Subgroups — C₃×D₅×C₁₁×C₅₃ #31775811

Order 17490.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₁×C₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₁₁×C₅₃	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₅₃	D₅	1	1	yes	characteristic, direct product factor, Hall
6	C₃×D₅×C₅₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₅₃	—	5	1	no	Hall
8	C₃×C₅×C₅₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₅₃	C₃×D₅	1	1	yes	characteristic, direct product factor, Hall
10	D₅×C₅₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃×D₅×C₁₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₅₃	—	5	1	no	Hall
13	C₅×C₅₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₁	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅₃	D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	D₅×C₁₁	C₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅₃	—	5	1	no	Hall
18	C₂×C₃×C₁₁	—	5	1	no	Hall
19	C₅×C₁₁	C₂×C₃×C₅₃	1	1	yes	characteristic, complemented, Hall
20	C₅₃	C₃×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₁	D₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
22	C₃×D₅	C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₁	—	5	1	no	Hall
24	C₃×C₅	C₂×C₁₁×C₅₃	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₃×D₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	C₃×C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	5	1	no	Hall
28	C₅	C₂×C₃×C₁₁×C₅₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅×C₁₁×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₅₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₁₁×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₅₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₁₁×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₅₃	C₂	semidirect
2. D₅×C₁₁×C₅₃	C₃	direct (N × H)
4. C₅×C₁₁×C₅₃	C₂×C₃	semidirect
5. C₃×C₁₁×C₅₃	D₅	direct (N × H)
6. C₃×D₅×C₅₃	C₁₁	direct (N × H)
8. C₃×C₅×C₅₃	C₂×C₁₁	semidirect
9. C₁₁×C₅₃	C₃×D₅	direct (N × H)
10. D₅×C₅₃	C₃×C₁₁	direct (N × H)
11. C₃×D₅×C₁₁	C₅₃	direct (N × H)
13. C₅×C₅₃	C₂×C₃×C₁₁	semidirect
14. C₃×C₅×C₁₁	C₂×C₅₃	semidirect
15. C₃×C₅₃	D₅×C₁₁	direct (N × H)
16. D₅×C₁₁	C₃×C₅₃	direct (N × H)
19. C₅×C₁₁	C₂×C₃×C₅₃	semidirect
20. C₅₃	C₃×D₅×C₁₁	direct (N × H)
21. C₃×C₁₁	D₅×C₅₃	direct (N × H)
22. C₃×D₅	C₁₁×C₅₃	direct (N × H)
24. C₃×C₅	C₂×C₁₁×C₅₃	semidirect
25. C₁₁	C₃×D₅×C₅₃	direct (N × H)
26. D₅	C₃×C₁₁×C₅₃	direct (N × H)
28. C₅	C₂×C₃×C₁₁×C₅₃	semidirect
29. C₃	D₅×C₁₁×C₅₃	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×C₁₁×C₅₃	2
D₅×C₁₁×C₅₃	3
C₂×C₃×C₁₁×C₅₃	5
C₃×D₅×C₅₃	11
C₃×D₅×C₁₁	53

Subgroups — C3×D5×C11×C53 #31775811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₁₁×C₅₃ #31775811