Subgroups — C₁₉⋊(Dic₇₁⋊C₅) #41008685

Order 26980.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₇₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₃₄₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₉×C₇₁	C₂×C₅	1	1	yes	characteristic
5	Dic₇₁⋊C₅	—	19	1	no	maximal, Hall
6	C₁₉×C₇₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇₁⋊C₅	D₁₉	1	1	yes	characteristic
8	C₅×Dic₁₉	—	71	1	no	maximal, Hall
9	C₇₁⋊C₅	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	Dic₇₁	—	19	1	no	Hall
11	C₂×C₅×C₁₉	—	71	1	no	—
12	C₂×C₇₁	C₅×D₁₉	1	1	yes	characteristic
13	C₅×C₁₉	—	71	1	no	Hall
14	Dic₁₉	—	355	1	no	Hall
15	C₇₁	C₅×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	D₇₁⋊C₅	1	1	yes	characteristic
17	C₄×C₅	—	1349	1	no	Hall
18	C₁₉	Dic₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	71	1	no	—
20	C₅	—	71	1	no	Sylow
21	C₄	—	6745	1	no	Sylow
22	C₂	C₁₉⋊(D₇₁⋊C₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₉⋊(D₇₁⋊C₅)
commutator, hypocenter	C₁₉×C₇₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₁₉×C₇₁	C₂×C₅
prime radical	C₂×C₁₉×C₇₁⋊C₅	C₂
LCS	G ▷ C₁₉×C₇₁
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.