Subgroups — C₉×C₁₇×ΓL(1,𝔽₃₂) #37557331

Order 23715.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×ΓL(1,𝔽₃₂)	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₇×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×ΓL(1,𝔽₃₂)	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₁₇×C₃₁	C₃×C₅	1	1	yes	characteristic
5	C₉×ΓL(1,𝔽₃₂)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₉×C₁₇	—	31	1	no	maximal, Hall
7	C₁₇×C₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×ΓL(1,𝔽₃₂)	C₃×C₁₇	1	1	yes	characteristic
9	C₉×C₃₁	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₁₇	—	31	1	no	—
11	ΓL(1,𝔽₃₂)	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₉×C₁₇	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₃₁	C₃×C₅×C₁₇	1	1	yes	characteristic
14	C₅×C₁₇	—	31	1	no	Hall
15	C₃×C₁₇	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
16	C₅×C₉	—	31	1	no	Hall
17	C₃₁	C₅×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
18	C₁₇	C₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	—	31	1	no	—
20	C₉	C₁₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	—	31	1	no	Sylow
22	C₃	C₃×C₁₇×ΓL(1,𝔽₃₂)	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.