Subgroups — C₁₃×C₁₉×Dic₁₇ #30680985

Order 16796.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₇×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×Dic₁₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₁₃×C₁₉	—	17	1	no	maximal, Hall
5	C₁₃×Dic₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₇×C₁₉	C₂×C₁₃	1	1	yes	characteristic
7	C₂×C₁₃×C₁₉	D₁₇	1	1	yes	characteristic
8	C₂×C₁₃×C₁₇	C₂×C₁₉	1	1	yes	characteristic
9	C₁₇×C₁₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃×C₁₉	Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃×C₁₇	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
12	C₄×C₁₉	—	17	1	no	Hall
13	Dic₁₇	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₁₃	—	17	1	no	Hall
15	C₂×C₁₉	C₁₃×D₁₇	1	1	yes	characteristic
16	C₂×C₁₇	C₂×C₁₃×C₁₉	1	1	yes	characteristic
17	C₂×C₁₃	C₁₉×D₁₇	1	1	yes	characteristic
18	C₁₉	C₁₃×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₇	C₄×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
20	C₁₃	C₁₉×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	17	1	no	Sylow
22	C₂	C₁₃×C₁₉×D₁₇	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.