Subgroups — C₃×C₅₃×D₅₅ #31775813

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	C₅₃×D₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₁×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, complemented, Hall
6	C₃×D₅×C₅₃	—	11	1	no	maximal, Hall
7	D₁₁×C₅₃	—	5	1	no	Hall
8	C₃×C₅×C₅₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₅₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×C₅₃	—	11	1	no	Hall
11	C₃×D₅₅	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₅₃	—	55	1	no	Hall
13	C₅×C₅₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₁	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅₃	D₅₅	1	1	yes	characteristic, direct product factor, Hall
16	D₅₅	C₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅₃	—	55	1	no	Hall
18	C₃×D₁₁	—	5	1	no	Hall
19	C₅×C₁₁	C₂×C₃×C₅₃	1	1	yes	characteristic, complemented, Hall
20	C₅₃	C₃×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₁	D₅×C₅₃	1	1	yes	characteristic, complemented, Hall
22	C₃×D₅	—	11	1	no	Hall
23	D₁₁	—	5	1	no	Hall
24	C₃×C₅	D₁₁×C₅₃	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₃×D₅×C₅₃	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	11	1	no	Hall
27	C₂×C₃	—	55	1	no	Hall
28	C₅	C₃×D₁₁×C₅₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₅₃×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅₃	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₅₃	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₃×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. C₅₃×D₅₅	C₃	direct (N × H)
4. C₅×C₁₁×C₅₃	C₂×C₃	semidirect
5. C₃×C₁₁×C₅₃	D₅	semidirect
8. C₃×C₅×C₅₃	D₁₁	semidirect
9. C₁₁×C₅₃	C₃×D₅	semidirect
11. C₃×D₅₅	C₅₃	direct (N × H)
13. C₅×C₅₃	C₃×D₁₁	semidirect
14. C₃×C₅×C₁₁	C₂×C₅₃	semidirect
15. C₃×C₅₃	D₅₅	direct (N × H)
16. D₅₅	C₃×C₅₃	direct (N × H)
19. C₅×C₁₁	C₂×C₃×C₅₃	semidirect
20. C₅₃	C₃×D₅₅	direct (N × H)
21. C₃×C₁₁	D₅×C₅₃	semidirect
24. C₃×C₅	D₁₁×C₅₃	semidirect
25. C₁₁	C₃×D₅×C₅₃	semidirect
28. C₅	C₃×D₁₁×C₅₃	semidirect
29. C₃	C₅₃×D₅₅	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
C₅₃×D₅₅	3
C₃×D₁₁×C₅₃	5
C₃×D₅×C₅₃	11
C₃×D₅₅	53

Subgroups — C3×C53×D55 #31775813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅₃×D₅₅ #31775813