Subgroups — C₅⋊(C₇⋊AGL(1,𝔽₂₃)) #31799331

Order 17710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊AGL(1,𝔽₂₃)	—	5	1	no	maximal, Hall
3	C₅⋊AGL(1,𝔽₂₃)	—	7	1	no	maximal, Hall
4	C₇×C₂₃⋊C₁₁	D₅	1	1	yes	characteristic, complemented, Hall
5	D₈₀₅	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
6	C₅×C₂₃⋊C₁₁	D₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×D₃₅	—	23	1	no	maximal, Hall
9	AGL(1,𝔽₂₃)	—	35	1	no	Hall
10	C₅×C₇×C₁₁	—	23	1	no	Hall
11	D₁₆₁	—	5	1	no	Hall
12	C₂₃⋊C₁₁	D₃₅	1	1	yes	characteristic, complemented, Hall
13	D₁₁₅	—	7	1	no	Hall
14	C₇×C₂₃	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×D₇	—	115	1	no	Hall
16	C₅×C₂₃	C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
17	D₅×C₁₁	—	161	1	no	Hall
18	C₇×C₁₁	—	23	1	no	Hall
19	D₃₅	—	253	1	no	Hall
20	C₅×C₁₁	—	23	1	no	Hall
21	D₂₃	—	35	1	no	Hall
22	C₅×C₇	AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Hall
23	C₂₃	C₁₁×D₃₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₁₁	—	805	1	no	Hall
25	D₇	—	1265	1	no	Hall
26	C₁₁	—	23	1	no	Sylow
27	D₅	—	1771	1	no	Hall
28	C₇	C₅⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Sylow
29	C₅	C₇⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	8855	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₂₃	C₂×C₁₁
LCS	G ▷ C₅×C₇×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.