Subgroups — C₉×C₄₉ #89200

Order 441.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉	C₃	1	1	yes	maximal, characteristic
2	C₇×C₉	C₇	1	1	yes	maximal, characteristic
3	C₄₉	C₉	1	1	yes	characteristic, direct product factor, Sylow
4	C₃×C₇	C₃×C₇	1	1	yes	characteristic
5	C₉	C₄₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₇	C₇×C₉	1	1	yes	characteristic
7	C₃	C₃×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, socle, prime radical, cosocle	C₃×C₇	C₃×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

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

N	H ≅ G/N	type
3. C₄₉	C₉	direct (N × H)
5. C₉	C₄₉	direct (N × H)

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

subgroup	index
C₃×C₄₉	3
C₇×C₉	7