Subgroups — C₅×C₁₉×D₆₁⋊C₃ #46851925

Order 34770.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×C₆₁⋊C₃	C₂	semidirect
2. C₅×C₁₉×D₆₁	C₃	semidirect
3. C₁₉×D₆₁⋊C₃	C₅	direct (N × H)
4. C₅×C₁₉×C₆₁	C₂×C₃	semidirect
5. C₁₉×C₆₁⋊C₃	C₂×C₅	semidirect
6. C₁₉×D₆₁	C₃×C₅	semidirect
7. C₅×D₆₁⋊C₃	C₁₉	direct (N × H)
8. C₁₉×C₆₁	C₂×C₃×C₅	semidirect
9. C₅×C₆₁⋊C₃	C₂×C₁₉	semidirect
10. C₅×D₆₁	C₃×C₁₉	semidirect
12. D₆₁⋊C₃	C₅×C₁₉	direct (N × H)
13. C₅×C₆₁	C₂×C₃×C₁₉	semidirect
16. C₆₁⋊C₃	C₂×C₅×C₁₉	semidirect
17. D₆₁	C₃×C₅×C₁₉	semidirect
19. C₅×C₁₉	D₆₁⋊C₃	direct (N × H)
20. C₆₁	C₂×C₃×C₅×C₁₉	semidirect
24. C₁₉	C₅×D₆₁⋊C₃	direct (N × H)
28. C₅	C₁₉×D₆₁⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₉×C₆₁⋊C₃	2
C₅×C₁₉×D₆₁	3
C₁₉×D₆₁⋊C₃	5
C₅×D₆₁⋊C₃	19
C₂×C₃×C₅×C₁₉	61

Subgroups — C5×C19×D61⋊C3 #46851925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×D₆₁⋊C₃ #46851925