Subgroups — C₂₃×C₅⋊(C₁₁⋊D₁₁) #42123747

Order 27830.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×C₁₁⋊D₁₁	—	5	1	no	maximal, Hall
3	C₁₁²×C₂₃	D₅	1	1	yes	characteristic, complemented, Hall
4	C₂₃×D₅₅	—	11	12	no	maximal
5	C₅×C₁₁×C₂₃	D₁₁	1	12	yes	complemented
6	C₅⋊(C₁₁⋊D₁₁)	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁²	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
8	D₁₁×C₂₃	—	55	12	no	—
9	C₁₁×C₂₃	D₅₅	1	12	yes	complemented
10	C₁₁⋊D₁₁	—	5	1	no	Hall
11	D₅×C₂₃	—	121	1	no	Hall
12	C₁₁²	D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
13	C₅×C₂₃	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
14	D₅₅	—	11	12	no	—
15	C₅×C₁₁	D₁₁×C₂₃	1	12	yes	complemented
16	C₂×C₂₃	—	605	1	no	Hall
17	C₂₃	C₅⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, direct product factor, Sylow
18	D₁₁	—	55	12	no	—
19	C₁₁	C₂₃×D₅₅	1	12	yes	complemented
20	D₅	—	121	1	no	Hall
21	C₅	C₂₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	605	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	C₅⋊(C₁₁⋊D₁₁)
commutator, cosocle, hypocenter	C₅×C₁₁²	C₂×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₂₃	C₂
LCS	G ▷ C₅×C₁₁²
UCS	C₁ ◁ C₂₃

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.