Subgroups — C₃×C₁₉⋊(D₆₁⋊C₅) #46851920

Order 34770.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₆₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊(D₆₁⋊C₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₁₅₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉×C₆₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₁₁₅₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₆₁⋊C₅	—	19	1	no	maximal, Hall
8	C₁₉×C₆₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₆₁⋊C₅	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₆₁⋊C₅	—	19	1	no	Hall
11	C₃×C₅×D₁₉	—	61	1	no	maximal, Hall
12	C₃×D₆₁	—	19	1	no	Hall
13	C₆₁⋊C₅	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₉	—	61	1	no	Hall
15	C₅×D₁₉	—	61	1	no	Hall
16	C₃×C₆₁	C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
17	D₆₁	—	19	1	no	Hall
18	C₃×D₁₉	—	61	1	no	Hall
19	C₅×C₁₉	—	61	1	no	Hall
20	C₆₁	C₃×C₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₉	D₆₁⋊C₅	1	1	yes	characteristic, complemented, Hall
22	D₁₉	—	61	1	no	Hall
23	C₂×C₃×C₅	—	1159	1	no	Hall
24	C₁₉	C₃×D₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	—	61	1	no	Hall
26	C₂×C₅	—	1159	1	no	Hall
27	C₂×C₃	—	1159	1	no	Hall
28	C₅	—	61	1	no	Sylow
29	C₃	C₁₉⋊(D₆₁⋊C₅)	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	1159	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₉⋊(D₆₁⋊C₅)
commutator, cosocle, hypocenter	C₁₉×C₆₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₆₁	C₂×C₅
LCS	G ▷ C₁₉×C₆₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₆₁⋊C₅	C₂	semidirect
2. C₁₉⋊(D₆₁⋊C₅)	C₃	direct (N × H)
3. C₃×D₁₁₅₉	C₅	semidirect
4. C₁₉×C₆₁⋊C₅	C₂×C₃	semidirect
5. C₃×C₁₉×C₆₁	C₂×C₅	semidirect
6. D₁₁₅₉	C₃×C₅	semidirect
8. C₁₉×C₆₁	C₂×C₃×C₅	semidirect
9. C₃×C₆₁⋊C₅	D₁₉	semidirect
13. C₆₁⋊C₅	C₃×D₁₉	semidirect
16. C₃×C₆₁	C₅×D₁₉	semidirect
20. C₆₁	C₃×C₅×D₁₉	semidirect
21. C₃×C₁₉	D₆₁⋊C₅	semidirect
24. C₁₉	C₃×D₆₁⋊C₅	semidirect
29. C₃	C₁₉⋊(D₆₁⋊C₅)	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×C₁₉×C₆₁⋊C₅	2
C₁₉⋊(D₆₁⋊C₅)	3
C₃×D₁₁₅₉	5
C₃×D₆₁⋊C₅	19
C₃×C₅×D₁₉	61

Subgroups — C3×C19⋊(D61⋊C5) #46851920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉⋊(D₆₁⋊C₅) #46851920