Subgroups — C₁₉×D₁₇×C₄₉ #44539601

Order 31654.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₉×D₁₇	C₇	1	1	yes	maximal, characteristic
3	C₇×C₁₇×C₁₉	C₂×C₇	1	1	yes	characteristic
4	C₂×C₁₉×C₄₉	—	17	1	no	maximal, Hall
5	D₁₇×C₄₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₄₉	D₁₇	1	1	yes	characteristic, direct product factor, Hall
7	C₁₇×C₄₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₁₉×D₁₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
9	C₁₇×C₁₉	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₁₉	—	17	1	no	—
11	C₇×D₁₇	C₇×C₁₉	1	1	yes	characteristic
12	C₇×C₁₉	C₇×D₁₇	1	1	yes	characteristic
13	C₇×C₁₇	C₂×C₇×C₁₉	1	1	yes	characteristic
14	C₂×C₄₉	—	17	1	no	Hall
15	C₄₉	C₁₉×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	—	17	1	no	Hall
17	D₁₇	C₁₉×C₄₉	1	1	yes	characteristic, direct product factor, Hall
18	C₁₉	D₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₇	C₂×C₁₉×C₄₉	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₇	—	17	1	no	—
21	C₇	C₇×C₁₉×D₁₇	1	1	yes	characteristic
22	C₂	—	17	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.