Subgroups — #72267591

Order 61440.

At least 79795 conjugacy classes of subgroups; only the 12 normal subgroups are shown.

normal subgroups only

This group has at least 79795 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×2₋¹⁺⁴	A₅	1	1	yes	maximal normal, characteristic
2	C₂⁴×2₋¹⁺⁴	SL(2,𝔽₅)	1	1	yes	characteristic, complemented
3	C₂⁶	#11757163	1	1	yes	characteristic
4	C₂×2₋¹⁺⁴	#11757162	1	1	yes	characteristic
5	C₂⁵	#14515304	1	1	yes	characteristic
6	2₋¹⁺⁴	#14515302	1	1	yes	characteristic
7	C₂²	#72209715	1	1	yes	characteristic
8	C₂	#72211634	1	1	yes	characteristic
9	C₂	#72212895	1	1	yes	characteristic
10	C₂	#72226616	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂²	#72209715
commutator, hypocenter	G	C₁
Fitting, cosocle	C₂⁵×2₋¹⁺⁴	A₅
LCS	G
UCS	C₁ ◁ C₂²

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

N	H ≅ G/N	type
2. C₂⁴×2₋¹⁺⁴	SL(2,𝔽₅)	semidirect

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