D₅₇	semidirect
22. C₃×C₁₉	C₅×D₅₇	semidirect
23. C₃²×C₅	C₁₉⋊D₁₉	semidirect
26. C₁₉	C₅×C₃⋊D₅₇	semidirect
28. C₃×C₅	C₃⋊(C₁₉⋊D₁₉)	semidirect
30. C₃²	C₅×C₁₉⋊D₁₉	semidirect
32. C₅	C₃⋊(C₃⋊(C₁₉⋊D₁₉))	direct (N × H)
33. C₃	C₅×C₃⋊(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
C₅×C₃⋊(C₁₉⋊D₁₉)	3
C₃⋊(C₃⋊(C₁₉⋊D₁₉))	5
C₅×C₃⋊D₅₇	19

Subgroups — C5×C3⋊(C3⋊(C19⋊D19)) #44570634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊(C₃⋊(C₁₉⋊D₁₉)) #44570634