Subgroups — C₁₁⋊(C₁₁⋊#63120) #44538255

Order 31460.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₁²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊Dic₁₄₃	—	5	1	no	maximal, Hall
4	C₂×C₁₁²×C₁₃	—	5	1	no	—
5	C₁₁⋊#63120	—	11	12	no	maximal
6	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	—	13	1	no	maximal, Hall
7	C₁₁²×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	D₅×C₁₁×C₁₃	D₁₁	1	12	yes	—
9	D₅×C₁₁²	D₁₃	1	1	yes	characteristic
10	C₅×C₁₁×C₁₃	Dic₁₁	1	12	yes	complemented
11	C₅×C₁₁²	Dic₁₃	1	1	yes	characteristic, complemented, Hall
12	Dic₁₄₃	—	55	12	no	—
13	C₁₁⋊Dic₁₁	—	65	1	no	Hall
14	C₂×C₁₁×C₁₃	—	5	12	no	—
15	#63120	—	121	1	no	Hall
16	C₂×C₁₁²	—	5	1	no	—
17	C₁₁⋊AGL(1,𝔽₅)	—	143	12	no	—
18	C₁₁×C₁₃	C₁₁⋊AGL(1,𝔽₅)	1	12	yes	complemented
19	D₅×C₁₃	C₁₁⋊D₁₁	1	1	yes	characteristic
20	C₁₁²	#63120	1	1	yes	characteristic, complemented, Sylow
21	D₅×C₁₁	D₁₄₃	1	12	yes	—
22	C₅×C₁₃	C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₁	Dic₁₄₃	1	12	yes	complemented
24	Dic₁₃	—	605	1	no	Hall
25	Dic₁₁	—	715	12	no	—
26	C₂×C₁₃	—	5	1	no	—
27	C₂×C₁₁	—	5	12	no	—
28	AGL(1,𝔽₅)	—	1573	1	no	Hall
29	C₁₃	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	C₁₁⋊#63120	1	12	yes	complemented
31	D₅	C₁₁⋊D₁₄₃	1	1	yes	characteristic
32	C₅	C₁₁⋊Dic₁₄₃	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	7865	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₁²×C₁₃	C₄
prime radical, cosocle	D₅×C₁₁²×C₁₃	C₂
LCS	G ▷ C₅×C₁₁²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁²×C₁₃	C₄	semidirect
7. C₁₁²×C₁₃	AGL(1,𝔽₅)	semidirect
10. C₅×C₁₁×C₁₃	Dic₁₁	semidirect
11. C₅×C₁₁²	Dic₁₃	semidirect
18. C₁₁×C₁₃	C₁₁⋊AGL(1,𝔽₅)	semidirect
20. C₁₁²	#63120	semidirect
22. C₅×C₁₃	C₁₁⋊Dic₁₁	semidirect
23. C₅×C₁₁	Dic₁₄₃	semidirect
29. C₁₃	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	semidirect
30. C₁₁	C₁₁⋊#63120	semidirect
32. C₅	C₁₁⋊Dic₁₄₃	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₁₁²×C₁₃	2
C₁₁⋊Dic₁₄₃	5
C₁₁⋊#63120	11
C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	13

Subgroups — C11⋊(C11⋊#63120) #44538255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊(C₁₁⋊#63120) #44538255