Subgroups — C₁₁×#15668502 #44541990

Order 31900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₇₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₂₅×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#10596814	—	5	1	no	maximal
4	C₁₁×D₁₄₅	—	5	1	no	—
5	#15668502	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic
7	D₇₂₅	C₂×C₁₁	1	1	yes	characteristic
8	C₁₁×#1181	—	25	1	no	Hall
9	C₁₁×#1035	—	29	1	no	maximal, Hall
10	C₂₅×C₂₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁×D₂₉	—	25	1	no	—
12	#10596814	—	5	1	no	—
13	C₁₁×D₂₅	—	29	1	no	—
14	C₁₁×C₂₉	#1035	1	1	yes	characteristic, complemented, Hall
15	D₁₄₅	—	5	1	no	—
16	C₁₁×C₂₅	#1181	1	1	yes	characteristic, complemented, Hall
17	C₁₁×AGL(1,𝔽₅)	—	145	1	no	—
18	C₅×C₂₉	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
19	#1181	—	25	1	no	Hall
20	D₅×C₁₁	—	145	1	no	—
21	#1035	—	29	1	no	Hall
22	D₂₉	—	25	1	no	—
23	C₅×C₁₁	#10596814	1	1	yes	characteristic
24	D₂₅	—	29	1	no	—
25	C₄×C₁₁	—	725	1	no	Hall
26	C₂₉	C₁₁×#1035	1	1	yes	characteristic, complemented, Sylow
27	C₂₅	C₁₁×#1181	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₁	—	725	1	no	—
29	AGL(1,𝔽₅)	—	145	1	no	—
30	C₁₁	#15668502	1	1	yes	characteristic, direct product factor, Sylow
31	D₅	—	145	1	no	—
32	C₅	C₁₁×#10596814	1	1	yes	characteristic
33	C₄	—	725	1	no	Sylow
34	C₂	—	725	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.