Subgroups — C₃²×C₇₅₇⋊C₃ #35205487

Order 20439.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇₅₇	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇₅₇⋊C₃	C₃	1	12	yes	maximal, direct product factor
3	C₃×C₇₅₇	C₃²	1	4	yes	complemented
4	C₇₅₇⋊C₃	C₃²	1	9	yes	direct product factor
5	C₇₅₇	C₃³	1	1	yes	characteristic, complemented, Sylow
6	C₃³	—	757	1	no	maximal, Sylow
7	C₃²	—	757	12	no	—
8	C₃²	C₇₅₇⋊C₃	1	1	yes	characteristic, direct product factor
9	C₃	—	757	9	no	—
10	C₃	C₃×C₇₅₇⋊C₃	1	4	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃²	C₇₅₇⋊C₃
commutator, cosocle, hypocenter	C₇₅₇	C₃³
Frattini	C₁	G
Fitting, socle	C₃²×C₇₅₇	C₃
LCS	G ▷ C₇₅₇
UCS	C₁ ◁ C₃²

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

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