Subgroups — C₃×D₅×D₂₆₉ #30633265

Order 16140.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₂₆₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₂₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₂₆₉	—	5	1	no	maximal, Hall
7	D₁₃₄₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₂₆₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₅×C₂₆₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₂₆₉	—	5	1	no	—
11	C₃×D₂₆₉	—	5	1	no	—
12	C₃×D₂₆₉	D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₂₆₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₂₆₉	—	5	1	no	Hall
15	C₃×C₂₆₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₂₆₉	—	5	1	no	—
17	D₂₆₉	—	5	1	no	—
18	D₂₆₉	C₃×D₅	1	1	yes	characteristic, direct product factor
19	C₂₆₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×D₅	—	269	1	no	maximal, Hall
21	C₂×C₃×C₅	—	269	1	no	—
22	C₃×D₅	—	269	1	no	—
23	C₃×D₅	D₂₆₉	1	1	yes	characteristic, direct product factor
24	C₂×D₅	—	269	1	no	Hall
25	C₃×C₅	C₂×D₂₆₉	1	1	yes	characteristic, complemented, Hall
26	C₂²×C₃	—	1345	1	no	Hall
27	C₂×C₅	—	269	1	no	—
28	D₅	—	269	1	no	—
29	D₅	C₃×D₂₆₉	1	1	yes	characteristic, direct product factor
30	C₂×C₃	—	5	1	no	—
31	C₂×C₃	—	269	1	no	—
32	C₂×C₃	—	1345	1	no	—
33	C₅	C₂×C₃×D₂₆₉	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	1345	1	no	Sylow
35	C₃	D₅×D₂₆₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	5	1	no	—
37	C₂	—	269	1	no	—
38	C₂	—	1345	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₂₆₉
commutator, cosocle, hypocenter	C₅×C₂₆₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₆₉	C₂²
LCS	G ▷ C₅×C₂₆₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃₄₅	C₂	semidirect
2. C₃×D₅×C₂₆₉	C₂	semidirect
3. C₃×C₅×D₂₆₉	C₂	semidirect
4. D₅×D₂₆₉	C₃	direct (N × H)
5. C₃×C₅×C₂₆₉	C₂²	semidirect
7. D₁₃₄₅	C₂×C₃	semidirect
8. C₅×D₂₆₉	C₂×C₃	semidirect
9. D₅×C₂₆₉	C₂×C₃	semidirect
12. C₃×D₂₆₉	D₅	direct (N × H)
13. C₅×C₂₆₉	C₂²×C₃	semidirect
15. C₃×C₂₆₉	C₂×D₅	semidirect
18. D₂₆₉	C₃×D₅	direct (N × H)
19. C₂₆₉	C₂×C₃×D₅	semidirect
23. C₃×D₅	D₂₆₉	direct (N × H)
25. C₃×C₅	C₂×D₂₆₉	semidirect
29. D₅	C₃×D₂₆₉	direct (N × H)
33. C₅	C₂×C₃×D₂₆₉	semidirect
35. C₃	D₅×D₂₆₉	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×D₁₃₄₅	2
C₃×D₅×C₂₆₉	2
C₃×C₅×D₂₆₉	2
D₅×D₂₆₉	3
C₂×C₃×D₂₆₉	5
C₂×C₃×D₅	269

Subgroups — C3×D5×D269 #30633265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₂₆₉ #30633265