Subgroups — C₃⋊#26013203 #45686830

Order 33330.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19149922	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#26013203	—	3	1	no	maximal, Hall
3	D₃₃₃₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	#19149922	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₁₀₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₃⋊(D₁₀₁⋊C₅)	—	11	1	no	maximal, Hall
7	D₁₁₁₁	—	3	1	no	Hall
8	C₃×C₁₀₁⋊C₅	—	11	1	no	Hall
9	C₁₁×C₁₀₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	D₁₀₁⋊C₅	—	33	1	no	Hall
11	D₃₀₃	—	11	1	no	Hall
12	C₁₀₁⋊C₅	—	11	1	no	Hall
13	C₃⋊AGL(1,𝔽₁₁)	—	101	1	no	maximal, Hall
14	C₃×C₁₀₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
15	D₁₀₁	—	33	1	no	Hall
16	C₃×C₁₁⋊C₅	—	101	1	no	Hall
17	AGL(1,𝔽₁₁)	—	303	1	no	Hall
18	C₁₀₁	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
19	D₃₃	—	101	1	no	Hall
20	C₁₁⋊C₅	—	101	1	no	Hall
21	C₃×C₁₁	D₁₀₁⋊C₅	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	1111	1	no	Hall
23	D₁₁	—	303	1	no	Hall
24	C₃×C₅	—	1111	1	no	Hall
25	C₁₁	C₃⋊(D₁₀₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	3333	1	no	Hall
27	D₃	—	1111	1	no	Hall
28	C₅	—	1111	1	no	Sylow
29	C₃	#26013203	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	3333	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₀₁	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₁₀₁
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.