Subgroups — C₂²×C₁₉⋊(C₅²⋊C₃) #19152892

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	3	yes	maximal, direct product factor
2	C₂²×C₅²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉⋊(C₅²⋊C₃)	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅²×C₁₉	C₂×C₃	1	3	yes	complemented
5	C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₅×C₁₉	—	3	2	no	—
7	C₂²×C₅²⋊C₃	—	19	1	no	maximal, Hall
8	C₂²×C₁₉⋊C₃	—	25	1	no	maximal, Hall
9	C₂×C₅×C₁₉	—	3	6	no	—
10	C₂×C₅²⋊C₃	—	19	3	no	—
11	C₂×C₁₉⋊C₃	—	25	3	no	—
12	C₂²×C₅²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₅×C₁₉	—	3	2	no	—
14	C₂²×C₁₉	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₅²⋊C₃	—	19	1	no	Hall
16	C₁₉⋊C₃	—	25	1	no	Hall
17	C₂×C₅²	C₂×C₁₉⋊C₃	1	3	yes	complemented
18	C₂×C₁₉	C₂×C₅²⋊C₃	1	3	yes	complemented
19	C₅²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₅	—	3	2	no	—
21	C₁₉	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₃	—	475	1	no	Hall
23	C₂×C₅	—	3	6	no	—
24	C₂×C₃	—	475	3	no	—
25	C₅	—	3	2	no	—
26	C₂²	C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
27	C₃	—	475	1	no	Sylow
28	C₂	C₂×C₁₉⋊(C₅²⋊C₃)	1	3	yes	direct product factor

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