Subgroups — C₂×D₃×C₃₁×C₄₃ #30630633

Order 15996.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₃₁×C₄₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₃₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×C₄₃	—	3	1	no	maximal, Hall
4	C₃×C₃₁×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×C₄₃	—	3	2	no	—
6	C₂×C₃₁×C₄₃	D₃	1	1	yes	characteristic, direct product factor
7	C₃₁×C₄₃	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×D₃×C₄₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×D₃×C₃₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₄₃	C₂×C₃₁	1	1	yes	characteristic, complemented
11	D₃×C₄₃	C₂×C₃₁	1	2	yes	direct product factor
12	C₂×C₃×C₃₁	C₂×C₄₃	1	1	yes	characteristic, complemented
13	D₃×C₃₁	C₂×C₄₃	1	2	yes	direct product factor
14	C₂²×C₄₃	—	3	1	no	Hall
15	C₃×C₄₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃₁	—	3	1	no	Hall
17	C₃×C₃₁	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₃	—	3	2	no	—
19	C₂×C₄₃	D₃×C₃₁	1	1	yes	characteristic, direct product factor
20	C₂×C₃₁	—	3	2	no	—
21	C₂×C₃₁	D₃×C₄₃	1	1	yes	characteristic, direct product factor
22	C₄₃	C₂×D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₁	C₂×D₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃	C₃₁×C₄₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃	C₂×C₃₁×C₄₃	1	1	yes	characteristic, complemented
26	D₃	C₂×C₃₁×C₄₃	1	2	yes	direct product factor
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₃₁×C₄₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	D₃×C₃₁×C₄₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁×C₄₃	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃₁×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₃₁×C₄₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃₁×C₄₃

Complements

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

N	H ≅ G/N	type
1. D₃×C₃₁×C₄₃	C₂	direct (N × H)
2. C₂×C₃×C₃₁×C₄₃	C₂	semidirect
4. C₃×C₃₁×C₄₃	C₂²	semidirect
6. C₂×C₃₁×C₄₃	D₃	direct (N × H)
7. C₃₁×C₄₃	C₂×D₃	direct (N × H)
8. C₂×D₃×C₄₃	C₃₁	direct (N × H)
9. C₂×D₃×C₃₁	C₄₃	direct (N × H)
10. C₂×C₃×C₄₃	C₂×C₃₁	semidirect
11. D₃×C₄₃	C₂×C₃₁	direct (N × H)
12. C₂×C₃×C₃₁	C₂×C₄₃	semidirect
13. D₃×C₃₁	C₂×C₄₃	direct (N × H)
15. C₃×C₄₃	C₂²×C₃₁	semidirect
17. C₃×C₃₁	C₂²×C₄₃	semidirect
19. C₂×C₄₃	D₃×C₃₁	direct (N × H)
21. C₂×C₃₁	D₃×C₄₃	direct (N × H)
22. C₄₃	C₂×D₃×C₃₁	direct (N × H)
23. C₃₁	C₂×D₃×C₄₃	direct (N × H)
24. C₂×D₃	C₃₁×C₄₃	direct (N × H)
25. C₂×C₃	C₂×C₃₁×C₄₃	semidirect
26. D₃	C₂×C₃₁×C₄₃	direct (N × H)
28. C₃	C₂²×C₃₁×C₄₃	semidirect
30. C₂	D₃×C₃₁×C₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃×C₃₁×C₄₃	2
C₂×C₃×C₃₁×C₄₃	2
C₂²×C₃₁×C₄₃	3
C₂×D₃×C₄₃	31
C₂×D₃×C₃₁	43

Subgroups — C2×D3×C31×C43 #30630633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₃₁×C₄₃ #30630633