Subgroups — C₅²×C₂²⋊(C₁₉⋊C₃) #19152894

Order 5700.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₁₉⋊C₃	—	4	1	no	maximal, Hall
3	C₅×C₂²⋊(C₁₉⋊C₃)	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅²×C₁₉	—	3	1	no	—
5	C₅²×C₁₉	A₄	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₅×C₁₉	C₃×C₅	1	6	yes	complemented
7	C₅²×A₄	—	19	1	no	maximal, Hall
8	C₅×C₁₉⋊C₃	—	4	6	no	—
9	C₂²⋊(C₁₉⋊C₃)	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₁₉	—	3	6	no	—
11	C₂²×C₅²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₉	C₅×A₄	1	6	yes	complemented
13	C₂²×C₁₉	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅²	—	76	1	no	Hall
15	C₅×A₄	—	19	6	no	—
16	C₁₉⋊C₃	—	4	1	no	Hall
17	C₂×C₅²	—	3	1	no	—
18	C₂×C₁₉	—	3	1	no	—
19	C₅²	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²×C₅	C₅×C₁₉⋊C₃	1	6	yes	complemented
21	C₁₉	C₅²×A₄	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₅	—	76	6	no	—
23	A₄	—	19	1	no	Hall
24	C₂×C₅	—	3	6	no	—
25	C₅	C₅×C₂²⋊(C₁₉⋊C₃)	1	6	yes	direct product factor
26	C₂²	C₅²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	76	1	no	Sylow
28	C₂	—	3	1	no	—

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