Subgroups — #34035374

Order 18723.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉²	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₇₉⋊C₃	—	79	2	no	maximal
3	C₇₉	—	3	26	no	—
4	C₇₉	C₇₉⋊C₃	1	2	yes	complemented
5	C₃	—	6241	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇₉²	C₃
LCS	G ▷ C₇₉²
UCS	C₁

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

N	H ≅ G/N	type
1. C₇₉²	C₃	semidirect
4. C₇₉	C₇₉⋊C₃	semidirect

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

subgroup	index
C₇₉²	3
C₇₉⋊C₃	79