Subgroups — C₅×C₂²⋊#11762245 #36343278

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	C₅×#11762245	—	4	1	no	maximal, Hall
3	C₂²⋊#11762245	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, complemented, Hall
6	C₂²×C₁₉²	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₂²⋊(C₁₉⋊C₃)	—	19	20	no	maximal
8	#11762245	—	4	1	no	Hall
9	C₂×C₁₉²	—	3	1	no	—
10	C₂²×C₅×C₁₉	C₁₉⋊C₃	1	20	yes	complemented
11	C₁₉²	C₅×A₄	1	1	yes	characteristic, complemented, Sylow
12	C₅×C₁₉⋊C₃	—	76	20	no	—
13	C₂²⋊(C₁₉⋊C₃)	—	19	20	no	—
14	C₂×C₅×C₁₉	—	3	20	no	—
15	C₅×C₁₉	C₂²⋊(C₁₉⋊C₃)	1	20	yes	complemented
16	C₂²×C₁₉	C₅×C₁₉⋊C₃	1	20	yes	complemented
17	C₅×A₄	—	361	1	no	Hall
18	C₁₉⋊C₃	—	76	20	no	—
19	C₂×C₁₉	—	3	20	no	—
20	C₂²×C₅	#11762245	1	1	yes	characteristic, complemented, Hall
21	C₁₉	C₅×C₂²⋊(C₁₉⋊C₃)	1	20	yes	complemented
22	C₃×C₅	—	1444	1	no	Hall
23	A₄	—	361	1	no	Hall
24	C₂×C₅	—	3	1	no	—
25	C₅	C₂²⋊#11762245	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	C₅×#11762245	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	1444	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₂²⋊#11762245
commutator, cosocle, hypocenter	C₂²×C₁₉²	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₉²	C₃
LCS	G ▷ C₂²×C₁₉²
UCS	C₁ ◁ C₅

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.