Subgroups — C₃×C₇×C₁₃×D₄₃ #37553431

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₃×D₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×D₄₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×D₄₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₁₃×D₄₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇×C₄₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₇×D₄₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₁₃×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇×C₁₃	—	43	1	no	maximal, Hall
12	C₇×C₄₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×C₁₃	D₄₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×D₄₃	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₇×C₁₃	—	43	1	no	Hall
16	C₃×C₄₃	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₃	C₃×D₄₃	1	1	yes	characteristic, direct product factor, Hall
18	D₄₃	C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₁₃	—	43	1	no	Hall
20	C₄₃	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₇	—	43	1	no	Hall
22	C₃×C₁₃	C₇×D₄₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₃	—	43	1	no	Hall
24	C₃×C₇	C₁₃×D₄₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	—	43	1	no	Hall
26	C₁₃	C₃×C₇×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₃×C₁₃×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	43	1	no	Hall
29	C₃	C₇×C₁₃×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₃	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₄₃	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×C₄₃	C₂	semidirect
2. C₇×C₁₃×D₄₃	C₃	direct (N × H)
3. C₇×C₁₃×C₄₃	C₂×C₃	semidirect
4. C₃×C₁₃×D₄₃	C₇	direct (N × H)
5. C₃×C₇×D₄₃	C₁₃	direct (N × H)
6. C₃×C₁₃×C₄₃	C₂×C₇	semidirect
7. C₁₃×D₄₃	C₃×C₇	direct (N × H)
8. C₃×C₇×C₄₃	C₂×C₁₃	semidirect
9. C₇×D₄₃	C₃×C₁₃	direct (N × H)
10. C₁₃×C₄₃	C₂×C₃×C₇	semidirect
12. C₇×C₄₃	C₂×C₃×C₁₃	semidirect
13. C₃×C₇×C₁₃	D₄₃	direct (N × H)
14. C₃×D₄₃	C₇×C₁₃	direct (N × H)
16. C₃×C₄₃	C₂×C₇×C₁₃	semidirect
17. C₇×C₁₃	C₃×D₄₃	direct (N × H)
18. D₄₃	C₃×C₇×C₁₃	direct (N × H)
20. C₄₃	C₂×C₃×C₇×C₁₃	semidirect
22. C₃×C₁₃	C₇×D₄₃	direct (N × H)
24. C₃×C₇	C₁₃×D₄₃	direct (N × H)
26. C₁₃	C₃×C₇×D₄₃	direct (N × H)
27. C₇	C₃×C₁₃×D₄₃	direct (N × H)
29. C₃	C₇×C₁₃×D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×C₄₃	2
C₇×C₁₃×D₄₃	3
C₃×C₁₃×D₄₃	7
C₃×C₇×D₄₃	13
C₂×C₃×C₇×C₁₃	43

Subgroups — C3×C7×C13×D43 #37553431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₃×D₄₃ #37553431