Subgroups — C₃×C₁₁×Dic₅×C₂₉ #34062313

Order 19140.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₅×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₁×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄×C₁₁×C₂₉	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₁×C₂₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₂₉	D₅	1	1	yes	characteristic
7	C₃×Dic₅×C₂₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₄×C₁₁×C₂₉	—	5	1	no	Hall
10	C₃×C₁₁×C₂₉	Dic₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₅×C₂₉	C₂×C₁₁	1	1	yes	characteristic
12	C₃×C₁₁×Dic₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₁×C₂₉	C₃×D₅	1	1	yes	characteristic
14	Dic₅×C₂₉	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₂₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄×C₂₉	—	5	1	no	Hall
17	C₂×C₃×C₅×C₁₁	C₂×C₂₉	1	1	yes	characteristic
18	C₁₁×C₂₉	C₃×Dic₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅×C₂₉	C₂×C₃×C₁₁	1	1	yes	characteristic
20	C₁₁×Dic₅	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₂₉	D₅×C₁₁	1	1	yes	characteristic
22	C₃×C₅×C₁₁	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
23	C₅×C₂₉	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₄×C₁₁	—	5	1	no	Hall
25	C₄×C₂₉	—	5	1	no	Hall
26	C₂×C₅×C₁₁	C₂×C₃×C₂₉	1	1	yes	characteristic
27	C₃×C₂₉	C₁₁×Dic₅	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₁₁	D₅×C₂₉	1	1	yes	characteristic
29	C₃×Dic₅	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₂₉	C₃×D₅×C₁₁	1	1	yes	characteristic
31	C₅×C₁₁	C₃×C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
32	C₄×C₁₁	—	5	1	no	Hall
33	C₃×C₁₁	Dic₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₅	C₂×C₁₁×C₂₉	1	1	yes	characteristic
35	C₂₉	C₃×C₁₁×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₁₁	C₃×D₅×C₂₉	1	1	yes	characteristic
37	Dic₅	C₃×C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	C₄×C₁₁×C₂₉	1	1	yes	characteristic, complemented, Hall
39	C₃×C₄	—	5	1	no	Hall
40	C₁₁	C₃×Dic₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	C₂×C₃×C₁₁×C₂₉	1	1	yes	characteristic
42	C₂×C₃	D₅×C₁₁×C₂₉	1	1	yes	characteristic
43	C₅	C₃×C₄×C₁₁×C₂₉	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	5	1	no	Sylow
45	C₃	C₁₁×Dic₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×D₅×C₁₁×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁×C₂₉	D₅
commutator, hypocenter	C₅	C₃×C₄×C₁₁×C₂₉
Frattini	C₂	C₃×D₅×C₁₁×C₂₉
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁×C₂₉	C₂
cosocle	C₂×C₅	C₂×C₃×C₁₁×C₂₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₁₁×C₂₉

Complements

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

N	H ≅ G/N	type
2. C₁₁×Dic₅×C₂₉	C₃	direct (N × H)
3. C₃×C₅×C₁₁×C₂₉	C₄	semidirect
7. C₃×Dic₅×C₂₉	C₁₁	direct (N × H)
8. C₅×C₁₁×C₂₉	C₃×C₄	semidirect
10. C₃×C₁₁×C₂₉	Dic₅	direct (N × H)
12. C₃×C₁₁×Dic₅	C₂₉	direct (N × H)
14. Dic₅×C₂₉	C₃×C₁₁	direct (N × H)
15. C₃×C₅×C₂₉	C₄×C₁₁	semidirect
18. C₁₁×C₂₉	C₃×Dic₅	direct (N × H)
20. C₁₁×Dic₅	C₃×C₂₉	direct (N × H)
22. C₃×C₅×C₁₁	C₄×C₂₉	semidirect
23. C₅×C₂₉	C₃×C₄×C₁₁	semidirect
27. C₃×C₂₉	C₁₁×Dic₅	direct (N × H)
29. C₃×Dic₅	C₁₁×C₂₉	direct (N × H)
31. C₅×C₁₁	C₃×C₄×C₂₉	semidirect
33. C₃×C₁₁	Dic₅×C₂₉	direct (N × H)
35. C₂₉	C₃×C₁₁×Dic₅	direct (N × H)
37. Dic₅	C₃×C₁₁×C₂₉	direct (N × H)
38. C₃×C₅	C₄×C₁₁×C₂₉	semidirect
40. C₁₁	C₃×Dic₅×C₂₉	direct (N × H)
43. C₅	C₃×C₄×C₁₁×C₂₉	semidirect
45. C₃	C₁₁×Dic₅×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
C₂×C₃×C₅×C₁₁×C₂₉	2
C₁₁×Dic₅×C₂₉	3
C₃×C₄×C₁₁×C₂₉	5
C₃×Dic₅×C₂₉	11
C₃×C₁₁×Dic₅	29

Subgroups — C3×C11×Dic5×C29 #34062313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×Dic₅×C₂₉ #34062313