Subgroups — C₁₁⋊(C₁₁⋊#1044) #27130980

Order 12100.

224 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	2	no	maximal
4	D₅×C₁₁²	—	5	2	no	—
5	D₅×C₁₁²	—	10	2	no	—
6	C₁₁⋊#1044	—	11	12	no	maximal
7	C₅×C₁₁²	—	2	2	no	—
8	C₅×C₁₁²	AGL(1,𝔽₅)	1	2	yes	complemented
9	C₁₁×C₅⋊D₅	D₁₁	1	12	yes	—
10	C₁₁⋊Dic₁₁	—	25	1	no	Hall
11	C₅²×C₁₁	Dic₁₁	1	12	yes	complemented
12	C₂×C₁₁²	—	25	1	no	—
13	C₁₁⋊AGL(1,𝔽₅)	—	55	24	no	—
14	C₁₁²	#1044	1	1	yes	characteristic, complemented, Sylow
15	D₅×C₁₁	—	5	24	no	—
16	D₅×C₁₁	—	10	24	no	—
17	#1044	—	121	1	no	Hall
18	C₅×C₁₁	—	2	24	no	—
19	C₅×C₁₁	C₁₁⋊AGL(1,𝔽₅)	1	24	yes	complemented
20	C₅⋊D₅	C₁₁⋊D₁₁	1	1	yes	characteristic
21	Dic₁₁	—	275	12	no	—
22	C₅²	C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₁	—	25	12	no	—
24	AGL(1,𝔽₅)	—	605	2	no	—
25	C₁₁	C₁₁⋊#1044	1	12	yes	complemented
26	D₅	—	5	2	no	—
27	D₅	—	10	2	no	—
28	C₅	—	2	2	no	—
29	C₅	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	1	2	yes	complemented
30	C₄	—	3025	1	no	Sylow
31	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.