Subgroups — C₃⋊D₃×C₁₉²⋊C₅ #44570565

Order 32490.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉²⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₉²⋊C₅	—	3	4	no	maximal
3	C₃⋊D₃×C₁₉²	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₁₉²⋊C₅	D₃	1	4	yes	complemented
5	C₂×C₁₉²⋊C₅	—	9	1	no	Hall
6	C₃²×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₃×C₁₉²	—	3	4	no	—
8	C₁₉²⋊C₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₉²	C₅×D₃	1	4	yes	complemented
10	C₂×C₁₉²	—	9	1	no	Hall
11	C₁₉²	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊D₃×C₁₉	—	5	4	no	—
13	C₃²×C₁₉	—	5	4	no	—
14	D₃×C₁₉	—	15	16	no	—
15	C₅×C₃⋊D₃	—	361	1	no	maximal, Hall
16	C₃×C₁₉	—	5	16	no	—
17	C₃²×C₅	—	361	1	no	Hall
18	C₂×C₁₉	—	45	4	no	—
19	C₅×D₃	—	1083	4	no	—
20	C₁₉	—	5	4	no	—
21	C₃⋊D₃	C₁₉²⋊C₅	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₅	—	361	4	no	—
23	C₂×C₅	—	3249	1	no	Hall
24	C₃²	C₂×C₁₉²⋊C₅	1	1	yes	characteristic, complemented, Sylow
25	D₃	—	3	4	no	—
26	C₅	—	361	1	no	Sylow
27	C₃	D₃×C₁₉²⋊C₅	1	4	yes	complemented
28	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₉²	C₂×C₅
LCS	G ▷ C₃²×C₁₉²
UCS	C₁

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.