Subgroups — C₃⋊(C₇⋊(C₁₉⋊D₁₉)) #29503155

Order 15162.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊(C₁₉⋊D₁₉)	—	3	1	no	maximal, Hall
3	C₇×C₁₉²	D₃	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₁₉⋊D₁₉)	—	7	1	no	maximal, Hall
5	C₃×C₁₉²	D₇	1	1	yes	characteristic, complemented, Hall
6	D₃₉₉	—	19	20	no	maximal
7	C₁₉⋊D₁₉	—	21	1	no	Hall
8	C₃×C₇×C₁₉	D₁₉	1	20	yes	complemented
9	C₁₉²	D₂₁	1	1	yes	characteristic, complemented, Sylow
10	D₁₃₃	—	57	20	no	—
11	C₇×C₁₉	D₅₇	1	20	yes	complemented
12	D₅₇	—	133	20	no	—
13	C₃×C₁₉	D₁₃₃	1	20	yes	complemented
14	D₂₁	—	361	1	no	Hall
15	D₁₉	—	399	20	no	—
16	C₃×C₇	C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Hall
17	C₁₉	D₃₉₉	1	20	yes	complemented
18	D₇	—	1083	1	no	Hall
19	C₇	C₃⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	2527	1	no	Hall
21	C₃	C₇⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	7581	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₉²	C₂
LCS	G ▷ C₃×C₇×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.