Subgroups — C₂₅×C₁₄₉₉ #49154113

Order 37475.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₄₉₉	C₅	1	1	yes	maximal, characteristic
2	C₁₄₉₉	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
3	C₂₅	C₁₄₉₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₅	C₅×C₁₄₉₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₁₄₉₉	C₂₅	direct (N × H)
3. C₂₅	C₁₄₉₉	direct (N × H)

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

subgroup	index
C₅×C₁₄₉₉	5
C₂₅	1499