Subgroups — C₁₁⋊(C₁₁⋊#1043) #27130976

Order 12100.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	—	5	6	no	maximal
4	D₅×C₁₁²	—	5	6	no	—
5	C₁₁⋊#1043	—	11	12	no	maximal
6	C₅×C₁₁²	AGL(1,𝔽₅)	1	6	yes	complemented
7	C₁₁×C₅⋊D₅	D₁₁	1	12	yes	—
8	C₁₁⋊Dic₁₁	—	25	1	no	Hall
9	C₅²×C₁₁	Dic₁₁	1	12	yes	complemented
10	C₂×C₁₁²	—	25	1	no	—
11	C₁₁⋊AGL(1,𝔽₅)	—	55	72	no	—
12	C₁₁²	#1043	1	1	yes	characteristic, complemented, Sylow
13	D₅×C₁₁	—	5	72	no	—
14	#1043	—	121	1	no	Hall
15	C₅×C₁₁	C₁₁⋊AGL(1,𝔽₅)	1	72	yes	complemented
16	C₅⋊D₅	C₁₁⋊D₁₁	1	1	yes	characteristic
17	Dic₁₁	—	275	12	no	—
18	C₅²	C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₁	—	25	12	no	—
20	AGL(1,𝔽₅)	—	605	6	no	—
21	C₁₁	C₁₁⋊#1043	1	12	yes	complemented
22	D₅	—	5	6	no	—
23	C₅	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	1	6	yes	complemented
24	C₄	—	3025	1	no	Sylow
25	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₁²	C₄
prime radical, cosocle	C₁₁²×C₅⋊D₅	C₂
LCS	G ▷ C₅²×C₁₁²
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.