Subgroups — C₃×C₁₉×#67063 #35204331

Order 20292.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#67063	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₉×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉×D₈₉	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₈₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#67063	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×D₈₉	C₂×C₁₉	1	1	yes	characteristic
8	#67063	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₈₉	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₄×C₁₉	—	89	1	no	maximal, Hall
11	D₈₉	C₂×C₃×C₁₉	1	1	yes	characteristic
12	C₂×C₃×C₁₉	—	89	1	no	—
13	C₈₉	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
14	C₄×C₁₉	—	89	1	no	Hall
15	C₃×C₁₉	#67063	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₉	—	89	1	no	—
17	C₁₉	C₃×#67063	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	89	1	no	Hall
19	C₂×C₃	—	89	1	no	—
20	C₄	—	89	1	no	Sylow
21	C₃	C₁₉×#67063	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	89	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.