Subgroups — C₃×C₁₉×C₅⋊D₅₅ #44535530

Order 31350.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₅⋊D₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₉×D₅₅	—	5	6	no	maximal
4	C₅²×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₉	D₅	1	6	yes	complemented
6	C₃×C₁₉×C₅⋊D₅	—	11	1	no	maximal, Hall
7	C₁₉×D₅₅	—	5	6	no	—
8	C₃×C₅⋊D₅₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅²×C₁₉	D₁₁	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₉×D₁₁	—	25	1	no	Hall
11	C₅×C₁₁×C₁₉	C₃×D₅	1	6	yes	complemented
12	C₁₉×C₅⋊D₅	—	11	1	no	Hall
13	C₃×C₅²×C₁₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₃×D₅×C₁₉	—	55	6	no	—
16	C₅⋊D₅₅	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
17	C₅²×C₁₉	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
18	C₁₉×D₁₁	—	25	1	no	Hall
19	C₃×D₅₅	—	5	6	no	—
20	C₃×C₅×C₁₉	D₅₅	1	6	yes	complemented
21	C₅²×C₁₁	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
22	C₁₁×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
23	D₅×C₁₉	—	55	6	no	—
24	C₃×C₅×C₁₁	D₅×C₁₉	1	6	yes	complemented
25	C₃×C₅⋊D₅	—	11	1	no	Hall
26	C₂×C₃×C₁₉	—	275	1	no	Hall
27	D₅₅	—	5	6	no	—
28	C₅×C₁₉	C₃×D₅₅	1	6	yes	complemented
29	C₃×C₅²	C₁₉×D₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₁	—	25	1	no	Hall
31	C₃×C₁₉	C₅⋊D₅₅	1	1	yes	characteristic, direct product factor, Hall
32	C₅×C₁₁	C₃×D₅×C₁₉	1	6	yes	complemented
33	C₅⋊D₅	—	11	1	no	Hall
34	C₂×C₁₉	—	275	1	no	Hall
35	C₃×C₁₁	C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
36	C₃×D₅	—	55	6	no	—
37	C₅²	C₃×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
38	D₁₁	—	25	1	no	Hall
39	C₁₉	C₃×C₅⋊D₅₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₅	C₁₉×D₅₅	1	6	yes	complemented
41	C₁₁	C₃×C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
42	D₅	—	55	6	no	—
43	C₂×C₃	—	275	1	no	Hall
44	C₅	C₃×C₁₉×D₅₅	1	6	yes	complemented
45	C₃	C₁₉×C₅⋊D₅₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	275	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₅⋊D₅₅
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₉	C₂
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₉	C₂	semidirect
2. C₁₉×C₅⋊D₅₅	C₃	direct (N × H)
4. C₅²×C₁₁×C₁₉	C₂×C₃	semidirect
5. C₃×C₅×C₁₁×C₁₉	D₅	semidirect
8. C₃×C₅⋊D₅₅	C₁₉	direct (N × H)
9. C₃×C₅²×C₁₉	D₁₁	semidirect
11. C₅×C₁₁×C₁₉	C₃×D₅	semidirect
13. C₃×C₅²×C₁₁	C₂×C₁₉	semidirect
14. C₃×C₁₁×C₁₉	C₅⋊D₅	semidirect
16. C₅⋊D₅₅	C₃×C₁₉	direct (N × H)
17. C₅²×C₁₉	C₃×D₁₁	semidirect
20. C₃×C₅×C₁₉	D₅₅	semidirect
21. C₅²×C₁₁	C₂×C₃×C₁₉	semidirect
22. C₁₁×C₁₉	C₃×C₅⋊D₅	semidirect
24. C₃×C₅×C₁₁	D₅×C₁₉	semidirect
28. C₅×C₁₉	C₃×D₅₅	semidirect
29. C₃×C₅²	C₁₉×D₁₁	semidirect
31. C₃×C₁₉	C₅⋊D₅₅	direct (N × H)
32. C₅×C₁₁	C₃×D₅×C₁₉	semidirect
35. C₃×C₁₁	C₁₉×C₅⋊D₅	semidirect
37. C₅²	C₃×C₁₉×D₁₁	semidirect
39. C₁₉	C₃×C₅⋊D₅₅	direct (N × H)
40. C₃×C₅	C₁₉×D₅₅	semidirect
41. C₁₁	C₃×C₁₉×C₅⋊D₅	semidirect
44. C₅	C₃×C₁₉×D₅₅	semidirect
45. C₃	C₁₉×C₅⋊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×C₅²×C₁₁×C₁₉	2
C₁₉×C₅⋊D₅₅	3
C₃×C₁₉×D₅₅	5
C₃×C₁₉×C₅⋊D₅	11
C₃×C₅⋊D₅₅	19

Subgroups — C3×C19×C5⋊D55 #44535530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×C₅⋊D₅₅ #44535530