Subgroups — C₇⋊(C₁₉⋊AGL(1,𝔽₁₁)) #28410708

Order 14630.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₄₆₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉⋊AGL(1,𝔽₁₁)	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×D₁₃₃	—	11	1	no	maximal, Hall
6	C₁₉×C₁₁⋊C₅	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇⋊AGL(1,𝔽₁₁)	—	19	1	no	maximal, Hall
8	C₅×C₇×C₁₉	—	11	1	no	Hall
9	D₂₀₉	—	7	1	no	Hall
10	C₇×C₁₁⋊C₅	D₁₉	1	1	yes	characteristic, complemented, Hall
11	D₁₃₃	—	55	1	no	Hall
12	C₁₁×C₁₉	C₅×D₇	1	1	yes	characteristic, complemented, Hall
13	C₅×D₁₉	—	77	1	no	Hall
14	D₇₇	—	19	1	no	Hall
15	C₇×C₁₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
16	AGL(1,𝔽₁₁)	—	133	1	no	Hall
17	C₅×C₁₉	—	11	1	no	Hall
18	C₇×C₁₁	C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
19	C₅×D₇	—	209	1	no	Hall
20	C₁₁⋊C₅	D₁₃₃	1	1	yes	characteristic, complemented, Hall
21	D₁₉	—	385	1	no	Hall
22	C₅×C₇	—	11	1	no	Hall
23	D₁₁	—	133	1	no	Hall
24	C₁₉	C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
25	D₇	—	1045	1	no	Hall
26	C₁₁	C₅×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	1463	1	no	Hall
28	C₇	C₁₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
29	C₅	—	11	1	no	Sylow
30	C₂	—	7315	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₁₉	C₂×C₅
LCS	G ▷ C₇×C₁₁×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.