Subgroups — C₃×D₁₃×C₄₃⋊C₃ #23758477

Order 10062.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₄₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₃×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃×C₄₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	D₁₃×C₄₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₄₃⋊C₃	—	13	1	no	maximal, Hall
8	C₁₃×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₄₃⋊C₃	D₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₄₃	—	13	1	no	—
11	C₂×C₄₃⋊C₃	—	13	3	no	—
12	C₃²×D₁₃	—	43	1	no	maximal, Hall
13	C₃×C₄₃	C₃×D₁₃	1	1	yes	characteristic, complemented
14	C₄₃⋊C₃	C₃×D₁₃	1	3	yes	direct product factor
15	C₃²×C₁₃	—	43	1	no	Hall
16	C₂×C₄₃	—	13	1	no	Hall
17	C₃×D₁₃	—	43	3	no	—
18	C₃×D₁₃	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
19	C₄₃	C₃²×D₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₁₃	—	43	3	no	—
21	C₃×C₁₃	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
22	D₁₃	C₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃²	—	559	1	no	Hall
24	C₁₃	C₂×C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	43	1	no	Sylow
26	C₂×C₃	—	13	1	no	—
27	C₂×C₃	—	559	3	no	—
28	C₃	—	43	3	no	—
29	C₃	D₁₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₃×C₄₃⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₄₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₁₃×C₄₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₄₃⋊C₃	C₂	semidirect
2. D₁₃×C₄₃⋊C₃	C₃	direct (N × H)
3. C₃×D₁₃×C₄₃	C₃	semidirect
4. C₃×C₁₃×C₄₃	C₂×C₃	semidirect
5. C₁₃×C₄₃⋊C₃	C₂×C₃	semidirect
6. D₁₃×C₄₃	C₃²	semidirect
8. C₁₃×C₄₃	C₂×C₃²	semidirect
9. C₃×C₄₃⋊C₃	D₁₃	direct (N × H)
13. C₃×C₄₃	C₃×D₁₃	semidirect
14. C₄₃⋊C₃	C₃×D₁₃	direct (N × H)
18. C₃×D₁₃	C₄₃⋊C₃	direct (N × H)
19. C₄₃	C₃²×D₁₃	semidirect
21. C₃×C₁₃	C₂×C₄₃⋊C₃	semidirect
22. D₁₃	C₃×C₄₃⋊C₃	direct (N × H)
24. C₁₃	C₂×C₃×C₄₃⋊C₃	semidirect
29. C₃	D₁₃×C₄₃⋊C₃	direct (N × H)

Subgroups — C3×D13×C43⋊C3 #23758477

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₃×C₄₃⋊C₃ #23758477