Subgroups — C₁₁⋊#11927414 #27211894

Order 13420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₁×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₆₇₁	—	5	1	no	maximal, Hall
4	C₂×C₁₁×C₆₁	—	5	1	no	—
5	#11927414	—	11	1	no	maximal, Hall
6	C₁₁×C₆₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₆₁	D₁₁	1	1	yes	characteristic
8	C₅×C₆₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	Dic₆₁	—	55	1	no	Hall
10	C₁₁⋊AGL(1,𝔽₅)	—	61	1	no	maximal, Hall
11	C₂×C₆₁	—	5	1	no	—
12	D₅×C₁₁	D₆₁	1	1	yes	characteristic
13	C₆₁	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₁	Dic₆₁	1	1	yes	characteristic, complemented, Hall
15	Dic₁₁	—	305	1	no	Hall
16	C₂×C₁₁	—	5	1	no	—
17	AGL(1,𝔽₅)	—	671	1	no	Hall
18	C₁₁	#11927414	1	1	yes	characteristic, complemented, Sylow
19	D₅	D₆₇₁	1	1	yes	characteristic
20	C₅	Dic₆₇₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	3355	1	no	Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₁×C₆₁	C₄
prime radical, cosocle	D₅×C₁₁×C₆₁	C₂
LCS	G ▷ C₅×C₁₁×C₆₁
UCS	C₁

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.