Subgroups — C₅×C₁₁²×D₂₃ #42123738

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	C₁₁²×D₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁²×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₁₁×D₂₃	C₁₁	1	12	yes	maximal, direct product factor
5	C₅×C₁₁×C₂₃	C₂×C₁₁	1	12	yes	complemented
6	C₂×C₅×C₁₁²	—	23	1	no	maximal, Hall
7	C₅×C₁₁²	D₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×D₂₃	C₅×C₁₁	1	12	yes	direct product factor
9	C₁₁×C₂₃	C₂×C₅×C₁₁	1	12	yes	complemented
10	C₂×C₁₁²	—	23	1	no	Hall
11	C₅×D₂₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁²	C₅×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₅×C₂₃	C₂×C₁₁²	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₁₁	—	23	12	no	—
15	C₅×C₁₁	C₁₁×D₂₃	1	12	yes	direct product factor
16	D₂₃	C₅×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
17	C₂₃	C₂×C₅×C₁₁²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁	—	23	12	no	—
19	C₁₁	C₅×C₁₁×D₂₃	1	12	yes	direct product factor
20	C₂×C₅	—	23	1	no	Hall
21	C₅	C₁₁²×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	23	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁²	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₅×C₁₁²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₅×C₁₁²

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.