Subgroups — C₁₉⋊#11925897 #37527384

Order 22990.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#10597244	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₂₀₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₁₉⋊AGL(1,𝔽₁₁)	—	11	1	no	maximal
5	D₁₉×C₁₁⋊C₅	—	11	1	no	maximal
6	#11925897	—	19	1	no	maximal, Hall
7	C₁₉×C₁₁⋊C₅	—	11	1	no	—
8	C₁₉×C₁₁⋊C₅	—	11	1	no	—
9	#10597244	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₂₀₉	C₁₁⋊C₅	1	1	yes	characteristic, complemented
11	C₁₁×D₁₉	—	11	1	no	—
12	C₁₁×D₁₁	—	19	1	no	Hall
13	C₁₁×C₁₉	—	10	1	no	—
14	C₁₁×C₁₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
15	C₁₁×C₁₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
16	C₅×D₁₉	—	121	1	no	Hall
17	C₁₁²	C₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁⋊C₅	—	209	1	no	—
19	AGL(1,𝔽₁₁)	—	209	1	no	—
20	C₅×C₁₉	—	121	1	no	Hall
21	C₁₁⋊C₅	—	11	1	no	—
22	C₁₁⋊C₅	—	11	1	no	—
23	D₁₉	—	55	1	no	Hall
24	C₂×C₁₁	—	1045	1	no	—
25	D₁₁	—	19	1	no	—
26	C₁₉	#11925897	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	—	10	1	no	—
28	C₁₁	D₁₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented
29	C₁₁	C₁₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
30	C₂×C₅	—	2299	1	no	Hall
31	C₅	—	121	1	no	Sylow
32	C₂	—	1045	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₁₉	C₂×C₅
LCS	G ▷ C₁₁²×C₁₉
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.