Subgroups — (C₁₁⋊C₅)⋊(D₁₀₉⋊C₃) #49112596

Order 35970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₁⋊C₅)⋊D₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊(D₁₀₉⋊C₃)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁⋊C₅×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₁₀₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₁₀₉⋊C₃	—	11	1	no	maximal, Hall
7	D₁₁₉₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₀₉⋊C₃	—	11	1	no	Hall
9	C₁₁×C₁₀₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×D₁₀₉	—	11	1	no	Hall
11	D₁₀₉⋊C₃	—	11	1	no	Hall
12	C₅×C₁₀₉	—	11	1	no	Hall
13	C₃×AGL(1,𝔽₁₁)	—	109	1	no	maximal, Hall
14	C₁₀₉⋊C₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
15	D₁₀₉	—	11	1	no	Hall
16	C₃×C₁₁⋊C₅	—	109	1	no	Hall
17	AGL(1,𝔽₁₁)	—	109	1	no	Hall
18	C₁₀₉	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₁₁	—	109	1	no	Hall
20	C₁₁⋊C₅	D₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	—	109	1	no	Hall
22	C₂×C₃×C₅	—	1199	1	no	Hall
23	D₁₁	—	109	1	no	Hall
24	C₃×C₅	—	1199	1	no	Hall
25	C₁₁	C₅×D₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	1199	1	no	Hall
27	C₂×C₃	—	1199	1	no	Hall
28	C₅	—	11	1	no	Sylow
29	C₃	—	109	1	no	Sylow
30	C₂	—	1199	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₀₉	C₂×C₃×C₅
LCS	G ▷ C₁₁×C₁₀₉
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.