Subgroups — C₂³×C₃×C₅×C₂₆₉ #72209010

Order 32280.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₂₆₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂³×C₃×C₂₆₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂²×C₃×C₅×C₂₆₉	C₂	1	7	yes	maximal, direct product factor
4	C₂×C₃×C₅×C₂₆₉	C₂²	1	7	yes	direct product factor
5	C₂²×C₅×C₂₆₉	C₂×C₃	1	7	yes	direct product factor
6	C₃×C₅×C₂₆₉	C₂³	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₃×C₂₆₉	C₂×C₅	1	7	yes	direct product factor
8	C₂×C₅×C₂₆₉	C₂²×C₃	1	7	yes	direct product factor
9	C₂³×C₂₆₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₂₆₉	C₂²×C₅	1	7	yes	direct product factor
11	C₅×C₂₆₉	C₂³×C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₂₆₉	C₂×C₃×C₅	1	7	yes	direct product factor
13	C₃×C₂₆₉	C₂³×C₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₂₆₉	C₂²×C₃×C₅	1	7	yes	direct product factor
15	C₂₆₉	C₂³×C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂³×C₃×C₅	C₂₆₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅	C₂×C₂₆₉	1	7	yes	direct product factor
18	C₂³×C₅	C₃×C₂₆₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₅	C₂²×C₂₆₉	1	7	yes	direct product factor
20	C₂³×C₃	C₅×C₂₆₉	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₅	C₂×C₃×C₂₆₉	1	7	yes	direct product factor
22	C₃×C₅	C₂³×C₂₆₉	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₃	C₂×C₅×C₂₆₉	1	7	yes	direct product factor
24	C₂×C₅	C₂²×C₃×C₂₆₉	1	7	yes	direct product factor
25	C₂³	C₃×C₅×C₂₆₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₃	C₂²×C₅×C₂₆₉	1	7	yes	direct product factor
27	C₅	C₂³×C₃×C₂₆₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	C₂×C₃×C₅×C₂₆₉	1	7	yes	direct product factor
29	C₃	C₂³×C₅×C₂₆₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₂²×C₃×C₅×C₂₆₉	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×C₂₆₉	C₃	direct (N × H)
2. C₂³×C₃×C₂₆₉	C₅	direct (N × H)
3. C₂²×C₃×C₅×C₂₆₉	C₂	direct (N × H)
4. C₂×C₃×C₅×C₂₆₉	C₂²	direct (N × H)
5. C₂²×C₅×C₂₆₉	C₂×C₃	direct (N × H)
6. C₃×C₅×C₂₆₉	C₂³	direct (N × H)
7. C₂²×C₃×C₂₆₉	C₂×C₅	direct (N × H)
8. C₂×C₅×C₂₆₉	C₂²×C₃	direct (N × H)
9. C₂³×C₂₆₉	C₃×C₅	direct (N × H)
10. C₂×C₃×C₂₆₉	C₂²×C₅	direct (N × H)
11. C₅×C₂₆₉	C₂³×C₃	direct (N × H)
12. C₂²×C₂₆₉	C₂×C₃×C₅	direct (N × H)
13. C₃×C₂₆₉	C₂³×C₅	direct (N × H)
14. C₂×C₂₆₉	C₂²×C₃×C₅	direct (N × H)
15. C₂₆₉	C₂³×C₃×C₅	direct (N × H)
16. C₂³×C₃×C₅	C₂₆₉	direct (N × H)
17. C₂²×C₃×C₅	C₂×C₂₆₉	direct (N × H)
18. C₂³×C₅	C₃×C₂₆₉	direct (N × H)
19. C₂×C₃×C₅	C₂²×C₂₆₉	direct (N × H)
20. C₂³×C₃	C₅×C₂₆₉	direct (N × H)
21. C₂²×C₅	C₂×C₃×C₂₆₉	direct (N × H)
22. C₃×C₅	C₂³×C₂₆₉	direct (N × H)
23. C₂²×C₃	C₂×C₅×C₂₆₉	direct (N × H)
24. C₂×C₅	C₂²×C₃×C₂₆₉	direct (N × H)
25. C₂³	C₃×C₅×C₂₆₉	direct (N × H)
26. C₂×C₃	C₂²×C₅×C₂₆₉	direct (N × H)
27. C₅	C₂³×C₃×C₂₆₉	direct (N × H)
28. C₂²	C₂×C₃×C₅×C₂₆₉	direct (N × H)
29. C₃	C₂³×C₅×C₂₆₉	direct (N × H)
30. C₂	C₂²×C₃×C₅×C₂₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×C₂₆₉	3
C₂³×C₃×C₂₆₉	5
C₂²×C₃×C₅×C₂₆₉	2
C₂³×C₃×C₅	269

Subgroups — C23×C3×C5×C269 #72209010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₅×C₂₆₉ #72209010