Subgroups — C₅×D₃₂₁₁ #44545763

Order 32110.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₂₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₆₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₂₄₇	—	13	1	no	maximal
5	C₅×D₁₆₉	—	19	1	no	maximal, Hall
6	C₅×C₁₃×C₁₉	D₁₃	1	1	yes	characteristic
7	C₅×C₁₆₉	D₁₉	1	1	yes	characteristic, complemented, Hall
8	D₂₄₇	—	13	1	no	—
9	D₁₆₉	—	19	1	no	Hall
10	C₁₃×C₁₉	C₅×D₁₃	1	1	yes	characteristic
11	C₅×D₁₉	—	169	1	no	Hall
12	C₁₆₉	C₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
13	C₅×D₁₃	—	247	1	no	—
14	C₅×C₁₉	D₁₆₉	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₃	D₂₄₇	1	1	yes	characteristic
16	D₁₉	—	169	1	no	Hall
17	D₁₃	—	247	1	no	—
18	C₁₉	C₅×D₁₆₉	1	1	yes	characteristic, complemented, Sylow
19	C₁₃	C₅×D₂₄₇	1	1	yes	characteristic
20	C₂×C₅	—	3211	1	no	Hall
21	C₅	D₃₂₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	3211	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₂₁₁
commutator, cosocle, hypocenter	C₁₉×C₁₆₉	C₂×C₅
Frattini	C₁₃	C₅×D₂₄₇
Fitting	C₅×C₁₉×C₁₆₉	C₂
socle	C₅×C₁₃×C₁₉	D₁₃
LCS	G ▷ C₁₉×C₁₆₉
UCS	C₁ ◁ C₅

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.