Subgroups — C₈₁×C₂₆₃ #36319166

Order 21303.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₇×C₂₆₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₂₆₃	C₉	1	1	yes	characteristic
3	C₃×C₂₆₃	C₂₇	1	1	yes	characteristic
4	C₂₆₃	C₈₁	1	1	yes	characteristic, direct product factor, Sylow
5	C₈₁	C₂₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂₇	C₃×C₂₆₃	1	1	yes	characteristic
7	C₉	C₉×C₂₆₃	1	1	yes	characteristic
8	C₃	C₂₇×C₂₆₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂₆₃	C₈₁	direct (N × H)
5. C₈₁	C₂₆₃	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₇×C₂₆₃	3
C₈₁	263