Subgroups — C₃×C₁₁⋊C₅×D₅₉ #34085697

Order 19470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁⋊C₅×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁⋊C₅×D₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×D₅₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁⋊C₅×C₅₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×D₅₉	—	11	1	no	maximal, Hall
7	C₁₁×D₅₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×C₅₉	—	11	1	no	Hall
9	C₁₁×C₅₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×D₅₉	—	11	1	no	Hall
11	C₃×D₅₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₁₁⋊C₅	—	59	1	no	maximal, Hall
13	C₅×C₅₉	—	11	1	no	Hall
14	C₃×C₅₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁⋊C₅	D₅₉	1	1	yes	characteristic, direct product factor, Hall
16	D₅₉	C₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₁⋊C₅	—	59	1	no	Hall
18	C₂×C₃×C₁₁	—	59	1	no	Hall
19	C₅₉	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
20	C₁₁⋊C₅	C₃×D₅₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁	C₅×D₅₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅	—	649	1	no	Hall
23	C₂×C₁₁	—	59	1	no	Hall
24	C₃×C₅	—	11	1	no	Hall
25	C₁₁	C₃×C₅×D₅₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	649	1	no	Hall
27	C₂×C₃	—	59	1	no	Hall
28	C₅	—	11	1	no	Sylow
29	C₃	C₁₁⋊C₅×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	59	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₁⋊C₅×D₅₉
commutator, cosocle, hypocenter	C₁₁×C₅₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₅₉	C₂×C₅
LCS	G ▷ C₁₁×C₅₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁⋊C₅×C₅₉	C₂	semidirect
2. C₁₁⋊C₅×D₅₉	C₃	direct (N × H)
3. C₃×C₁₁×D₅₉	C₅	semidirect
4. C₁₁⋊C₅×C₅₉	C₂×C₃	semidirect
5. C₃×C₁₁×C₅₉	C₂×C₅	semidirect
7. C₁₁×D₅₉	C₃×C₅	semidirect
9. C₁₁×C₅₉	C₂×C₃×C₅	semidirect
11. C₃×D₅₉	C₁₁⋊C₅	direct (N × H)
14. C₃×C₅₉	C₂×C₁₁⋊C₅	semidirect
15. C₃×C₁₁⋊C₅	D₅₉	direct (N × H)
16. D₅₉	C₃×C₁₁⋊C₅	direct (N × H)
19. C₅₉	C₂×C₃×C₁₁⋊C₅	semidirect
20. C₁₁⋊C₅	C₃×D₅₉	direct (N × H)
21. C₃×C₁₁	C₅×D₅₉	semidirect
25. C₁₁	C₃×C₅×D₅₉	semidirect
29. C₃	C₁₁⋊C₅×D₅₉	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×C₁₁⋊C₅×C₅₉	2
C₁₁⋊C₅×D₅₉	3
C₃×C₁₁×D₅₉	5
C₃×C₅×D₅₉	11
C₂×C₃×C₁₁⋊C₅	59

Subgroups — C3×C11⋊C5×D59 #34085697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁⋊C₅×D₅₉ #34085697