Subgroups — C₅×D₇×C₁₉² #38760144

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	D₇×C₁₉²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₁₉²	—	7	1	no	maximal, Hall
4	C₇×C₁₉²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₉²	D₇	1	1	yes	characteristic, direct product factor, Hall
6	C₅×D₇×C₁₉	C₁₉	1	20	yes	maximal, direct product factor
7	C₂×C₁₉²	—	7	1	no	Hall
8	C₅×C₇×C₁₉	C₂×C₁₉	1	20	yes	complemented
9	C₁₉²	C₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
10	D₇×C₁₉	C₅×C₁₉	1	20	yes	direct product factor
11	C₂×C₅×C₁₉	—	7	20	no	—
12	C₇×C₁₉	C₂×C₅×C₁₉	1	20	yes	complemented
13	C₅×C₁₉	D₇×C₁₉	1	20	yes	direct product factor
14	C₅×D₇	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₉	—	7	20	no	—
16	C₅×C₇	C₂×C₁₉²	1	1	yes	characteristic, complemented, Hall
17	C₁₉	C₅×D₇×C₁₉	1	20	yes	direct product factor
18	D₇	C₅×C₁₉²	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	—	7	1	no	Hall
20	C₇	C₂×C₅×C₁₉²	1	1	yes	characteristic, complemented, Sylow
21	C₅	D₇×C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₉²	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅×C₁₉²
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₉²	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₁₉²

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.