Subgroups — C₂₃×#11759816 #37552237

Order 23322.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#92789	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×C₁₃⋊D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₃×D₁₃⋊C₃	—	13	2	no	maximal
5	#11759816	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂₃×C₁₃⋊C₃	—	13	2	no	—
7	C₂₃×D₁₃	—	13	2	no	—
8	C₂₃×D₁₃	—	39	4	no	—
9	#92789	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃⋊D₁₃	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₂₃	—	3	4	no	—
12	C₁₃×C₂₃	D₁₃⋊C₃	1	2	yes	complemented
13	C₁₃²	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₃×C₂₃	—	169	1	no	Hall
15	D₁₃⋊C₃	—	13	2	no	—
16	C₃×C₂₃	—	169	1	no	Hall
17	C₂×C₂₃	—	169	1	no	Hall
18	C₁₃⋊C₃	—	13	2	no	—
19	D₁₃	—	13	2	no	—
20	D₁₃	—	39	4	no	—
21	C₂₃	#11759816	1	1	yes	characteristic, direct product factor, Sylow
22	C₁₃	—	3	4	no	—
23	C₁₃	C₂₃×D₁₃⋊C₃	1	2	yes	complemented
24	C₂×C₃	—	169	1	no	Hall
25	C₃	—	169	1	no	Sylow
26	C₂	—	169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	#11759816
commutator, cosocle, hypocenter	C₁₃²	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₃²×C₂₃	C₂×C₃
LCS	G ▷ C₁₃²
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.