Subgroups — C₅×C₄₃×C₂²⋊(C₁₃⋊C₃) #46776595

Order 33540.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₃×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₃⋊C₃×C₄₃	—	4	1	no	maximal, Hall
3	C₄₃×C₂²⋊(C₁₃⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₁₃×C₄₃	—	3	1	no	—
5	C₅×C₁₃×C₄₃	A₄	1	1	yes	characteristic, complemented, Hall
6	C₅×A₄×C₄₃	—	13	1	no	maximal, Hall
7	C₂²×C₁₃×C₄₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₁₃⋊C₃×C₄₃	—	4	1	no	Hall
9	C₂×C₁₃×C₄₃	—	3	1	no	—
10	C₂²×C₅×C₄₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂²⋊(C₁₃⋊C₃)	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₅×C₄₃	—	52	1	no	Hall
13	C₁₃×C₄₃	C₅×A₄	1	1	yes	characteristic, complemented, Hall
14	A₄×C₄₃	—	13	1	no	Hall
15	C₂×C₅×C₄₃	—	3	1	no	—
16	C₂²×C₅×C₁₃	C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
17	C₅×C₄₃	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₁₃⋊C₃	—	4	1	no	Hall
19	C₂²×C₄₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂²⋊(C₁₃⋊C₃)	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₁₃	—	3	1	no	—
22	C₃×C₄₃	—	52	1	no	Hall
23	C₂×C₄₃	—	3	1	no	—
24	C₅×C₁₃	A₄×C₄₃	1	1	yes	characteristic, complemented, Hall
25	C₅×A₄	—	13	1	no	Hall
26	C₂²×C₁₃	C₃×C₅×C₄₃	1	1	yes	characteristic, complemented, Hall
27	C₄₃	C₅×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
28	C₁₃⋊C₃	—	4	1	no	Hall
29	C₂×C₁₃	—	3	1	no	—
30	C₂²×C₅	C₁₃⋊C₃×C₄₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅	—	52	1	no	Hall
32	C₁₃	C₅×A₄×C₄₃	1	1	yes	characteristic, complemented, Sylow
33	A₄	—	13	1	no	Hall
34	C₂×C₅	—	3	1	no	—
35	C₅	C₄₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₅×C₁₃⋊C₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	52	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₄₃	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₃×C₅×C₄₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃×C₄₃	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₅×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₃×C₄₃	C₃	semidirect
3. C₄₃×C₂²⋊(C₁₃⋊C₃)	C₅	direct (N × H)
5. C₅×C₁₃×C₄₃	A₄	semidirect
7. C₂²×C₁₃×C₄₃	C₃×C₅	semidirect
10. C₂²×C₅×C₄₃	C₁₃⋊C₃	semidirect
11. C₅×C₂²⋊(C₁₃⋊C₃)	C₄₃	direct (N × H)
13. C₁₃×C₄₃	C₅×A₄	semidirect
16. C₂²×C₅×C₁₃	C₃×C₄₃	semidirect
17. C₅×C₄₃	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
19. C₂²×C₄₃	C₅×C₁₃⋊C₃	semidirect
20. C₂²⋊(C₁₃⋊C₃)	C₅×C₄₃	direct (N × H)
24. C₅×C₁₃	A₄×C₄₃	semidirect
26. C₂²×C₁₃	C₃×C₅×C₄₃	semidirect
27. C₄₃	C₅×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
30. C₂²×C₅	C₁₃⋊C₃×C₄₃	semidirect
32. C₁₃	C₅×A₄×C₄₃	semidirect
35. C₅	C₄₃×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
36. C₂²	C₅×C₁₃⋊C₃×C₄₃	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×C₄₃	3
C₅×C₁₃⋊C₃×C₄₃	4
C₄₃×C₂²⋊(C₁₃⋊C₃)	5
C₅×A₄×C₄₃	13
C₅×C₂²⋊(C₁₃⋊C₃)	43

Subgroups — C5×C43×C22⋊(C13⋊C3) #46776595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄₃×C₂²⋊(C₁₃⋊C₃) #46776595