Subgroups — C₃×D₃×C₁₃×C₁₃₇ #44545403

Order 32058.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₃₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₁₃×C₁₃₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₃₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₁₃×C₁₃₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×C₁₃₇	C₂	semidirect
2. D₃×C₁₃×C₁₃₇	C₃	direct (N × H)
5. C₃×C₁₃×C₁₃₇	D₃	direct (N × H)
6. C₃×C₁₃×C₁₃₇	C₂×C₃	semidirect
8. C₃×D₃×C₁₃₇	C₁₃	direct (N × H)
9. C₁₃×C₁₃₇	C₃×D₃	direct (N × H)
10. C₃²×C₁₃₇	C₂×C₁₃	semidirect
12. D₃×C₁₃₇	C₃×C₁₃	direct (N × H)
14. C₃×C₁₃₇	D₃×C₁₃	direct (N × H)
15. C₃×C₁₃₇	C₂×C₃×C₁₃	semidirect
17. C₃×D₃×C₁₃	C₁₃₇	direct (N × H)
18. C₁₃₇	C₃×D₃×C₁₃	direct (N × H)
19. C₃²×C₁₃	C₂×C₁₃₇	semidirect
21. D₃×C₁₃	C₃×C₁₃₇	direct (N × H)
23. C₃×C₁₃	D₃×C₁₃₇	direct (N × H)
24. C₃×C₁₃	C₂×C₃×C₁₃₇	semidirect
26. C₃×D₃	C₁₃×C₁₃₇	direct (N × H)
27. C₁₃	C₃×D₃×C₁₃₇	direct (N × H)
28. C₃²	C₂×C₁₃×C₁₃₇	semidirect
30. D₃	C₃×C₁₃×C₁₃₇	direct (N × H)
32. C₃	C₂×C₃×C₁₃×C₁₃₇	semidirect
33. C₃	D₃×C₁₃×C₁₃₇	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×C₁₃₇	2
D₃×C₁₃×C₁₃₇	3
C₂×C₃×C₁₃×C₁₃₇	3
C₃×D₃×C₁₃₇	13
C₃×D₃×C₁₃	137

Subgroups — C3×D3×C13×C137 #44545403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₁₃×C₁₃₇ #44545403