Subgroups — C₁₁×C₁₁⋊#1043 #27130975

Order 12100.

176 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	C₁₁	1	1	yes	maximal, characteristic, direct product factor
6	C₁₁×#1043	—	11	1	no	maximal
7	C₅×C₁₁²	AGL(1,𝔽₅)	1	6	yes	complemented
8	C₁₁×C₅⋊D₅	—	2	5	no	—
9	C₁₁×C₅⋊D₅	D₁₁	1	1	yes	characteristic
10	C₁₁×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic
11	C₁₁×Dic₁₁	—	25	1	no	Hall
12	C₅²×C₁₁	—	2	5	no	—
13	C₅²×C₁₁	Dic₁₁	1	1	yes	characteristic, complemented
14	C₅²×C₁₁	C₄×C₁₁	1	1	yes	characteristic, complemented
15	C₂×C₁₁²	—	25	1	no	—
16	C₁₁⋊AGL(1,𝔽₅)	—	5	6	no	—
17	C₁₁×AGL(1,𝔽₅)	—	55	6	no	—
18	C₁₁²	#1043	1	1	yes	characteristic, complemented, Sylow
19	D₅×C₁₁	—	5	6	no	—
20	D₅×C₁₁	—	5	6	no	—
21	D₅×C₁₁	—	10	30	no	—
22	#1043	—	11	1	no	Hall
23	C₅×C₁₁	—	2	30	no	—
24	C₅×C₁₁	C₁₁×AGL(1,𝔽₅)	1	6	yes	complemented
25	C₅×C₁₁	C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
26	C₅⋊D₅	C₁₁×D₁₁	1	1	yes	characteristic
27	C₄×C₁₁	—	275	1	no	—
28	Dic₁₁	—	25	1	no	—
29	C₅²	C₁₁×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₁₁	—	25	1	no	—
31	C₂×C₁₁	—	25	1	no	—
32	C₂×C₁₁	—	50	5	no	—
33	AGL(1,𝔽₅)	—	55	6	no	—
34	C₁₁	—	2	5	no	—
35	C₁₁	C₁₁×#1043	1	1	yes	characteristic, complemented
36	C₁₁	C₁₁⋊#1043	1	1	yes	characteristic, direct product factor
37	D₅	—	5	6	no	—
38	C₅	C₁₁×C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
39	C₄	—	275	1	no	Sylow
40	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	C₁₁⋊#1043
commutator, hypocenter	C₅²×C₁₁	C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁²	C₄
prime radical	C₁₁²×C₅⋊D₅	C₂
cosocle	C₁₁×C₅⋊D₅	C₂×C₁₁
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁²	C₄	semidirect
5. C₁₁⋊#1043	C₁₁	direct (N × H)
7. C₅×C₁₁²	AGL(1,𝔽₅)	semidirect
13. C₅²×C₁₁	Dic₁₁	semidirect
14. C₅²×C₁₁	C₄×C₁₁	semidirect
18. C₁₁²	#1043	semidirect
24. C₅×C₁₁	C₁₁×AGL(1,𝔽₅)	semidirect
25. C₅×C₁₁	C₁₁⋊AGL(1,𝔽₅)	semidirect
29. C₅²	C₁₁×Dic₁₁	semidirect
35. C₁₁	C₁₁×#1043	semidirect
36. C₁₁	C₁₁⋊#1043	direct (N × H)
38. C₅	C₁₁×C₁₁⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₁₁²×C₅⋊D₅	2
C₁₁×C₁₁⋊AGL(1,𝔽₅)	5
C₁₁⋊#1043	11
C₁₁×#1043	11

Subgroups — C11×C11⋊#1043 #27130975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₁⋊#1043 #27130975