Subgroups — C₂×C₃×D₁₉×C₁₀₉ #38733197

Order 24852.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₉×C₁₀₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₉×C₁₀₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₉×C₁₀₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₉×C₁₀₉	C₂×C₃	1	2	yes	direct product factor
7	C₁₉×C₁₀₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₃×C₁₀₉	—	19	1	no	maximal, Hall
9	C₂×C₃×C₁₀₉	—	19	2	no	—
10	C₂×C₃×C₁₀₉	D₁₉	1	1	yes	characteristic, direct product factor
11	C₂²×C₁₀₉	—	19	1	no	Hall
12	C₃×C₁₀₉	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×D₁₉	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₀₉	—	19	2	no	—
15	C₂×C₁₀₉	C₃×D₁₉	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₁₉	C₂×C₁₀₉	1	1	yes	characteristic, complemented
17	C₃×D₁₉	C₂×C₁₀₉	1	2	yes	direct product factor
18	C₁₀₉	C₂×C₃×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×D₁₉	C₃×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₉	C₂²×C₁₀₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₉	C₂×C₃×C₁₀₉	1	1	yes	characteristic, complemented
22	D₁₉	C₂×C₃×C₁₀₉	1	2	yes	direct product factor
23	C₁₉	C₂²×C₃×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	19	1	no	Hall
25	C₂×C₃	—	19	2	no	—
26	C₂×C₃	D₁₉×C₁₀₉	1	1	yes	characteristic, direct product factor
27	C₂²	—	19	1	no	Sylow
28	C₃	C₂×D₁₉×C₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	19	2	no	—
30	C₂	C₃×D₁₉×C₁₀₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₀₉	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₁₀₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₁₀₉

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₉×C₁₀₉	C₂	direct (N × H)
2. C₂×C₃×C₁₉×C₁₀₉	C₂	semidirect
3. C₂×D₁₉×C₁₀₉	C₃	direct (N × H)
4. C₃×C₁₉×C₁₀₉	C₂²	semidirect
5. C₂×C₁₉×C₁₀₉	C₂×C₃	semidirect
6. D₁₉×C₁₀₉	C₂×C₃	direct (N × H)
7. C₁₉×C₁₀₉	C₂²×C₃	semidirect
10. C₂×C₃×C₁₀₉	D₁₉	direct (N × H)
12. C₃×C₁₀₉	C₂×D₁₉	direct (N × H)
13. C₂×C₃×D₁₉	C₁₀₉	direct (N × H)
15. C₂×C₁₀₉	C₃×D₁₉	direct (N × H)
16. C₂×C₃×C₁₉	C₂×C₁₀₉	semidirect
17. C₃×D₁₉	C₂×C₁₀₉	direct (N × H)
18. C₁₀₉	C₂×C₃×D₁₉	direct (N × H)
19. C₂×D₁₉	C₃×C₁₀₉	direct (N × H)
20. C₃×C₁₉	C₂²×C₁₀₉	semidirect
21. C₂×C₁₉	C₂×C₃×C₁₀₉	semidirect
22. D₁₉	C₂×C₃×C₁₀₉	direct (N × H)
23. C₁₉	C₂²×C₃×C₁₀₉	semidirect
26. C₂×C₃	D₁₉×C₁₀₉	direct (N × H)
28. C₃	C₂×D₁₉×C₁₀₉	direct (N × H)
30. C₂	C₃×D₁₉×C₁₀₉	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×D₁₉×C₁₀₉	2
C₂×C₃×C₁₉×C₁₀₉	2
C₂×D₁₉×C₁₀₉	3
C₂²×C₃×C₁₀₉	19
C₂×C₃×D₁₉	109

Subgroups — C2×C3×D19×C109 #38733197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₉×C₁₀₉ #38733197