Subgroups — #35204992

Order 20367.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₇₃	C₃	1	1	yes	maximal, characteristic
2	C₃₁×C₇₃	C₉	1	1	yes	characteristic, complemented, Hall
3	#10620321	—	31	1	no	maximal, Hall
4	C₃₁⋊C₉	—	73	1	no	maximal, Hall
5	C₃×C₇₃	C₃₁⋊C₃	1	1	yes	characteristic
6	C₃×C₃₁	C₇₃⋊C₃	1	1	yes	characteristic
7	C₇₃	C₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
8	C₃₁	#10620321	1	1	yes	characteristic, complemented, Sylow
9	C₉	—	2263	1	no	Sylow
10	C₃	#20291756	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	#20291756
commutator, hypocenter	C₃₁×C₇₃	C₉
Fitting, socle, prime radical, cosocle	C₃×C₃₁×C₇₃	C₃
LCS	G ▷ C₃₁×C₇₃
UCS	C₁ ◁ C₃

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.