Subgroups — D₃×D₂₉×C₁₀₉ #49181925

Order 37932.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂₉×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₉×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₉×C₁₀₉	—	3	1	no	maximal, Hall
5	C₃×C₂₉×C₁₀₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₂₉×C₁₀₉	—	3	1	no	—
7	D₂₉×C₁₀₉	—	3	1	no	—
8	D₂₉×C₁₀₉	D₃	1	1	yes	characteristic, direct product factor
9	C₂₉×C₁₀₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃×C₁₀₉	—	29	1	no	maximal, Hall
11	C₂×C₃×C₁₀₉	—	29	1	no	—
12	D₃×C₁₀₉	—	29	1	no	—
13	D₃×C₁₀₉	D₂₉	1	1	yes	characteristic, direct product factor
14	C₂²×C₁₀₉	—	87	1	no	Hall
15	D₃×D₂₉	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₁₀₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₀₉	—	3	1	no	—
18	C₂×C₁₀₉	—	29	1	no	—
19	C₂×C₁₀₉	—	87	1	no	—
20	D₈₇	C₂×C₁₀₉	1	1	yes	characteristic, complemented
21	C₃×D₂₉	C₂×C₁₀₉	1	1	yes	characteristic, complemented
22	D₃×C₂₉	C₂×C₁₀₉	1	1	yes	characteristic, complemented
23	C₂×D₂₉	—	3	1	no	Hall
24	C₁₀₉	D₃×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₂₉	C₂²×C₁₀₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₂₉	—	3	1	no	—
27	D₂₉	—	3	1	no	—
28	D₂₉	D₃×C₁₀₉	1	1	yes	characteristic, direct product factor
29	C₂₉	C₂×D₃×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	29	1	no	Hall
31	C₂×C₃	—	29	1	no	—
32	D₃	—	29	1	no	—
33	D₃	D₂₉×C₁₀₉	1	1	yes	characteristic, direct product factor
34	C₂²	—	87	1	no	Sylow
35	C₃	C₂×D₂₉×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	29	1	no	—
38	C₂	—	87	1	no	—

	subgroup	G/H
center, hypercenter	C₁₀₉	D₃×D₂₉
commutator, cosocle, hypocenter	C₃×C₂₉	C₂²×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₁₀₉	C₂²
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₁₀₉

Complements

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

N	H ≅ G/N	type
1. C₁₀₉×D₈₇	C₂	semidirect
2. D₃×C₂₉×C₁₀₉	C₂	semidirect
3. C₃×D₂₉×C₁₀₉	C₂	semidirect
5. C₃×C₂₉×C₁₀₉	C₂²	semidirect
8. D₂₉×C₁₀₉	D₃	direct (N × H)
9. C₂₉×C₁₀₉	C₂×D₃	semidirect
13. D₃×C₁₀₉	D₂₉	direct (N × H)
15. D₃×D₂₉	C₁₀₉	direct (N × H)
16. C₃×C₁₀₉	C₂×D₂₉	semidirect
20. D₈₇	C₂×C₁₀₉	semidirect
21. C₃×D₂₉	C₂×C₁₀₉	semidirect
22. D₃×C₂₉	C₂×C₁₀₉	semidirect
24. C₁₀₉	D₃×D₂₉	direct (N × H)
25. C₃×C₂₉	C₂²×C₁₀₉	semidirect
28. D₂₉	D₃×C₁₀₉	direct (N × H)
29. C₂₉	C₂×D₃×C₁₀₉	semidirect
33. D₃	D₂₉×C₁₀₉	direct (N × H)
35. C₃	C₂×D₂₉×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₉×D₈₇	2
D₃×C₂₉×C₁₀₉	2
C₃×D₂₉×C₁₀₉	2
C₂×D₂₉×C₁₀₉	3
C₂×D₃×C₁₀₉	29
D₃×D₂₉	109

Subgroups — D3×D29×C109 #49181925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₉×C₁₀₉ #49181925