Subgroups — C₁₉×#89137⋊C₃ #38733152

Order 24852.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#89137	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×C₁₀₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉×D₁₀₉	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₁₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#89137⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₁₀₉⋊C₃	C₂×C₁₉	1	1	yes	characteristic
8	#89137	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
9	C₁₀₉⋊C₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₄×C₁₉	—	109	1	no	maximal, Hall
11	D₁₀₉	C₂×C₃×C₁₉	1	1	yes	characteristic
12	C₂×C₃×C₁₉	—	109	1	no	—
13	C₁₀₉	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
14	C₄×C₁₉	—	109	1	no	Hall
15	C₃×C₁₉	—	109	1	no	Hall
16	C₂×C₁₉	—	109	1	no	—
17	C₁₉	#89137⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	109	1	no	Hall
19	C₂×C₃	—	109	1	no	—
20	C₄	—	109	1	no	Sylow
21	C₃	—	109	1	no	Sylow
22	C₂	—	109	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.