Subgroups — C₂×(C₅⋊D₅)⋊(C₁₉⋊C₃) #19152847

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	(C₅⋊D₅)⋊(C₁₉⋊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	—	19	1	no	maximal, Hall
10	C₂²×C₁₉⋊C₃	—	25	1	no	maximal, Hall
11	C₂×C₅×C₁₉	—	3	2	no	—
12	D₅×C₁₉	—	15	4	no	—
13	C₂×C₅²⋊C₃	—	19	1	no	—
14	(C₅⋊D₅)⋊C₃	—	19	2	no	—
15	C₂×C₁₉⋊C₃	—	25	2	no	—
16	C₂×C₁₉⋊C₃	—	25	1	no	—
17	C₂×C₅⋊D₅	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₅×C₁₉	—	3	2	no	—
19	C₂²×C₁₉	—	25	1	no	Hall
20	C₅²⋊C₃	—	19	1	no	Hall
21	C₁₉⋊C₃	—	25	1	no	Hall
22	C₂×C₅²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
23	C₅⋊D₅	C₂×C₁₉⋊C₃	1	2	yes	complemented
24	C₂×C₁₉	—	25	2	no	—
25	C₂×C₁₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
26	C₅²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₅	—	15	2	no	—
28	C₁₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₃	—	475	1	no	Hall
30	C₂×C₅	—	3	2	no	—
31	D₅	—	15	4	no	—
32	C₂×C₃	—	475	2	no	—
33	C₂×C₃	—	475	1	no	—
34	C₅	—	3	2	no	—
35	C₂²	—	25	1	no	Sylow
36	C₃	—	475	1	no	Sylow
37	C₂	—	25	2	no	—
38	C₂	(C₅⋊D₅)⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉⋊(C₅²⋊C₃)	C₂	semidirect
2. (C₅⋊D₅)⋊(C₁₉⋊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
17. C₂×C₅⋊D₅	C₁₉⋊C₃	semidirect
22. C₂×C₅²	C₂×C₁₉⋊C₃	semidirect
23. C₅⋊D₅	C₂×C₁₉⋊C₃	semidirect
25. C₂×C₁₉	(C₅⋊D₅)⋊C₃	semidirect
26. C₅²	C₂²×C₁₉⋊C₃	semidirect
28. C₁₉	C₂×(C₅⋊D₅)⋊C₃	semidirect
38. C₂	(C₅⋊D₅)⋊(C₁₉⋊C₃)	direct (N × H)

Subgroups — C2×(C5⋊D5)⋊(C19⋊C3) #19152847

Conjugacy classes of subgroups

Complements

Subgroups — C₂×(C₅⋊D₅)⋊(C₁₉⋊C₃) #19152847