Subgroups — C₅×D₃×D₂₆₉ #30633267

Order 16140.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₈₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₂₆₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₂₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₂₆₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₂₆₉	—	3	1	no	—
8	C₅×D₂₆₉	—	3	1	no	—
9	C₅×D₂₆₉	D₃	1	1	yes	characteristic, direct product factor
10	D₈₀₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×D₂₆₉	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₂₆₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₂₆₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₂₆₉	—	3	1	no	Hall
15	C₃×C₂₆₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₂₆₉	—	3	1	no	—
17	D₂₆₉	—	3	1	no	—
18	D₂₆₉	C₅×D₃	1	1	yes	characteristic, direct product factor
19	C₂₆₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅×D₃	—	269	1	no	maximal, Hall
21	C₂×C₃×C₅	—	269	1	no	—
22	C₅×D₃	—	269	1	no	—
23	C₅×D₃	D₂₆₉	1	1	yes	characteristic, direct product factor
24	C₂²×C₅	—	807	1	no	Hall
25	C₃×C₅	C₂×D₂₆₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃	—	269	1	no	Hall
27	C₂×C₅	—	3	1	no	—
28	C₂×C₅	—	269	1	no	—
29	C₂×C₅	—	807	1	no	—
30	C₂×C₃	—	269	1	no	—
31	D₃	—	269	1	no	—
32	D₃	C₅×D₂₆₉	1	1	yes	characteristic, direct product factor
33	C₅	D₃×D₂₆₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	807	1	no	Sylow
35	C₃	C₂×C₅×D₂₆₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	269	1	no	—
38	C₂	—	807	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃×D₂₆₉
commutator, cosocle, hypocenter	C₃×C₂₆₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₆₉	C₂²
LCS	G ▷ C₃×C₂₆₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₈₀₇	C₂	semidirect
2. C₅×D₃×C₂₆₉	C₂	semidirect
3. C₃×C₅×D₂₆₉	C₂	semidirect
5. C₃×C₅×C₂₆₉	C₂²	semidirect
6. D₃×D₂₆₉	C₅	direct (N × H)
9. C₅×D₂₆₉	D₃	direct (N × H)
10. D₈₀₇	C₂×C₅	semidirect
11. C₃×D₂₆₉	C₂×C₅	semidirect
12. D₃×C₂₆₉	C₂×C₅	semidirect
13. C₅×C₂₆₉	C₂×D₃	semidirect
15. C₃×C₂₆₉	C₂²×C₅	semidirect
18. D₂₆₉	C₅×D₃	direct (N × H)
19. C₂₆₉	C₂×C₅×D₃	semidirect
23. C₅×D₃	D₂₆₉	direct (N × H)
25. C₃×C₅	C₂×D₂₆₉	semidirect
32. D₃	C₅×D₂₆₉	direct (N × H)
33. C₅	D₃×D₂₆₉	direct (N × H)
35. C₃	C₂×C₅×D₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₈₀₇	2
C₅×D₃×C₂₆₉	2
C₃×C₅×D₂₆₉	2
C₂×C₅×D₂₆₉	3
D₃×D₂₆₉	5
C₂×C₅×D₃	269

Subgroups — C5×D3×D269 #30633267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₂₆₉ #30633267