Subgroups — C₅×A₄×C₁₃×C₄₁ #44544483

Order 31980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₃×C₄₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₃×C₄₁	—	4	1	no	maximal, Hall
3	A₄×C₁₃×C₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₁₃×C₄₁	—	3	1	no	—
5	C₅×C₁₃×C₄₁	A₄	1	1	yes	characteristic, direct product factor, Hall
6	C₅×A₄×C₄₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₁₃×C₄₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₄₁	—	4	1	no	Hall
9	C₂×C₁₃×C₄₁	—	3	1	no	—
10	C₂²×C₅×C₄₁	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₅×A₄×C₁₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₅×C₄₁	—	4	1	no	Hall
13	C₁₃×C₄₁	C₅×A₄	1	1	yes	characteristic, direct product factor, Hall
14	A₄×C₄₁	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅×C₄₁	—	3	1	no	—
16	C₂²×C₅×C₁₃	C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
17	C₅×C₄₁	A₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₅×C₁₃	—	4	1	no	Hall
19	C₂²×C₄₁	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
20	A₄×C₁₃	C₅×C₄₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₁₃	—	3	1	no	—
22	C₃×C₄₁	—	4	1	no	Hall
23	C₂×C₄₁	—	3	1	no	—
24	C₅×C₁₃	A₄×C₄₁	1	1	yes	characteristic, direct product factor, Hall
25	C₅×A₄	C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₁₃	C₃×C₅×C₄₁	1	1	yes	characteristic, complemented, Hall
27	C₄₁	C₅×A₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₃×C₁₃	—	4	1	no	Hall
29	C₂×C₁₃	—	3	1	no	—
30	C₂²×C₅	C₃×C₁₃×C₄₁	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅	—	4	1	no	Hall
32	C₁₃	C₅×A₄×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
33	A₄	C₅×C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₅	—	3	1	no	—
35	C₅	A₄×C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₃×C₅×C₁₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	4	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₃×C₄₁	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅×C₁₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃×C₄₁	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₁₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₃×C₄₁	C₃	semidirect
3. A₄×C₁₃×C₄₁	C₅	direct (N × H)
5. C₅×C₁₃×C₄₁	A₄	direct (N × H)
6. C₅×A₄×C₄₁	C₁₃	direct (N × H)
7. C₂²×C₁₃×C₄₁	C₃×C₅	semidirect
10. C₂²×C₅×C₄₁	C₃×C₁₃	semidirect
11. C₅×A₄×C₁₃	C₄₁	direct (N × H)
13. C₁₃×C₄₁	C₅×A₄	direct (N × H)
14. A₄×C₄₁	C₅×C₁₃	direct (N × H)
16. C₂²×C₅×C₁₃	C₃×C₄₁	semidirect
17. C₅×C₄₁	A₄×C₁₃	direct (N × H)
19. C₂²×C₄₁	C₃×C₅×C₁₃	semidirect
20. A₄×C₁₃	C₅×C₄₁	direct (N × H)
24. C₅×C₁₃	A₄×C₄₁	direct (N × H)
25. C₅×A₄	C₁₃×C₄₁	direct (N × H)
26. C₂²×C₁₃	C₃×C₅×C₄₁	semidirect
27. C₄₁	C₅×A₄×C₁₃	direct (N × H)
30. C₂²×C₅	C₃×C₁₃×C₄₁	semidirect
32. C₁₃	C₅×A₄×C₄₁	direct (N × H)
33. A₄	C₅×C₁₃×C₄₁	direct (N × H)
35. C₅	A₄×C₁₃×C₄₁	direct (N × H)
36. C₂²	C₃×C₅×C₁₃×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₁₃×C₄₁	3
C₃×C₅×C₁₃×C₄₁	4
A₄×C₁₃×C₄₁	5
C₅×A₄×C₄₁	13
C₅×A₄×C₁₃	41

Subgroups — C5×A4×C13×C41 #44544483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×A₄×C₁₃×C₄₁ #44544483