Subgroups — C₅×C₁₉×A₅ #19152908

Order 5700.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₄×C₁₉	—	5	1	no	maximal
2	C₁₉×A₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×D₅×C₁₉	—	6	1	no	maximal
4	C₅×D₃×C₁₉	—	10	1	no	maximal
5	C₅²×C₁₉	—	6	1	no	Hall
6	C₂²×C₅×C₁₉	—	5	1	no	—
7	C₅×A₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×C₁₉	—	10	1	no	—
9	A₄×C₁₉	—	5	1	no	Hall
10	C₂×C₅×C₁₉	—	15	1	no	—
11	D₅×C₁₉	—	6	1	no	—
12	D₃×C₁₉	—	10	1	no	—
13	C₅×C₁₉	—	6	1	no	—
14	C₅×C₁₉	—	12	2	no	—
15	C₅×C₁₉	A₅	1	1	yes	maximal normal, characteristic, direct product factor
16	C₂²×C₁₉	—	5	1	no	Hall
17	C₅×A₄	—	5	1	no	—
18	A₅	C₅×C₁₉	1	1	yes	characteristic, direct product factor
19	C₃×C₁₉	—	10	1	no	Hall
20	C₅×D₅	—	6	1	no	—
21	C₂×C₁₉	—	15	1	no	—
22	C₅×D₃	—	10	1	no	—
23	C₅²	—	6	1	no	Sylow
24	C₂²×C₅	—	5	1	no	—
25	C₁₉	C₅×A₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₅	—	10	1	no	—
27	A₄	—	5	1	no	Hall
28	C₂×C₅	—	15	1	no	—
29	D₅	—	6	1	no	—
30	D₃	—	10	1	no	—
31	C₅	—	6	1	no	—
32	C₅	—	12	2	no	—
33	C₅	C₁₉×A₅	1	1	yes	characteristic, direct product factor
34	C₂²	—	5	1	no	Sylow
35	C₃	—	10	1	no	Sylow
36	C₂	—	15	1	no	—

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