Subgroups — C₅×C₉×C₁₁×C₂₉ #28385155

Order 14355.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₂₉	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₁×C₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₁×C₂₉	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₅×C₉×C₂₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×C₂₉	C₃×C₅	1	1	yes	characteristic
6	C₅×C₉×C₁₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×C₂₉	C₃×C₁₁	1	1	yes	characteristic
8	C₁₁×C₂₉	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₉×C₂₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₁₁	C₃×C₂₉	1	1	yes	characteristic
11	C₅×C₂₉	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₉×C₁₁	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₂₉	C₃×C₅×C₁₁	1	1	yes	characteristic
14	C₅×C₁₁	C₉×C₂₉	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₉	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁	C₃×C₅×C₂₉	1	1	yes	characteristic
17	C₂₉	C₅×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₅	C₃×C₁₁×C₂₉	1	1	yes	characteristic
19	C₁₁	C₅×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₉	C₅×C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₉×C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₅×C₁₁×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₁₁×C₂₉
socle, prime radical	C₃×C₅×C₁₁×C₂₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₁×C₂₉	C₅	direct (N × H)
3. C₅×C₁₁×C₂₉	C₉	direct (N × H)
4. C₅×C₉×C₂₉	C₁₁	direct (N × H)
6. C₅×C₉×C₁₁	C₂₉	direct (N × H)
8. C₁₁×C₂₉	C₅×C₉	direct (N × H)
9. C₉×C₂₉	C₅×C₁₁	direct (N × H)
11. C₅×C₂₉	C₉×C₁₁	direct (N × H)
12. C₉×C₁₁	C₅×C₂₉	direct (N × H)
14. C₅×C₁₁	C₉×C₂₉	direct (N × H)
15. C₅×C₉	C₁₁×C₂₉	direct (N × H)
17. C₂₉	C₅×C₉×C₁₁	direct (N × H)
19. C₁₁	C₅×C₉×C₂₉	direct (N × H)
20. C₉	C₅×C₁₁×C₂₉	direct (N × H)
21. C₅	C₉×C₁₁×C₂₉	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×C₅×C₁₁×C₂₉	3
C₉×C₁₁×C₂₉	5
C₅×C₉×C₂₉	11
C₅×C₉×C₁₁	29

Subgroups — C5×C9×C11×C29 #28385155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₁₁×C₂₉ #28385155