Subgroups — Dic₁₉×C₄₁⋊C₅ #29509986

Order 15580.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₁×Dic₁₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₉×C₄₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₄₁⋊C₅	—	19	1	no	maximal, Hall
6	C₁₉×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₄₁⋊C₅	D₁₉	1	1	yes	characteristic
8	C₅×Dic₁₉	—	41	1	no	maximal, Hall
9	C₄₁⋊C₅	Dic₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₁₉	—	41	1	no	—
11	C₄×C₄₁	—	19	1	no	Hall
12	C₅×C₁₉	—	41	1	no	Hall
13	C₂×C₄₁	C₅×D₁₉	1	1	yes	characteristic
14	Dic₁₉	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₄₁	C₅×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	C₂×C₄₁⋊C₅	1	1	yes	characteristic
17	C₄×C₅	—	779	1	no	Hall
18	C₁₉	C₄×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	41	1	no	—
20	C₅	—	41	1	no	Sylow
21	C₄	—	19	1	no	Sylow
22	C₂	D₁₉×C₄₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₉×C₄₁⋊C₅
commutator, hypocenter	C₁₉×C₄₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₁₉×C₄₁	C₂×C₅
prime radical	C₂×C₁₉×C₄₁⋊C₅	C₂
LCS	G ▷ C₁₉×C₄₁
UCS	C₁ ◁ C₂

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.