Subgroups — C₂×#22555291 #30684698

Order 17050.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22555291	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic
3	C₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
4	C₂×C₃₁⋊C₂₅	—	11	1	no	maximal, Hall
5	C₃₁⋊C₂₅	—	11	1	no	Hall
6	C₂×C₁₁×C₃₁	C₂₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₁⋊C₂₅	—	31	1	no	maximal, Hall
8	C₁₁×C₃₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₃₁	C₁₁⋊C₅	1	1	yes	characteristic
10	C₁₁⋊C₂₅	—	31	1	no	Hall
11	C₅×C₃₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic
12	C₂×C₅×C₁₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic
13	C₂×C₃₁	C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
15	C₂×C₂₅	—	341	1	no	Hall
16	C₃₁	C₂×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
17	C₂₅	—	341	1	no	Sylow
18	C₂×C₁₁	C₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Hall
19	C₁₁	C₂×C₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	#13133721	1	1	yes	characteristic
21	C₅	C₂×#13133721	1	1	yes	characteristic
22	C₂	#22555291	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.