Subgroups — C₂×C₅×C₁₁×C₁₁⋊C₅ #20258451

Order 6050.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₁²	C₅	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×C₁₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
4	C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
5	C₁₁×C₁₁⋊C₅	C₂×C₅	1	5	yes	direct product factor
6	C₂×C₅²×C₁₁	—	11	1	no	maximal
7	C₂×C₅×C₁₁⋊C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor
8	C₅²×C₁₁	—	11	1	no	—
9	C₅×C₁₁⋊C₅	C₂×C₁₁	1	1	yes	characteristic, direct product factor
10	C₂×C₁₁²	C₅²	1	1	yes	characteristic, complemented, Hall
11	C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅×C₁₁	—	5	2	no	—
13	C₂×C₅×C₁₁	—	11	5	no	—
14	C₂×C₅×C₁₁	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
15	C₂×C₅×C₁₁	C₅×C₁₁	1	1	yes	characteristic, complemented
16	C₂×C₁₁⋊C₅	C₅×C₁₁	1	5	yes	direct product factor
17	C₅×C₁₁	—	5	2	no	—
18	C₅×C₁₁	—	11	5	no	—
19	C₅×C₁₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
20	C₅×C₁₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
21	C₁₁⋊C₅	C₂×C₅×C₁₁	1	5	yes	direct product factor
22	C₂×C₅²	—	11	1	no	Hall
23	C₅²	—	11	1	no	Sylow
24	C₂×C₁₁	—	5	2	no	—
25	C₂×C₁₁	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
26	C₂×C₁₁	C₅²×C₁₁	1	1	yes	characteristic, complemented
27	C₁₁	—	5	2	no	—
28	C₁₁	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
29	C₁₁	C₂×C₅²×C₁₁	1	1	yes	characteristic, complemented
30	C₂×C₅	—	11	5	no	—
31	C₂×C₅	C₁₁×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
32	C₅	—	11	5	no	—
33	C₅	C₂×C₁₁×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
34	C₂	C₅×C₁₁×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	C₁₁⋊C₅
commutator, hypocenter	C₁₁	C₂×C₅²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁²	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₁⋊C₅	C₂	direct (N × H)
2. C₂×C₅×C₁₁²	C₅	semidirect
3. C₂×C₁₁×C₁₁⋊C₅	C₅	direct (N × H)
4. C₅×C₁₁²	C₂×C₅	semidirect
5. C₁₁×C₁₁⋊C₅	C₂×C₅	direct (N × H)
7. C₂×C₅×C₁₁⋊C₅	C₁₁	direct (N × H)
9. C₅×C₁₁⋊C₅	C₂×C₁₁	direct (N × H)
10. C₂×C₁₁²	C₅²	semidirect
11. C₁₁²	C₂×C₅²	semidirect
14. C₂×C₅×C₁₁	C₁₁⋊C₅	direct (N × H)
15. C₂×C₅×C₁₁	C₅×C₁₁	semidirect
16. C₂×C₁₁⋊C₅	C₅×C₁₁	direct (N × H)
19. C₅×C₁₁	C₂×C₁₁⋊C₅	direct (N × H)
20. C₅×C₁₁	C₂×C₅×C₁₁	semidirect
21. C₁₁⋊C₅	C₂×C₅×C₁₁	direct (N × H)
25. C₂×C₁₁	C₅×C₁₁⋊C₅	direct (N × H)
26. C₂×C₁₁	C₅²×C₁₁	semidirect
28. C₁₁	C₂×C₅×C₁₁⋊C₅	direct (N × H)
29. C₁₁	C₂×C₅²×C₁₁	semidirect
31. C₂×C₅	C₁₁×C₁₁⋊C₅	direct (N × H)
33. C₅	C₂×C₁₁×C₁₁⋊C₅	direct (N × H)
34. C₂	C₅×C₁₁×C₁₁⋊C₅	direct (N × H)

Subgroups — C2×C5×C11×C11⋊C5 #20258451

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₁₁×C₁₁⋊C₅ #20258451