Subgroups — C₅×A₄×C₁₉² #36343276

Order 21660.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₉²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₉²	—	4	1	no	maximal, Hall
3	A₄×C₁₉²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₁₉²	—	3	1	no	—
5	C₅×C₁₉²	A₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₁₉²	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×A₄×C₁₉	C₁₉	1	20	yes	maximal, direct product factor
8	C₃×C₁₉²	—	4	1	no	Hall
9	C₂×C₁₉²	—	3	1	no	—
10	C₂²×C₅×C₁₉	C₃×C₁₉	1	20	yes	complemented
11	C₁₉²	C₅×A₄	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅×C₁₉	—	4	20	no	—
13	A₄×C₁₉	C₅×C₁₉	1	20	yes	direct product factor
14	C₂×C₅×C₁₉	—	3	20	no	—
15	C₅×C₁₉	A₄×C₁₉	1	20	yes	direct product factor
16	C₂²×C₁₉	C₃×C₅×C₁₉	1	20	yes	complemented
17	C₅×A₄	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₁₉	—	4	20	no	—
19	C₂×C₁₉	—	3	20	no	—
20	C₂²×C₅	C₃×C₁₉²	1	1	yes	characteristic, complemented, Hall
21	C₁₉	C₅×A₄×C₁₉	1	20	yes	direct product factor
22	C₃×C₅	—	4	1	no	Hall
23	A₄	C₅×C₁₉²	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅	—	3	1	no	—
25	C₅	A₄×C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	C₃×C₅×C₁₉²	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	4	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₉²	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅×C₁₉²
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₉²	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₁₉²

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.