Subgroups — D₃×C₁₃⋊C₃×C₁₃₇ #44545397

Order 32058.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊C₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₃×C₁₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃⋊C₃×C₁₃₇	—	3	1	no	maximal
4	C₃×C₁₃×C₁₃₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊C₃×C₁₃₇	—	2	1	no	—
6	C₁₃⋊C₃×C₁₃₇	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₁₃×C₁₃₇	—	3	1	no	Hall
8	C₃×D₃×C₁₃₇	—	13	1	no	maximal, Hall
9	C₁₃×C₁₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₃₇	—	13	1	no	Hall
11	C₂×C₃×C₁₃₇	—	39	1	no	—
12	D₃×C₁₃₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
13	C₃×C₁₃₇	—	13	1	no	—
14	C₃×C₁₃₇	—	26	1	no	—
15	C₃×C₁₃₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₂×C₁₃₇	—	3	1	no	Hall
17	D₃×C₁₃⋊C₃	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₃₇	D₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₁₃⋊C₃	C₂×C₁₃₇	1	1	yes	characteristic, complemented, Hall
20	D₃×C₁₃	C₃×C₁₃₇	1	1	yes	characteristic, complemented
21	C₂×C₁₃⋊C₃	—	3	1	no	—
22	C₃×C₁₃	C₂×C₃×C₁₃₇	1	1	yes	characteristic, complemented
23	C₁₃⋊C₃	—	2	1	no	—
24	C₁₃⋊C₃	D₃×C₁₃₇	1	1	yes	characteristic, direct product factor
25	C₂×C₁₃	—	3	1	no	Hall
26	C₃×D₃	—	13	1	no	Hall
27	C₁₃	C₃×D₃×C₁₃₇	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	13	1	no	Sylow
29	C₂×C₃	—	39	1	no	—
30	D₃	C₁₃⋊C₃×C₁₃₇	1	1	yes	characteristic, direct product factor
31	C₃	—	13	1	no	—
32	C₃	—	26	1	no	—
33	C₃	C₂×C₁₃⋊C₃×C₁₃₇	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃₇	D₃×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₃×C₁₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₃₇	C₂×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃⋊C₃×C₁₃₇	C₂	semidirect
2. D₃×C₁₃×C₁₃₇	C₃	semidirect
4. C₃×C₁₃×C₁₃₇	C₂×C₃	semidirect
6. C₁₃⋊C₃×C₁₃₇	D₃	direct (N × H)
9. C₁₃×C₁₃₇	C₃×D₃	semidirect
12. D₃×C₁₃₇	C₁₃⋊C₃	direct (N × H)
15. C₃×C₁₃₇	C₂×C₁₃⋊C₃	semidirect
17. D₃×C₁₃⋊C₃	C₁₃₇	direct (N × H)
18. C₁₃₇	D₃×C₁₃⋊C₃	direct (N × H)
19. C₃×C₁₃⋊C₃	C₂×C₁₃₇	semidirect
20. D₃×C₁₃	C₃×C₁₃₇	semidirect
22. C₃×C₁₃	C₂×C₃×C₁₃₇	semidirect
24. C₁₃⋊C₃	D₃×C₁₃₇	direct (N × H)
27. C₁₃	C₃×D₃×C₁₃₇	semidirect
30. D₃	C₁₃⋊C₃×C₁₃₇	direct (N × H)
33. C₃	C₂×C₁₃⋊C₃×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃⋊C₃×C₁₃₇	2
D₃×C₁₃×C₁₃₇	3
C₂×C₁₃⋊C₃×C₁₃₇	3
C₃×D₃×C₁₃₇	13
D₃×C₁₃⋊C₃	137

Subgroups — D3×C13⋊C3×C137 #44545397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₃⋊C₃×C₁₃₇ #44545397