Subgroups — C₅×C₉×Dic₂₉ #19104792

Order 5220.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×Dic₂₉	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×Dic₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₂₉	C₂×C₃	1	1	yes	characteristic
6	C₅×Dic₂₉	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₂₉	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₂₉	C₃×C₄	1	1	yes	characteristic
9	C₃×Dic₂₉	C₃×C₅	1	1	yes	characteristic
10	C₂×C₅×C₂₉	C₂×C₉	1	1	yes	characteristic
11	C₉×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₄×C₅×C₉	—	29	1	no	maximal, Hall
13	C₂×C₃×C₂₉	C₂×C₃×C₅	1	1	yes	characteristic
14	C₅×C₂₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	Dic₂₉	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅×C₉	D₂₉	1	1	yes	characteristic
17	C₃×C₂₉	C₃×C₄×C₅	1	1	yes	characteristic
18	C₃×C₄×C₅	—	29	1	no	—
19	C₂×C₂₉	C₂×C₅×C₉	1	1	yes	characteristic
20	C₅×C₉	Dic₂₉	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₉	—	29	1	no	Hall
22	C₂×C₃×C₅	C₃×D₂₉	1	1	yes	characteristic
23	C₂₉	C₄×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
24	C₄×C₅	—	29	1	no	Hall
25	C₂×C₉	C₅×D₂₉	1	1	yes	characteristic
26	C₃×C₅	C₃×Dic₂₉	1	1	yes	characteristic
27	C₃×C₄	—	29	1	no	—
28	C₂×C₅	C₉×D₂₉	1	1	yes	characteristic
29	C₉	C₅×Dic₂₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₃×C₅×D₂₉	1	1	yes	characteristic
31	C₅	C₉×Dic₂₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₄	—	29	1	no	Sylow
33	C₃	C₃×C₅×Dic₂₉	1	1	yes	characteristic
34	C₂	C₅×C₉×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉	D₂₉
commutator, hypocenter	C₂₉	C₄×C₅×C₉
Frattini	C₂×C₃	C₃×C₅×D₂₉
Fitting	C₂×C₅×C₉×C₂₉	C₂
socle	C₂×C₃×C₅×C₂₉	C₂×C₃
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₅×C₉

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₂₉	C₄	semidirect
4. C₉×Dic₂₉	C₅	direct (N × H)
6. C₅×Dic₂₉	C₉	direct (N × H)
11. C₉×C₂₉	C₄×C₅	semidirect
14. C₅×C₂₉	C₄×C₉	semidirect
15. Dic₂₉	C₅×C₉	direct (N × H)
20. C₅×C₉	Dic₂₉	direct (N × H)
23. C₂₉	C₄×C₅×C₉	semidirect
29. C₉	C₅×Dic₂₉	direct (N × H)
31. C₅	C₉×Dic₂₉	direct (N × H)

Subgroups — C5×C9×Dic29 #19104792

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₉×Dic₂₉ #19104792