Subgroups — C₂×C₅×D₃×C₁₁ #10620366

Order 660.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₁₁	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₅×C₁₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁	—	3	2	no	—
7	C₂×C₅×C₁₁	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₃×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
9	D₃×C₁₁	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₅×D₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₁₁	—	3	1	no	Hall
13	C₃×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₅×D₃	C₂×C₁₁	1	2	yes	direct product factor
16	C₂×C₁₁	—	3	2	no	—
17	C₂×C₁₁	C₅×D₃	1	1	yes	characteristic, direct product factor
18	C₂²×C₅	—	3	1	no	Hall
19	C₃×C₅	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₁₁	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₅	—	3	2	no	—
23	C₂×C₅	D₃×C₁₁	1	1	yes	characteristic, direct product factor
24	C₂×C₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
25	D₃	C₂×C₅×C₁₁	1	2	yes	direct product factor
26	C₅	C₂×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	C₅×D₃×C₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₁₁	C₂	semidirect
2. C₅×D₃×C₁₁	C₂	direct (N × H)
4. C₃×C₅×C₁₁	C₂²	semidirect
5. C₂×D₃×C₁₁	C₅	direct (N × H)
7. C₂×C₅×C₁₁	D₃	direct (N × H)
8. C₂×C₃×C₁₁	C₂×C₅	semidirect
9. D₃×C₁₁	C₂×C₅	direct (N × H)
10. C₂×C₅×D₃	C₁₁	direct (N × H)
11. C₅×C₁₁	C₂×D₃	direct (N × H)
13. C₃×C₁₁	C₂²×C₅	semidirect
14. C₂×C₃×C₅	C₂×C₁₁	semidirect
15. C₅×D₃	C₂×C₁₁	direct (N × H)
17. C₂×C₁₁	C₅×D₃	direct (N × H)
19. C₃×C₅	C₂²×C₁₁	semidirect
20. C₂×D₃	C₅×C₁₁	direct (N × H)
21. C₁₁	C₂×C₅×D₃	direct (N × H)
23. C₂×C₅	D₃×C₁₁	direct (N × H)
24. C₂×C₃	C₂×C₅×C₁₁	semidirect
25. D₃	C₂×C₅×C₁₁	direct (N × H)
26. C₅	C₂×D₃×C₁₁	direct (N × H)
28. C₃	C₂²×C₅×C₁₁	semidirect
30. C₂	C₅×D₃×C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₁	2
C₅×D₃×C₁₁	2
C₂²×C₅×C₁₁	3
C₂×D₃×C₁₁	5
C₂×C₅×D₃	11

Subgroups — C2×C5×D3×C11 #10620366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₁₁ #10620366