Subgroups — C₅×C₂²⋊#11762246 #36343279

Order 21660.

100 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×#11762246	—	4	1	no	maximal, Hall
3	C₂²⋊#11762246	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	2	no	maximal
8	#11762246	—	4	1	no	Hall
9	C₂×C₁₉²	—	3	1	no	—
10	C₂²×C₅×C₁₉	—	3	6	no	—
11	C₂²×C₅×C₁₉	C₁₉⋊C₃	1	2	yes	complemented
12	C₁₉²	C₅×A₄	1	1	yes	characteristic, complemented, Sylow
13	C₅×C₁₉⋊C₃	—	76	2	no	—
14	C₂²⋊(C₁₉⋊C₃)	—	19	2	no	—
15	C₂×C₅×C₁₉	—	3	18	no	—
16	C₂×C₅×C₁₉	—	3	2	no	—
17	C₅×C₁₉	—	3	6	no	—
18	C₅×C₁₉	C₂²⋊(C₁₉⋊C₃)	1	2	yes	complemented
19	C₂²×C₁₉	—	3	6	no	—
20	C₂²×C₁₉	C₅×C₁₉⋊C₃	1	2	yes	complemented
21	C₅×A₄	—	361	1	no	Hall
22	C₁₉⋊C₃	—	76	2	no	—
23	C₂×C₁₉	—	3	18	no	—
24	C₂×C₁₉	—	3	2	no	—
25	C₂²×C₅	#11762246	1	1	yes	characteristic, complemented, Hall
26	C₁₉	—	3	6	no	—
27	C₁₉	C₅×C₂²⋊(C₁₉⋊C₃)	1	2	yes	complemented
28	C₃×C₅	—	1444	1	no	Hall
29	A₄	—	361	1	no	Hall
30	C₂×C₅	—	3	1	no	—
31	C₅	C₂²⋊#11762246	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²	C₅×#11762246	1	1	yes	characteristic, complemented, Sylow
33	C₃	—	1444	1	no	Sylow
34	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₂²⋊#11762246
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.