Subgroups — C₂×C₁₉×(C₅⋊D₅)⋊C₃ #19152845

Order 5700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×(C₅⋊D₅)⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₉×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₉×C₅⋊D₅	C₂×C₃	1	2	yes	complemented
7	C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₅×C₁₉	—	15	2	no	—
9	C₂×(C₅⋊D₅)⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₁₉	—	25	1	no	maximal, Hall
11	C₂×C₅×C₁₉	—	3	2	no	—
12	D₅×C₁₉	—	15	4	no	—
13	C₂×C₅²⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented
14	(C₅⋊D₅)⋊C₃	C₂×C₁₉	1	2	yes	direct product factor
15	C₂×C₃×C₁₉	—	25	2	no	—
16	C₂×C₃×C₁₉	—	25	1	no	—
17	C₂×C₅⋊D₅	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₅×C₁₉	—	3	2	no	—
19	C₂²×C₁₉	—	25	1	no	Hall
20	C₅²⋊C₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₉	—	25	1	no	Hall
22	C₂×C₅²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
23	C₅⋊D₅	C₂×C₃×C₁₉	1	2	yes	complemented
24	C₂×C₁₉	—	25	2	no	—
25	C₂×C₁₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor
26	C₅²	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₅	—	15	2	no	—
28	C₁₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₃	—	25	1	no	Hall
30	C₂×C₅	—	3	2	no	—
31	D₅	—	15	4	no	—
32	C₂×C₃	—	25	2	no	—
33	C₂×C₃	—	25	1	no	—
34	C₅	—	3	2	no	—
35	C₂²	—	25	1	no	Sylow
36	C₃	—	25	1	no	Sylow
37	C₂	—	25	2	no	—
38	C₂	C₁₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉	(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×C₅²⋊C₃	C₂	semidirect
2. C₁₉×(C₅⋊D₅)⋊C₃	C₂	direct (N × H)
3. C₂×C₁₉×C₅⋊D₅	C₃	semidirect
4. C₁₉×C₅²⋊C₃	C₂²	semidirect
5. C₂×C₅²×C₁₉	C₂×C₃	semidirect
6. C₁₉×C₅⋊D₅	C₂×C₃	semidirect
7. C₅²×C₁₉	C₂²×C₃	semidirect
9. C₂×(C₅⋊D₅)⋊C₃	C₁₉	direct (N × H)
13. C₂×C₅²⋊C₃	C₂×C₁₉	semidirect
14. (C₅⋊D₅)⋊C₃	C₂×C₁₉	direct (N × H)
17. C₂×C₅⋊D₅	C₃×C₁₉	semidirect
20. C₅²⋊C₃	C₂²×C₁₉	semidirect
22. C₂×C₅²	C₂×C₃×C₁₉	semidirect
23. C₅⋊D₅	C₂×C₃×C₁₉	semidirect
25. C₂×C₁₉	(C₅⋊D₅)⋊C₃	direct (N × H)
26. C₅²	C₂²×C₃×C₁₉	semidirect
28. C₁₉	C₂×(C₅⋊D₅)⋊C₃	direct (N × H)
38. C₂	C₁₉×(C₅⋊D₅)⋊C₃	direct (N × H)

Subgroups — C2×C19×(C5⋊D5)⋊C3 #19152845

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₉×(C₅⋊D₅)⋊C₃ #19152845