Subgroups — C₅×C₁₉×#6923 #37550804

Order 23180.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×#6923	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₉×D₆₁	C₂×C₅	1	1	yes	characteristic
5	C₅×#6923	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₆₁	C₂×C₁₉	1	1	yes	characteristic
8	C₄×C₅×C₁₉	—	61	1	no	maximal, Hall
9	C₅×C₆₁	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
10	#6923	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₉	—	61	1	no	—
12	D₆₁	C₂×C₅×C₁₉	1	1	yes	characteristic
13	C₅×C₁₉	#6923	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₁₉	—	61	1	no	Hall
15	C₆₁	C₄×C₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	—	61	1	no	—
17	C₄×C₅	—	61	1	no	Hall
18	C₁₉	C₅×#6923	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	—	61	1	no	—
20	C₅	C₁₉×#6923	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	61	1	no	Sylow
22	C₂	—	61	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.