Subgroups — C₆₁×#92788 #44525739

Order 30927.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×C₆₁	—	13	14	no	maximal
3	C₁₃×C₆₁	C₁₃⋊C₃	1	14	yes	complemented
4	#92788	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₆₁	—	169	1	no	Hall
6	C₁₃²	C₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
7	C₆₁	#92788	1	1	yes	characteristic, direct product factor, Sylow
8	C₁₃⋊C₃	—	13	14	no	—
9	C₁₃	C₁₃⋊C₃×C₆₁	1	14	yes	complemented
10	C₃	—	169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₁	#92788
commutator, cosocle, hypocenter	C₁₃²	C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₁₃²×C₆₁	C₃
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₆₁

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.