Subgroups — C₂₃⋊(#4223⋊C₅) #34038201

Order 18860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₂₃×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃⋊#4223	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₃×D₄₁	C₂×C₅	1	1	yes	characteristic
5	C₂₃×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
6	#4223⋊C₅	—	23	1	no	maximal, Hall
7	C₅×Dic₂₃	—	41	1	no	maximal, Hall
8	D₄₁⋊C₅	D₂₃	1	1	yes	characteristic
9	C₂×C₅×C₂₃	—	41	1	no	—
10	C₄₁⋊C₅	Dic₂₃	1	1	yes	characteristic, complemented, Hall
11	#4223	—	23	1	no	Hall
12	C₅×C₂₃	—	41	1	no	Hall
13	Dic₂₃	—	205	1	no	Hall
14	D₄₁	C₅×D₂₃	1	1	yes	characteristic
15	C₂×C₂₃	—	205	1	no	—
16	C₄₁	C₅×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
17	C₂₃	#4223⋊C₅	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	943	1	no	Hall
19	C₂×C₅	—	41	1	no	—
20	C₅	—	41	1	no	Sylow
21	C₄	—	4715	1	no	Sylow
22	C₂	—	205	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₃×C₄₁	C₄×C₅
prime radical	C₂₃×D₄₁⋊C₅	C₂
cosocle	C₂₃×D₄₁	C₂×C₅
LCS	G ▷ C₂₃×C₄₁
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.