Subgroups — C₂×C₅²×C₁₃⋊C₉ #19154331

Order 5850.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₁₃⋊C₉	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₁₃	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅×C₁₃⋊C₉	C₂×C₅	1	6	yes	direct product factor
7	C₂×C₅²×C₉	—	13	1	no	maximal, Hall
8	C₂×C₃×C₅×C₁₃	C₃×C₅	1	6	yes	—
9	C₅²×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃⋊C₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅²×C₉	—	13	1	no	Hall
12	C₃×C₅×C₁₃	C₂×C₃×C₅	1	6	yes	—
13	C₂×C₃×C₅²	C₁₃⋊C₃	1	1	yes	characteristic
14	C₂×C₅×C₁₃	C₅×C₉	1	6	yes	complemented
15	C₁₃⋊C₉	C₂×C₅²	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅×C₉	—	13	6	no	—
17	C₂×C₃×C₁₃	C₃×C₅²	1	1	yes	characteristic
18	C₃×C₅²	C₂×C₁₃⋊C₃	1	1	yes	characteristic
19	C₅×C₁₃	C₂×C₅×C₉	1	6	yes	complemented
20	C₂×C₅²	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
21	C₅×C₉	—	13	6	no	—
22	C₃×C₁₃	C₂×C₃×C₅²	1	1	yes	characteristic
23	C₂×C₃×C₅	C₅×C₁₃⋊C₃	1	6	yes	—
24	C₂×C₁₃	C₅²×C₉	1	1	yes	characteristic, complemented, Hall
25	C₅²	C₂×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₉	—	13	1	no	Hall
27	C₃×C₅	C₂×C₅×C₁₃⋊C₃	1	6	yes	—
28	C₁₃	C₂×C₅²×C₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅	C₅×C₁₃⋊C₉	1	6	yes	direct product factor
30	C₉	—	13	1	no	Sylow
31	C₂×C₃	C₅²×C₁₃⋊C₃	1	1	yes	characteristic
32	C₅	C₂×C₅×C₁₃⋊C₉	1	6	yes	direct product factor
33	C₃	C₂×C₅²×C₁₃⋊C₃	1	1	yes	characteristic
34	C₂	C₅²×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₅²×C₉
Frattini	C₃	C₂×C₅²×C₁₃⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₃⋊C₉	C₂	direct (N × H)
3. C₂×C₅×C₁₃⋊C₉	C₅	direct (N × H)
5. C₂×C₅²×C₁₃	C₉	semidirect
6. C₅×C₁₃⋊C₉	C₂×C₅	direct (N × H)
9. C₅²×C₁₃	C₂×C₉	semidirect
10. C₂×C₁₃⋊C₉	C₅²	direct (N × H)
14. C₂×C₅×C₁₃	C₅×C₉	semidirect
15. C₁₃⋊C₉	C₂×C₅²	direct (N × H)
19. C₅×C₁₃	C₂×C₅×C₉	semidirect
20. C₂×C₅²	C₁₃⋊C₉	direct (N × H)
24. C₂×C₁₃	C₅²×C₉	semidirect
25. C₅²	C₂×C₁₃⋊C₉	direct (N × H)
28. C₁₃	C₂×C₅²×C₉	semidirect
29. C₂×C₅	C₅×C₁₃⋊C₉	direct (N × H)
32. C₅	C₂×C₅×C₁₃⋊C₉	direct (N × H)
34. C₂	C₅²×C₁₃⋊C₉	direct (N × H)

Subgroups — C2×C52×C13⋊C9 #19154331

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅²×C₁₃⋊C₉ #19154331