Subgroups — C₄×C₅×C₁₉×C₁₁⋊C₅ #35229863

Order 20900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₁₁⋊C₅	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₉×C₁₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
4	C₄×C₅×C₁₁×C₁₉	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×C₁₁⋊C₅	C₂×C₅	1	5	yes	—
6	C₂×C₅×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic
7	C₄×C₅²×C₁₉	—	11	1	no	maximal, Hall
8	C₄×C₅×C₁₁⋊C₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁×C₁₉	C₄×C₅	1	1	yes	characteristic, complemented
10	C₁₉×C₁₁⋊C₅	C₄×C₅	1	5	yes	direct product factor
11	C₂×C₅²×C₁₉	—	11	1	no	—
12	C₄×C₁₁×C₁₉	C₅²	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₁₁⋊C₅	C₂×C₁₉	1	1	yes	characteristic
14	C₅²×C₁₉	—	11	1	no	Hall
15	C₂×C₁₁×C₁₉	C₂×C₅²	1	1	yes	characteristic
16	C₄×C₅×C₁₉	—	11	5	no	—
17	C₄×C₅×C₁₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
18	C₅×C₁₁⋊C₅	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₄×C₅×C₁₁	C₅×C₁₉	1	1	yes	characteristic, complemented
20	C₄×C₁₁⋊C₅	C₅×C₁₉	1	5	yes	direct product factor
21	C₁₁×C₁₉	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×C₁₉	—	11	5	no	—
23	C₂×C₅×C₁₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic
24	C₂×C₅×C₁₁	C₂×C₅×C₁₉	1	1	yes	characteristic
25	C₂×C₁₁⋊C₅	C₂×C₅×C₁₉	1	5	yes	—
26	C₄×C₅²	—	11	1	no	Hall
27	C₅×C₁₉	—	11	5	no	—
28	C₅×C₁₉	C₄×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
29	C₄×C₁₉	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
30	C₅×C₁₁	C₄×C₅×C₁₉	1	1	yes	characteristic, complemented
31	C₁₁⋊C₅	C₄×C₅×C₁₉	1	5	yes	direct product factor
32	C₂×C₅²	—	11	1	no	—
33	C₄×C₁₁	C₅²×C₁₉	1	1	yes	characteristic, complemented, Hall
34	C₂×C₁₉	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic
35	C₅²	—	11	1	no	Sylow
36	C₂×C₁₁	C₂×C₅²×C₁₉	1	1	yes	characteristic
37	C₄×C₅	—	11	5	no	—
38	C₄×C₅	C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
39	C₁₉	C₄×C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₁₁	C₄×C₅²×C₁₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	11	5	no	—
42	C₂×C₅	C₂×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic
43	C₅	—	11	5	no	—
44	C₅	C₄×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
45	C₄	C₅×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₂×C₅×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅×C₁₉	C₁₁⋊C₅
commutator, hypocenter	C₁₁	C₄×C₅²×C₁₉
Frattini	C₂	C₂×C₅×C₁₉×C₁₁⋊C₅
Fitting	C₄×C₅×C₁₁×C₁₉	C₅
socle	C₂×C₅×C₁₁×C₁₉	C₂×C₅
prime radical	C₂×C₅×C₁₉×C₁₁⋊C₅	C₂
cosocle	C₂×C₁₁	C₂×C₅²×C₁₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₄×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₉×C₁₁⋊C₅	C₄	direct (N × H)
3. C₄×C₁₉×C₁₁⋊C₅	C₅	direct (N × H)
4. C₄×C₅×C₁₁×C₁₉	C₅	semidirect
8. C₄×C₅×C₁₁⋊C₅	C₁₉	direct (N × H)
9. C₅×C₁₁×C₁₉	C₄×C₅	semidirect
10. C₁₉×C₁₁⋊C₅	C₄×C₅	direct (N × H)
12. C₄×C₁₁×C₁₉	C₅²	semidirect
17. C₄×C₅×C₁₉	C₁₁⋊C₅	direct (N × H)
18. C₅×C₁₁⋊C₅	C₄×C₁₉	direct (N × H)
19. C₄×C₅×C₁₁	C₅×C₁₉	semidirect
20. C₄×C₁₁⋊C₅	C₅×C₁₉	direct (N × H)
21. C₁₁×C₁₉	C₄×C₅²	semidirect
28. C₅×C₁₉	C₄×C₁₁⋊C₅	direct (N × H)
29. C₄×C₁₉	C₅×C₁₁⋊C₅	direct (N × H)
30. C₅×C₁₁	C₄×C₅×C₁₉	semidirect
31. C₁₁⋊C₅	C₄×C₅×C₁₉	direct (N × H)
33. C₄×C₁₁	C₅²×C₁₉	semidirect
38. C₄×C₅	C₁₉×C₁₁⋊C₅	direct (N × H)
39. C₁₉	C₄×C₅×C₁₁⋊C₅	direct (N × H)
40. C₁₁	C₄×C₅²×C₁₉	semidirect
44. C₅	C₄×C₁₉×C₁₁⋊C₅	direct (N × H)
45. C₄	C₅×C₁₉×C₁₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₉×C₁₁⋊C₅	2
C₄×C₁₉×C₁₁⋊C₅	5
C₄×C₅×C₁₁×C₁₉	5
C₄×C₅²×C₁₉	11
C₄×C₅×C₁₁⋊C₅	19

Subgroups — C4×C5×C19×C11⋊C5 #35229863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₁₉×C₁₁⋊C₅ #35229863