Subgroups — C₁₁⋊#13184067 #34086613

Order 19580.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₄₄₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊#67063	—	5	1	no	maximal, Hall
4	C₁₁×D₈₉	—	5	1	no	—
5	#13184067	—	11	1	no	maximal, Hall
6	C₁₁×C₈₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₄₄₅	D₁₁	1	1	yes	characteristic
8	C₅×C₈₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	#67063	—	55	1	no	Hall
10	C₁₁⋊AGL(1,𝔽₅)	—	89	1	no	maximal, Hall
11	D₈₉	—	5	1	no	—
12	D₅×C₁₁	—	89	1	no	—
13	C₈₉	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₁	#67063	1	1	yes	characteristic, complemented, Hall
15	Dic₁₁	—	445	1	no	Hall
16	C₂×C₁₁	—	445	1	no	—
17	AGL(1,𝔽₅)	—	979	1	no	Hall
18	C₁₁	#13184067	1	1	yes	characteristic, complemented, Sylow
19	D₅	—	89	1	no	—
20	C₅	C₁₁⋊#67063	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	4895	1	no	Sylow
22	C₂	—	445	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₁×C₈₉	C₄
prime radical, cosocle	C₁₁×D₄₄₅	C₂
LCS	G ▷ C₅×C₁₁×C₈₉
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.