Subgroups — C₃×C₁₃×D₁₃×C₃₁ #44537694

Order 31434.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃×C₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃×C₁₃×C₃₁	—	13	1	no	maximal
6	C₃×C₁₃×C₃₁	—	2	6	no	—
7	C₃×C₁₃×C₃₁	D₁₃	1	1	yes	characteristic, direct product factor
8	C₃×C₁₃×C₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented
9	C₃×C₁₃×D₁₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₃₁	—	13	1	no	—
11	D₁₃×C₃₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor
12	C₃×C₁₃²	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
13	C₁₃×C₃₁	—	2	6	no	—
14	C₁₃×C₃₁	C₃×D₁₃	1	1	yes	characteristic, direct product factor
15	C₁₃×C₃₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₁₃×D₁₃	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₃₁	—	13	1	no	Hall
18	C₁₃²	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₃₁	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₁₃	—	13	1	no	—
21	C₃×D₁₃	C₁₃×C₃₁	1	1	yes	characteristic, direct product factor
22	C₂×C₃₁	—	13	1	no	Hall
23	C₃×C₁₃	—	2	6	no	—
24	C₃×C₁₃	D₁₃×C₃₁	1	1	yes	characteristic, direct product factor
25	C₃×C₁₃	C₂×C₁₃×C₃₁	1	1	yes	characteristic, complemented
26	C₃₁	C₃×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₃	—	13	1	no	—
28	D₁₃	C₃×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor
29	C₁₃	—	2	6	no	—
30	C₁₃	C₂×C₃×C₁₃×C₃₁	1	1	yes	characteristic, complemented
31	C₁₃	C₃×D₁₃×C₃₁	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	13	1	no	Hall
33	C₃	C₁₃×D₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₃₁	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₃₁	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃²×C₃₁	C₂	semidirect
2. C₁₃×D₁₃×C₃₁	C₃	direct (N × H)
3. C₁₃²×C₃₁	C₂×C₃	semidirect
4. C₃×D₁₃×C₃₁	C₁₃	direct (N × H)
7. C₃×C₁₃×C₃₁	D₁₃	direct (N × H)
8. C₃×C₁₃×C₃₁	C₂×C₁₃	semidirect
9. C₃×C₁₃×D₁₃	C₃₁	direct (N × H)
11. D₁₃×C₃₁	C₃×C₁₃	direct (N × H)
12. C₃×C₁₃²	C₂×C₃₁	semidirect
14. C₁₃×C₃₁	C₃×D₁₃	direct (N × H)
15. C₁₃×C₃₁	C₂×C₃×C₁₃	semidirect
16. C₁₃×D₁₃	C₃×C₃₁	direct (N × H)
18. C₁₃²	C₂×C₃×C₃₁	semidirect
19. C₃×C₃₁	C₁₃×D₁₃	direct (N × H)
21. C₃×D₁₃	C₁₃×C₃₁	direct (N × H)
24. C₃×C₁₃	D₁₃×C₃₁	direct (N × H)
25. C₃×C₁₃	C₂×C₁₃×C₃₁	semidirect
26. C₃₁	C₃×C₁₃×D₁₃	direct (N × H)
28. D₁₃	C₃×C₁₃×C₃₁	direct (N × H)
30. C₁₃	C₂×C₃×C₁₃×C₃₁	semidirect
31. C₁₃	C₃×D₁₃×C₃₁	direct (N × H)
33. C₃	C₁₃×D₁₃×C₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃²×C₃₁	2
C₁₃×D₁₃×C₃₁	3
C₃×D₁₃×C₃₁	13
C₂×C₃×C₁₃×C₃₁	13
C₃×C₁₃×D₁₃	31

Subgroups — C3×C13×D13×C31 #44537694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×D₁₃×C₃₁ #44537694