Subgroups — C₁₁⋊(C₁₁⋊#63122) #44538253

Order 31460.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊(C₁₁⋊#261)	—	5	1	no	maximal, Hall
4	C₁₁²×D₁₃	—	5	1	no	—
5	C₁₁⋊#63122	—	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	C₁₁×D₆₅	D₁₁	1	12	yes	—
9	D₅×C₁₁²	—	13	1	no	—
10	C₅×C₁₁×C₁₃	Dic₁₁	1	12	yes	complemented
11	C₅×C₁₁²	#261	1	1	yes	characteristic, complemented, Hall
12	C₁₁⋊#261	—	55	12	no	—
13	C₁₁⋊Dic₁₁	—	65	1	no	Hall
14	C₁₁×D₁₃	—	5	12	no	—
15	#63122	—	121	1	no	Hall
16	C₂×C₁₁²	—	65	1	no	—
17	C₁₁⋊AGL(1,𝔽₅)	—	143	12	no	—
18	C₁₁×C₁₃	C₁₁⋊AGL(1,𝔽₅)	1	12	yes	complemented
19	D₆₅	C₁₁⋊D₁₁	1	1	yes	characteristic
20	C₁₁²	#63122	1	1	yes	characteristic, complemented, Sylow
21	D₅×C₁₁	—	13	12	no	—
22	C₅×C₁₃	C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₁	C₁₁⋊#261	1	12	yes	complemented
24	#261	—	605	1	no	Hall
25	Dic₁₁	—	715	12	no	—
26	D₁₃	—	5	1	no	—
27	C₂×C₁₁	—	65	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⋊#63122	1	12	yes	complemented
31	D₅	—	13	1	no	—
32	C₅	C₁₁⋊(C₁₁⋊#261)	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	7865	1	no	Sylow
34	C₂	—	65	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₁²×C₁₃	C₄
prime radical, cosocle	C₁₁²×D₆₅	C₂
LCS	G ▷ C₅×C₁₁²×C₁₃
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.