Subgroups — C₃×#22555294 #38784530

Order 25575.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22555294	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₅×C₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic
3	C₃×C₃₁⋊C₂₅	—	11	1	no	maximal, Hall
4	C₅×C₁₁×C₃₁	C₃×C₅	1	1	yes	characteristic
5	C₃×C₁₁×C₃₁	C₂₅	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₁⋊C₂₅	—	31	1	no	maximal, Hall
7	C₃₁⋊C₂₅	—	11	1	no	Hall
8	C₃×C₅×C₃₁	C₁₁⋊C₅	1	1	yes	characteristic
9	C₁₁×C₃₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₁₁⋊C₂₅	—	31	1	no	Hall
11	C₃×C₅×C₁₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic
12	C₅×C₃₁	C₃×C₁₁⋊C₅	1	1	yes	characteristic
13	C₃×C₃₁	C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Hall
14	C₃×C₂₅	—	341	1	no	Hall
15	C₅×C₁₁	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
16	C₃×C₁₁	C₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Hall
17	C₃₁	C₃×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
18	C₂₅	—	341	1	no	Sylow
19	C₃×C₅	#13133724	1	1	yes	characteristic
20	C₁₁	C₃×C₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₃×#13133724	1	1	yes	characteristic
22	C₃	#22555294	1	1	yes	characteristic, direct product factor, 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.