Subgroups — C₃₁×Dic₅₇ #20296607

Order 7068.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×Dic₁₉	—	3	1	no	maximal, Hall
3	C₃×C₁₉×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₃₁	D₃	1	1	yes	characteristic
5	C₁₉×C₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₃×C₃₁	—	19	1	no	maximal, Hall
7	Dic₅₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₃₁	D₁₉	1	1	yes	characteristic
9	C₄×C₃₁	—	57	1	no	Hall
10	C₂×C₃×C₁₉	C₂×C₃₁	1	1	yes	characteristic
11	C₃×C₃₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
12	Dic₁₉	—	3	1	no	Hall
13	C₂×C₃₁	D₅₇	1	1	yes	characteristic
14	C₃×C₁₉	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₉	D₃×C₃₁	1	1	yes	characteristic
16	C₃₁	Dic₅₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₁₉	Dic₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	19	1	no	Hall
19	C₂×C₃	C₃₁×D₁₉	1	1	yes	characteristic
20	C₄	—	57	1	no	Sylow
21	C₃	C₃₁×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₃₁×D₅₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.