Subgroups — C₇₅₇⋊C₄₉ #49150613

Order 37093.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₇₅₇	C₇	1	1	yes	maximal, characteristic
2	C₇₅₇	C₄₉	1	1	yes	characteristic, complemented, Sylow
3	C₄₉	—	757	1	no	maximal, Sylow
4	C₇	C₇₅₇⋊C₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₇	C₇₅₇⋊C₇
commutator, hypocenter	C₇₅₇	C₄₉
Fitting, socle, prime radical, cosocle	C₇×C₇₅₇	C₇
LCS	G ▷ C₇₅₇
UCS	C₁ ◁ C₇

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

N	H ≅ G/N	type
2. C₇₅₇	C₄₉	semidirect

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

subgroup	index
C₇×C₇₅₇	7
C₄₉	757