Subgroups — C₂₃⋊((C₁₁⋊C₅)⋊D₁₁) #42123714

Order 27830.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁⋊D₂₅₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂₃⋊AGL(1,𝔽₁₁)	—	11	1	no	maximal
5	C₅×D₂₅₃	—	11	1	no	maximal
6	C₅×C₁₁×C₂₃	—	11	1	no	—
7	C₂₃×C₁₁⋊C₅	D₁₁	1	1	yes	characteristic, complemented
8	(C₁₁⋊C₅)⋊D₁₁	—	23	1	no	maximal, Hall
9	C₁₁×C₁₁⋊C₅	D₂₃	1	1	yes	characteristic, complemented, Hall
10	D₂₅₃	—	11	1	no	—
11	D₂₅₃	—	11	1	no	—
12	D₂₅₃	—	55	2	no	—
13	C₁₁×C₂₃	—	5	2	no	—
14	C₁₁×C₂₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
15	C₁₁×C₂₃	C₅×D₁₁	1	1	yes	characteristic, complemented
16	C₁₁⋊D₁₁	—	23	1	no	Hall
17	C₅×D₂₃	—	121	1	no	Hall
18	C₁₁²	C₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
19	C₅×C₂₃	—	11	1	no	Hall
20	C₅×D₁₁	—	253	1	no	—
21	AGL(1,𝔽₁₁)	—	253	1	no	—
22	C₅×C₁₁	—	11	1	no	—
23	C₁₁⋊C₅	D₂₅₃	1	1	yes	characteristic, complemented
24	D₂₃	—	121	1	no	Hall
25	C₂₃	(C₁₁⋊C₅)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
26	D₁₁	—	1265	2	no	—
27	D₁₁	—	253	1	no	—
28	D₁₁	—	253	1	no	—
29	C₁₁	—	5	2	no	—
30	C₁₁	C₅×D₂₅₃	1	1	yes	characteristic, complemented
31	C₁₁	C₂₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
32	C₂×C₅	—	2783	1	no	Hall
33	C₅	—	11	1	no	Sylow
34	C₂	—	2783	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₂₃	C₂×C₅
LCS	G ▷ C₁₁²×C₂₃
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.