Subgroups — C₉×C₁₉×D₇₁ #37566321

Order 24282.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×D₇₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₉×C₇₁	C₂×C₃	1	1	yes	characteristic
4	C₁₉×D₇₁	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₁₉×C₇₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	C₉×D₇₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₇₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₇₁	C₃×C₁₉	1	1	yes	characteristic
9	C₂×C₉×C₁₉	—	71	1	no	maximal, Hall
10	C₃×C₇₁	C₂×C₃×C₁₉	1	1	yes	characteristic
11	C₉×C₁₉	D₇₁	1	1	yes	characteristic, direct product factor, Hall
12	D₇₁	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₉	—	71	1	no	—
14	C₇₁	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₉	C₃×D₇₁	1	1	yes	characteristic
16	C₂×C₁₉	—	71	1	no	Hall
17	C₁₉	C₉×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₉	—	71	1	no	Hall
19	C₉	C₁₉×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	71	1	no	—
21	C₃	C₃×C₁₉×D₇₁	1	1	yes	characteristic
22	C₂	—	71	1	no	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.