Subgroups — C₃×A₄×C₁₃×C₃₁ #28408366

Order 14508.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₁₃×C₃₁	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃×C₃₁	—	4	1	no	maximal, Hall
4	C₂×C₃×C₁₃×C₃₁	—	3	1	no	—
5	C₂²×C₁₃×C₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₃₁	—	4	3	no	—
7	C₃×C₁₃×C₃₁	A₄	1	1	yes	characteristic, direct product factor
8	C₃×A₄×C₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₃×C₃₁	—	3	1	no	—
10	C₃×A₄×C₁₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₃×C₃₁	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₃×C₃₁	C₃×C₁₃	1	1	yes	characteristic, complemented
13	A₄×C₃₁	C₃×C₁₃	1	3	yes	direct product factor
14	C₃²×C₃₁	—	4	1	no	Hall
15	C₂×C₃×C₃₁	—	3	1	no	—
16	C₂²×C₃×C₁₃	C₃×C₃₁	1	1	yes	characteristic, complemented
17	A₄×C₁₃	C₃×C₃₁	1	3	yes	direct product factor
18	C₂²×C₃₁	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₁₃	—	4	1	no	Hall
20	C₃×C₃₁	—	4	3	no	—
21	C₃×C₃₁	A₄×C₁₃	1	1	yes	characteristic, direct product factor
22	C₂×C₃×C₁₃	—	3	1	no	—
23	C₂×C₃₁	—	3	1	no	—
24	C₂²×C₁₃	C₃²×C₃₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₃	—	4	3	no	—
26	C₃×C₁₃	A₄×C₃₁	1	1	yes	characteristic, direct product factor
27	C₃×A₄	C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃₁	C₃×A₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₁₃	—	3	1	no	—
30	C₁₃	C₃×A₄×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²×C₃	C₃×C₁₃×C₃₁	1	1	yes	characteristic, complemented
32	A₄	C₃×C₁₃×C₃₁	1	3	yes	direct product factor
33	C₃²	—	4	1	no	Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂²	C₃²×C₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	4	3	no	—
37	C₃	A₄×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₃₁	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃×C₃₁	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. A₄×C₁₃×C₃₁	C₃	direct (N × H)
2. C₂²×C₃×C₁₃×C₃₁	C₃	semidirect
5. C₂²×C₁₃×C₃₁	C₃²	semidirect
7. C₃×C₁₃×C₃₁	A₄	direct (N × H)
8. C₃×A₄×C₃₁	C₁₃	direct (N × H)
10. C₃×A₄×C₁₃	C₃₁	direct (N × H)
11. C₁₃×C₃₁	C₃×A₄	direct (N × H)
12. C₂²×C₃×C₃₁	C₃×C₁₃	semidirect
13. A₄×C₃₁	C₃×C₁₃	direct (N × H)
16. C₂²×C₃×C₁₃	C₃×C₃₁	semidirect
17. A₄×C₁₃	C₃×C₃₁	direct (N × H)
18. C₂²×C₃₁	C₃²×C₁₃	semidirect
21. C₃×C₃₁	A₄×C₁₃	direct (N × H)
24. C₂²×C₁₃	C₃²×C₃₁	semidirect
26. C₃×C₁₃	A₄×C₃₁	direct (N × H)
27. C₃×A₄	C₁₃×C₃₁	direct (N × H)
28. C₃₁	C₃×A₄×C₁₃	direct (N × H)
30. C₁₃	C₃×A₄×C₃₁	direct (N × H)
31. C₂²×C₃	C₃×C₁₃×C₃₁	semidirect
32. A₄	C₃×C₁₃×C₃₁	direct (N × H)
35. C₂²	C₃²×C₁₃×C₃₁	semidirect
37. C₃	A₄×C₁₃×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
A₄×C₁₃×C₃₁	3
C₂²×C₃×C₁₃×C₃₁	3
C₃²×C₁₃×C₃₁	4
C₃×A₄×C₃₁	13
C₃×A₄×C₁₃	31

Subgroups — C3×A4×C13×C31 #28408366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×A₄×C₁₃×C₃₁ #28408366