Subgroups — C₃×C₇×C₁₉×C₄₉ #72197218

Order 19551.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₇²×C₁₉	C₇	1	1	yes	maximal, characteristic
3	C₃×C₁₉×C₄₉	C₇	1	7	yes	maximal, direct product factor
4	C₃×C₇×C₄₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇²×C₁₉	C₃×C₇	1	1	yes	characteristic
6	C₁₉×C₄₉	C₃×C₇	1	7	yes	direct product factor
7	C₃×C₇×C₁₉	C₄₉	1	7	yes	direct product factor
8	C₃×C₇×C₁₉	C₇²	1	1	yes	characteristic
9	C₇×C₄₉	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₇²	C₇×C₁₉	1	1	yes	characteristic
11	C₃×C₄₉	C₇×C₁₉	1	7	yes	direct product factor
12	C₇×C₁₉	C₃×C₄₉	1	7	yes	direct product factor
13	C₇×C₁₉	C₃×C₇²	1	1	yes	characteristic
14	C₃×C₁₉	C₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
15	C₇²	C₃×C₇×C₁₉	1	1	yes	characteristic
16	C₄₉	C₃×C₇×C₁₉	1	7	yes	direct product factor
17	C₃×C₇	C₁₉×C₄₉	1	7	yes	direct product factor
18	C₃×C₇	C₇²×C₁₉	1	1	yes	characteristic
19	C₁₉	C₃×C₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₃×C₁₉×C₄₉	1	7	yes	direct product factor
21	C₇	C₃×C₇²×C₁₉	1	1	yes	characteristic
22	C₃	C₇×C₁₉×C₄₉	1	1	yes	characteristic, direct product factor, Sylow

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.