Subgroups — C₃×C₇×C₁₃×C₄₃⋊C₃ #47976261

Order 35217.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₄₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₇×C₁₃×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×C₄₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₃×C₄₃	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₄₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented
7	C₁₃×C₄₃⋊C₃	C₃×C₇	1	3	yes	direct product factor
8	C₃×C₇×C₄₃	C₃×C₁₃	1	1	yes	characteristic, complemented
9	C₇×C₄₃⋊C₃	C₃×C₁₃	1	3	yes	direct product factor
10	C₃²×C₇×C₁₃	—	43	1	no	maximal, Hall
11	C₁₃×C₄₃	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄₃⋊C₃	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₄₃	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₇×C₁₃	—	43	3	no	—
15	C₃×C₇×C₁₃	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
16	C₃×C₄₃	C₃×C₇×C₁₃	1	1	yes	characteristic, complemented
17	C₄₃⋊C₃	C₃×C₇×C₁₃	1	3	yes	direct product factor
18	C₃²×C₁₃	—	43	1	no	Hall
19	C₇×C₁₃	C₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃²×C₇	—	43	1	no	Hall
21	C₄₃	C₃²×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₃	—	43	3	no	—
23	C₃×C₁₃	C₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
24	C₃×C₇	—	43	3	no	—
25	C₃×C₇	C₁₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
26	C₁₃	C₃×C₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₃²	—	43	1	no	Sylow
28	C₇	C₃×C₁₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	43	3	no	—
30	C₃	C₇×C₁₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₃	C₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₃²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₄₃	C₃
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. C₇×C₁₃×C₄₃⋊C₃	C₃	direct (N × H)
2. C₃×C₇×C₁₃×C₄₃	C₃	semidirect
3. C₃×C₁₃×C₄₃⋊C₃	C₇	direct (N × H)
4. C₇×C₁₃×C₄₃	C₃²	semidirect
5. C₃×C₇×C₄₃⋊C₃	C₁₃	direct (N × H)
6. C₃×C₁₃×C₄₃	C₃×C₇	semidirect
7. C₁₃×C₄₃⋊C₃	C₃×C₇	direct (N × H)
8. C₃×C₇×C₄₃	C₃×C₁₃	semidirect
9. C₇×C₄₃⋊C₃	C₃×C₁₃	direct (N × H)
11. C₁₃×C₄₃	C₃²×C₇	semidirect
12. C₃×C₄₃⋊C₃	C₇×C₁₃	direct (N × H)
13. C₇×C₄₃	C₃²×C₁₃	semidirect
15. C₃×C₇×C₁₃	C₄₃⋊C₃	direct (N × H)
16. C₃×C₄₃	C₃×C₇×C₁₃	semidirect
17. C₄₃⋊C₃	C₃×C₇×C₁₃	direct (N × H)
19. C₇×C₁₃	C₃×C₄₃⋊C₃	direct (N × H)
21. C₄₃	C₃²×C₇×C₁₃	semidirect
23. C₃×C₁₃	C₇×C₄₃⋊C₃	direct (N × H)
25. C₃×C₇	C₁₃×C₄₃⋊C₃	direct (N × H)
26. C₁₃	C₃×C₇×C₄₃⋊C₃	direct (N × H)
28. C₇	C₃×C₁₃×C₄₃⋊C₃	direct (N × H)
30. C₃	C₇×C₁₃×C₄₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₃×C₄₃⋊C₃	3
C₃×C₇×C₁₃×C₄₃	3
C₃×C₁₃×C₄₃⋊C₃	7
C₃×C₇×C₄₃⋊C₃	13
C₃²×C₇×C₁₃	43

Subgroups — C3×C7×C13×C43⋊C3 #47976261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₃×C₄₃⋊C₃ #47976261