Subgroups — C₁₃×C₂₉×D₃₉ #44440628

Order 29406.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₃×C₂₉	—	3	1	no	maximal, Hall
3	C₁₃²×C₂₉	D₃	1	1	yes	characteristic, complemented, Hall
4	C₂₉×D₃₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	D₃×C₁₃×C₂₉	—	13	1	no	maximal
6	C₃×C₁₃×C₂₉	—	2	6	no	—
7	C₃×C₁₃×C₂₉	D₁₃	1	1	yes	characteristic, complemented
8	C₃×C₁₃×C₂₉	C₂×C₁₃	1	1	yes	characteristic, complemented
9	C₁₃×D₃₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₂₉	—	39	1	no	—
11	D₁₃×C₂₉	—	3	1	no	—
12	C₃×C₁₃²	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
13	C₁₃×C₂₉	—	2	6	no	—
14	C₁₃×C₂₉	D₃×C₁₃	1	1	yes	characteristic, complemented
15	C₁₃×C₂₉	D₃₉	1	1	yes	characteristic, direct product factor
16	C₁₃×D₁₃	—	3	1	no	Hall
17	D₃×C₂₉	—	13	1	no	Hall
18	C₁₃²	D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₂₉	C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
20	D₃₉	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor
21	D₃×C₁₃	—	13	1	no	—
22	C₂×C₂₉	—	39	1	no	Hall
23	C₃×C₁₃	—	2	6	no	—
24	C₃×C₁₃	D₁₃×C₂₉	1	1	yes	characteristic, complemented
25	C₃×C₁₃	C₂×C₁₃×C₂₉	1	1	yes	characteristic, complemented
26	C₂₉	C₁₃×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₃	—	39	1	no	—
28	D₁₃	—	3	1	no	—
29	C₁₃	—	2	6	no	—
30	C₁₃	D₃×C₁₃×C₂₉	1	1	yes	characteristic, complemented
31	C₁₃	C₂₉×D₃₉	1	1	yes	characteristic, direct product factor
32	D₃	—	13	1	no	Hall
33	C₃	C₁₃×D₁₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	39	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₂₉	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₁₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₂₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃²×C₂₉	C₂	semidirect
3. C₁₃²×C₂₉	D₃	semidirect
4. C₂₉×D₃₉	C₁₃	direct (N × H)
7. C₃×C₁₃×C₂₉	D₁₃	semidirect
8. C₃×C₁₃×C₂₉	C₂×C₁₃	semidirect
9. C₁₃×D₃₉	C₂₉	direct (N × H)
12. C₃×C₁₃²	C₂×C₂₉	semidirect
14. C₁₃×C₂₉	D₃×C₁₃	semidirect
15. C₁₃×C₂₉	D₃₉	direct (N × H)
18. C₁₃²	D₃×C₂₉	semidirect
19. C₃×C₂₉	C₁₃×D₁₃	semidirect
20. D₃₉	C₁₃×C₂₉	direct (N × H)
24. C₃×C₁₃	D₁₃×C₂₉	semidirect
25. C₃×C₁₃	C₂×C₁₃×C₂₉	semidirect
26. C₂₉	C₁₃×D₃₉	direct (N × H)
30. C₁₃	D₃×C₁₃×C₂₉	semidirect
31. C₁₃	C₂₉×D₃₉	direct (N × H)
33. C₃	C₁₃×D₁₃×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃²×C₂₉	2
C₁₃×D₁₃×C₂₉	3
C₂₉×D₃₉	13
D₃×C₁₃×C₂₉	13
C₁₃×D₃₉	29

Subgroups — C13×C29×D39 #44440628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₂₉×D₃₉ #44440628