Subgroups — C₃×D₃₉×C₁₂₇ #44446142

Order 29718.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₃×C₁₂₇	—	3	1	no	maximal
4	C₃×C₁₃×C₁₂₇	—	2	1	no	—
5	C₃×C₁₃×C₁₂₇	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₃×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₃×C₁₂₇	—	3	1	no	Hall
8	C₃×D₃×C₁₂₇	—	13	1	no	maximal, Hall
9	C₁₃×C₁₂₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₂₇	D₁₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₂₇	—	39	1	no	—
12	D₃×C₁₂₇	—	13	1	no	—
13	C₃×C₁₂₇	—	2	1	no	—
14	C₃×C₁₂₇	C₃×D₁₃	1	1	yes	characteristic, complemented
15	C₃×C₁₂₇	D₃₉	1	1	yes	characteristic, direct product factor
16	C₂×C₁₂₇	—	39	1	no	Hall
17	C₃×D₃₉	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₂₇	C₃×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²×C₁₃	C₂×C₁₂₇	1	1	yes	characteristic, complemented, Hall
20	D₃₉	C₃×C₁₂₇	1	1	yes	characteristic, direct product factor
21	C₃×D₁₃	—	3	1	no	—
22	C₃×C₁₃	—	2	1	no	—
23	C₃×C₁₃	D₃×C₁₂₇	1	1	yes	characteristic, complemented
24	C₃×C₁₃	C₂×C₃×C₁₂₇	1	1	yes	characteristic, complemented
25	D₁₃	—	3	1	no	Hall
26	C₃×D₃	—	13	1	no	Hall
27	C₁₃	C₃×D₃×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
28	C₃²	D₁₃×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	39	1	no	—
30	D₃	—	13	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₃×C₁₂₇	1	1	yes	characteristic, complemented
33	C₃	D₃₉×C₁₂₇	1	1	yes	characteristic, direct product factor
34	C₂	—	39	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₂₇	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₃×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₂₇	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₃×C₁₂₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×C₁₂₇	C₂	semidirect
2. D₃₉×C₁₂₇	C₃	direct (N × H)
5. C₃×C₁₃×C₁₂₇	D₃	semidirect
6. C₃×C₁₃×C₁₂₇	C₂×C₃	semidirect
9. C₁₃×C₁₂₇	C₃×D₃	semidirect
10. C₃²×C₁₂₇	D₁₃	semidirect
14. C₃×C₁₂₇	C₃×D₁₃	semidirect
15. C₃×C₁₂₇	D₃₉	direct (N × H)
17. C₃×D₃₉	C₁₂₇	direct (N × H)
18. C₁₂₇	C₃×D₃₉	direct (N × H)
19. C₃²×C₁₃	C₂×C₁₂₇	semidirect
20. D₃₉	C₃×C₁₂₇	direct (N × H)
23. C₃×C₁₃	D₃×C₁₂₇	semidirect
24. C₃×C₁₃	C₂×C₃×C₁₂₇	semidirect
27. C₁₃	C₃×D₃×C₁₂₇	semidirect
28. C₃²	D₁₃×C₁₂₇	semidirect
32. C₃	C₃×D₁₃×C₁₂₇	semidirect
33. C₃	D₃₉×C₁₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₁₂₇	2
D₃₉×C₁₂₇	3
C₃×D₁₃×C₁₂₇	3
C₃×D₃×C₁₂₇	13
C₃×D₃₉	127

Subgroups — C3×D39×C127 #44446142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₉×C₁₂₇ #44446142