Subgroups — D₅×C₁₃²×C₁₉ #44545774

Order 32110.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃²×C₁₉	—	5	1	no	maximal, Hall
3	C₁₃²×C₁₉	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₁₃×C₁₉	C₁₃	1	14	yes	maximal, direct product factor
5	D₅×C₁₃²	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₃×C₁₉	C₂×C₁₃	1	14	yes	complemented
7	C₅×C₁₃²	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₃×C₁₉	—	5	14	no	—
9	C₂×C₁₃²	—	5	1	no	Hall
10	C₁₃×C₁₉	D₅×C₁₃	1	14	yes	direct product factor
11	D₅×C₁₉	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃²	D₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
13	D₅×C₁₃	C₁₃×C₁₉	1	14	yes	direct product factor
14	C₅×C₁₉	C₂×C₁₃²	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₃	C₂×C₁₃×C₁₉	1	14	yes	complemented
16	C₂×C₁₉	—	5	1	no	Hall
17	C₂×C₁₃	—	5	14	no	—
18	C₁₉	D₅×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	D₅×C₁₃×C₁₉	1	14	yes	direct product factor
20	D₅	C₁₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
21	C₅	C₂×C₁₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃²×C₁₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₃²×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₃²×C₁₉

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.