Subgroups — C₂×C₃×C₅×D₅₆₉ #46802491

Order 34140.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅₆₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₅₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₅₆₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₅₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅₆₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₅₆₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₅₆₉	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅₆₉	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×D₅₆₉	C₂×C₅	1	2	yes	direct product factor
10	C₅×C₅₆₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅₆₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅₆₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₆₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
14	D₅₆₉	C₂×C₃×C₅	1	2	yes	direct product factor
15	C₅₆₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃×C₅	—	569	1	no	maximal, Hall
17	C₂×C₃×C₅	—	569	2	no	—
18	C₂×C₃×C₅	D₅₆₉	1	1	yes	characteristic, direct product factor
19	C₂²×C₅	—	569	1	no	Hall
20	C₃×C₅	C₂×D₅₆₉	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₃	—	569	1	no	Hall
22	C₂×C₅	—	569	2	no	—
23	C₂×C₅	C₃×D₅₆₉	1	1	yes	characteristic, direct product factor
24	C₂×C₃	—	569	2	no	—
25	C₂×C₃	C₅×D₅₆₉	1	1	yes	characteristic, direct product factor
26	C₅	C₂×C₃×D₅₆₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	569	1	no	Sylow
28	C₃	C₂×C₅×D₅₆₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	569	2	no	—
30	C₂	C₃×C₅×D₅₆₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₅₆₉
commutator, cosocle, hypocenter	C₅₆₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₅₆₉	C₂
LCS	G ▷ C₅₆₉
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅₆₉	C₂	direct (N × H)
2. C₂×C₃×C₅×C₅₆₉	C₂	semidirect
3. C₂×C₅×D₅₆₉	C₃	direct (N × H)
4. C₃×C₅×C₅₆₉	C₂²	semidirect
5. C₂×C₃×D₅₆₉	C₅	direct (N × H)
6. C₂×C₅×C₅₆₉	C₂×C₃	semidirect
7. C₅×D₅₆₉	C₂×C₃	direct (N × H)
8. C₂×C₃×C₅₆₉	C₂×C₅	semidirect
9. C₃×D₅₆₉	C₂×C₅	direct (N × H)
10. C₅×C₅₆₉	C₂²×C₃	semidirect
11. C₂×D₅₆₉	C₃×C₅	direct (N × H)
12. C₃×C₅₆₉	C₂²×C₅	semidirect
13. C₂×C₅₆₉	C₂×C₃×C₅	semidirect
14. D₅₆₉	C₂×C₃×C₅	direct (N × H)
15. C₅₆₉	C₂²×C₃×C₅	semidirect
18. C₂×C₃×C₅	D₅₆₉	direct (N × H)
20. C₃×C₅	C₂×D₅₆₉	direct (N × H)
23. C₂×C₅	C₃×D₅₆₉	direct (N × H)
25. C₂×C₃	C₅×D₅₆₉	direct (N × H)
26. C₅	C₂×C₃×D₅₆₉	direct (N × H)
28. C₃	C₂×C₅×D₅₆₉	direct (N × H)
30. C₂	C₃×C₅×D₅₆₉	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×C₅×D₅₆₉	2
C₂×C₃×C₅×C₅₆₉	2
C₂×C₅×D₅₆₉	3
C₂×C₃×D₅₆₉	5
C₂²×C₃×C₅	569

Subgroups — C2×C3×C5×D569 #46802491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×D₅₆₉ #46802491