Subgroups — C₃×C₁₃×Dic₁₉₉ #44526792

Order 31044.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₉₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₁₉₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₁₉₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₉₉	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₉₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₁₉₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₁₉₉	C₂×C₁₃	1	1	yes	characteristic
8	Dic₁₉₉	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₉₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₉₉	C₂×C₃×C₁₃	1	1	yes	characteristic
11	C₁₉₉	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₁₃	—	199	1	no	maximal, Hall
13	C₂×C₃×C₁₃	D₁₉₉	1	1	yes	characteristic
14	C₄×C₁₃	—	199	1	no	Hall
15	C₃×C₁₃	Dic₁₉₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃	C₃×D₁₉₉	1	1	yes	characteristic
17	C₁₃	C₃×Dic₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	199	1	no	Hall
19	C₂×C₃	C₁₃×D₁₉₉	1	1	yes	characteristic
20	C₄	—	199	1	no	Sylow
21	C₃	C₁₃×Dic₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₁₃×D₁₉₉	1	1	yes	characteristic

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.