Subgroups — C₇×C₅⋊(C₁₉⋊D₁₉) #38760149

Order 25270.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₉⋊D₁₉	—	5	1	no	maximal, Hall
3	C₅⋊(C₁₉⋊D₁₉)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₉²	D₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₉²	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×D₉₅	—	19	20	no	maximal
7	C₁₉⋊D₁₉	—	5	1	no	Hall
8	C₅×C₇×C₁₉	D₁₉	1	20	yes	complemented
9	C₁₉²	C₇×D₅	1	1	yes	characteristic, complemented, Sylow
10	C₇×D₁₉	—	95	20	no	—
11	D₉₅	—	19	20	no	—
12	C₇×C₁₉	D₉₅	1	20	yes	complemented
13	C₅×C₁₉	C₇×D₁₉	1	20	yes	complemented
14	C₇×D₅	—	361	1	no	Hall
15	D₁₉	—	95	20	no	—
16	C₅×C₇	C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Hall
17	C₁₉	C₇×D₉₅	1	20	yes	complemented
18	C₂×C₇	—	1805	1	no	Hall
19	D₅	—	361	1	no	Hall
20	C₇	C₅⋊(C₁₉⋊D₁₉)	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₇×C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	1805	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₅⋊(C₁₉⋊D₁₉)
commutator, cosocle, hypocenter	C₅×C₁₉²	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₉²	C₂
LCS	G ▷ C₅×C₁₉²
UCS	C₁ ◁ C₇

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.