Subgroups — C₃⋊(C₅⋊(C₁₉⋊D₁₉)) #24925340

Order 10830.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(C₁₉⋊D₁₉)	—	3	1	no	maximal, Hall
3	C₃⋊(C₁₉⋊D₁₉)	—	5	1	no	maximal, Hall
4	C₅×C₁₉²	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉²	D₅	1	1	yes	characteristic, complemented, Hall
6	C₁₉⋊D₁₉	—	15	1	no	Hall
7	D₂₈₅	—	19	20	no	maximal
8	C₁₉²	D₁₅	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₅×C₁₉	D₁₉	1	20	yes	complemented
10	D₉₅	—	57	20	no	—
11	D₅₇	—	95	20	no	—
12	C₅×C₁₉	D₅₇	1	20	yes	complemented
13	C₃×C₁₉	D₉₅	1	20	yes	complemented
14	D₁₉	—	285	20	no	—
15	D₁₅	—	361	1	no	Hall
16	C₁₉	D₂₈₅	1	20	yes	complemented
17	C₃×C₅	C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Hall
18	D₅	—	1083	1	no	Hall
19	D₃	—	1805	1	no	Hall
20	C₅	C₃⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
21	C₃	C₅⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	5415	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₉²	C₂
LCS	G ▷ C₃×C₅×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.