Subgroups — C₁₉×C₇₁⋊AGL(1,𝔽₅) #41008694

Order 26980.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×Dic₇₁	—	5	1	no	maximal, Hall
4	C₂×C₁₉×C₇₁	—	5	1	no	—
5	C₇₁⋊AGL(1,𝔽₅)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₇₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₇₁	C₂×C₁₉	1	1	yes	characteristic
8	C₁₉×AGL(1,𝔽₅)	—	71	1	no	maximal, Hall
9	C₅×C₇₁	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
10	Dic₇₁	—	5	1	no	Hall
11	D₅×C₁₉	D₇₁	1	1	yes	characteristic
12	C₂×C₇₁	—	5	1	no	—
13	C₅×C₁₉	Dic₇₁	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₉	—	355	1	no	Hall
15	C₇₁	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	—	5	1	no	—
17	AGL(1,𝔽₅)	—	71	1	no	Hall
18	C₁₉	C₇₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
19	D₅	C₁₉×D₇₁	1	1	yes	characteristic
20	C₅	C₁₉×Dic₇₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	355	1	no	Sylow
22	C₂	—	5	1	no	—

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.