Subgroups — C₅×#20266582 #44570463

Order 32490.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692429	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₉⋊D₁₉	C₃	1	1	yes	maximal, characteristic
3	#20266582	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₉⋊D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692429	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₉⋊D₁₉	C₃×C₅	1	1	yes	characteristic
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅×#4294⋊C₂	—	19	20	no	maximal
10	C₃×C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic
11	C₅×#4294	—	19	20	no	—
12	C₁₉⋊D₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×D₁₉	—	19	20	no	—
14	C₁₉²	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
15	#4294⋊C₂	—	19	20	no	—
16	C₃×C₅×C₁₉	D₁₉⋊C₃	1	20	yes	—
17	C₅×D₁₉	—	19	20	no	—
18	#4294	—	19	20	no	—
19	C₃×D₁₉	—	19	20	no	—
20	C₅×C₁₉	#4294⋊C₂	1	20	yes	complemented
21	C₂×C₅×C₉	—	361	1	no	Hall
22	C₃×C₁₉	C₅×D₁₉⋊C₃	1	20	yes	—
23	C₅×C₉	—	361	1	no	Hall
24	D₁₉	—	19	20	no	—
25	C₂×C₃×C₅	—	361	1	no	—
26	C₁₉	C₅×#4294⋊C₂	1	20	yes	complemented
27	C₂×C₉	—	361	1	no	Hall
28	C₃×C₅	#14524206	1	1	yes	characteristic
29	C₂×C₅	—	361	1	no	Hall
30	C₉	—	361	1	no	Sylow
31	C₂×C₃	—	361	1	no	—
32	C₅	#20266582	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₅×#14524206	1	1	yes	characteristic
34	C₂	—	361	1	no	Sylow

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.