Subgroups — C₁₇×C₁₃⋊C₃×C₄₉ #44570402

Order 32487.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×C₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic
3	C₃×C₁₇×C₄₉	—	13	1	no	maximal, Hall
4	C₁₃⋊C₃×C₄₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×C₁₇	C₃×C₇	1	1	yes	characteristic
6	C₁₇×C₄₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₁₇×C₁₃⋊C₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
8	C₁₃×C₄₉	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₁₇	—	13	1	no	—
10	C₇×C₁₃⋊C₃	C₇×C₁₇	1	1	yes	characteristic
11	C₁₃×C₁₇	C₃×C₄₉	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄₉	—	13	1	no	Hall
13	C₇×C₁₇	C₇×C₁₃⋊C₃	1	1	yes	characteristic
14	C₇×C₁₃	C₃×C₇×C₁₇	1	1	yes	characteristic
15	C₃×C₁₇	—	13	1	no	Hall
16	C₄₉	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₁₃⋊C₃	C₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₇	—	13	1	no	—
19	C₁₇	C₁₃⋊C₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₃	C₃×C₁₇×C₄₉	1	1	yes	characteristic, complemented, Sylow
21	C₇	C₇×C₁₇×C₁₃⋊C₃	1	1	yes	characteristic
22	C₃	—	13	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.