Subgroups — C₂₃×C₅₂₉ #27131579

Order 12167.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃²	C₂₃	1	1	yes	maximal, characteristic
2	C₅₂₉	C₂₃	1	23	yes	maximal, direct product factor
3	C₂₃	C₅₂₉	1	23	yes	direct product factor
4	C₂₃	C₂₃²	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₅₂₉	C₂₃	direct (N × H)
3. C₂₃	C₅₂₉	direct (N × H)

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

subgroup	index
C₂₃²	23
C₅₂₉	23