Subgroups — C₁₁×#13049908 #28384653

Order 14300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₃₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#63122	—	5	1	no	maximal
4	C₁₁×D₆₅	—	5	1	no	—
5	#13049908	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×#1035	—	13	1	no	maximal, Hall
7	C₅×C₁₁×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic
8	D₃₂₅	C₂×C₁₁	1	1	yes	characteristic
9	C₁₁×#261	—	25	1	no	Hall
10	C₁₁×D₂₅	—	13	1	no	—
11	C₁₃×C₂₅	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×D₁₃	—	25	1	no	—
13	C₁₁×C₂₅	#261	1	1	yes	characteristic, complemented, Hall
14	#63122	—	5	1	no	—
15	C₁₁×AGL(1,𝔽₅)	—	65	1	no	—
16	C₁₁×C₁₃	#1035	1	1	yes	characteristic, complemented, Hall
17	D₆₅	—	5	1	no	—
18	D₅×C₁₁	—	65	1	no	—
19	#1035	—	13	1	no	Hall
20	C₅×C₁₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₅×C₁₁	#63122	1	1	yes	characteristic
22	#261	—	25	1	no	Hall
23	D₂₅	—	13	1	no	—
24	C₄×C₁₁	—	325	1	no	Hall
25	D₁₃	—	25	1	no	—
26	C₂₅	C₁₁×#261	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	—	325	1	no	—
28	AGL(1,𝔽₅)	—	65	1	no	—
29	C₁₃	C₁₁×#1035	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	#13049908	1	1	yes	characteristic, direct product factor, Sylow
31	D₅	—	65	1	no	—
32	C₅	C₁₁×#63122	1	1	yes	characteristic
33	C₄	—	325	1	no	Sylow
34	C₂	—	325	1	no	—

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.