Subgroups — C₂×C₅×C₁₁⋊C₅×C₅₉ #44570098

Order 32450.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁⋊C₅×C₅₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁⋊C₅×C₅₉	C₅	1	5	yes	maximal, direct product factor
3	C₂×C₅×C₁₁×C₅₉	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented
5	C₁₁⋊C₅×C₅₉	C₂×C₅	1	5	yes	direct product factor
6	C₂×C₅²×C₅₉	—	11	1	no	maximal, Hall
7	C₅²×C₅₉	—	11	1	no	Hall
8	C₂×C₁₁×C₅₉	C₅²	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₅₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₅₉	—	11	5	no	—
11	C₂×C₅×C₅₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
12	C₂×C₅×C₁₁⋊C₅	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₅₉	—	11	5	no	—
14	C₅×C₅₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
15	C₅×C₁₁⋊C₅	C₂×C₅₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅₉	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₁	C₅×C₅₉	1	1	yes	characteristic, complemented
18	C₂×C₁₁⋊C₅	C₅×C₅₉	1	5	yes	direct product factor
19	C₅₉	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₅×C₁₁	C₂×C₅×C₅₉	1	1	yes	characteristic, complemented
21	C₁₁⋊C₅	C₂×C₅×C₅₉	1	5	yes	direct product factor
22	C₂×C₅²	—	11	1	no	Hall
23	C₅²	—	11	1	no	Sylow
24	C₂×C₁₁	C₅²×C₅₉	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₂×C₅²×C₅₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	11	5	no	—
27	C₂×C₅	C₁₁⋊C₅×C₅₉	1	1	yes	characteristic, direct product factor
28	C₅	—	11	5	no	—
29	C₅	C₂×C₁₁⋊C₅×C₅₉	1	1	yes	characteristic, direct product factor
30	C₂	C₅×C₁₁⋊C₅×C₅₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅×C₅₉	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₂×C₅²×C₅₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₅₉	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁⋊C₅×C₅₉	C₂	direct (N × H)
2. C₂×C₁₁⋊C₅×C₅₉	C₅	direct (N × H)
3. C₂×C₅×C₁₁×C₅₉	C₅	semidirect
4. C₅×C₁₁×C₅₉	C₂×C₅	semidirect
5. C₁₁⋊C₅×C₅₉	C₂×C₅	direct (N × H)
8. C₂×C₁₁×C₅₉	C₅²	semidirect
9. C₁₁×C₅₉	C₂×C₅²	semidirect
11. C₂×C₅×C₅₉	C₁₁⋊C₅	direct (N × H)
12. C₂×C₅×C₁₁⋊C₅	C₅₉	direct (N × H)
14. C₅×C₅₉	C₂×C₁₁⋊C₅	direct (N × H)
15. C₅×C₁₁⋊C₅	C₂×C₅₉	direct (N × H)
16. C₂×C₅₉	C₅×C₁₁⋊C₅	direct (N × H)
17. C₂×C₅×C₁₁	C₅×C₅₉	semidirect
18. C₂×C₁₁⋊C₅	C₅×C₅₉	direct (N × H)
19. C₅₉	C₂×C₅×C₁₁⋊C₅	direct (N × H)
20. C₅×C₁₁	C₂×C₅×C₅₉	semidirect
21. C₁₁⋊C₅	C₂×C₅×C₅₉	direct (N × H)
24. C₂×C₁₁	C₅²×C₅₉	semidirect
25. C₁₁	C₂×C₅²×C₅₉	semidirect
27. C₂×C₅	C₁₁⋊C₅×C₅₉	direct (N × H)
29. C₅	C₂×C₁₁⋊C₅×C₅₉	direct (N × H)
30. C₂	C₅×C₁₁⋊C₅×C₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁⋊C₅×C₅₉	2
C₂×C₁₁⋊C₅×C₅₉	5
C₂×C₅×C₁₁×C₅₉	5
C₂×C₅²×C₅₉	11
C₂×C₅×C₁₁⋊C₅	59

Subgroups — C2×C5×C11⋊C5×C59 #44570098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₁⋊C₅×C₅₉ #44570098