Subgroups — C₂₃⋊#90865 #24924579

Order 10764.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₃×C₂₃	—	6	2	no	—
4	Dic₂₉₉	—	9	1	no	maximal, Hall
5	C₃×C₁₃×C₂₃	—	2	2	no	—
6	C₂₃⋊#157	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₂₃	—	9	1	no	—
8	#90865	—	23	1	no	maximal, Hall
9	C₃⋊D₃×C₂₃	D₁₃	1	1	yes	characteristic
10	C₁₃×C₂₃	#157	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₃⋊D₃	D₂₃	1	1	yes	characteristic
12	C₃²×C₂₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
13	D₃×C₂₃	—	6	2	no	—
14	C₃²×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
15	Dic₂₃	—	117	1	no	Hall
16	D₃×C₁₃	—	6	2	no	—
17	C₃×C₂₃	—	2	2	no	—
18	Dic₁₃	—	207	1	no	Hall
19	C₂×C₂₃	—	9	1	no	—
20	C₃×C₁₃	—	2	2	no	—
21	#157	—	299	1	no	Hall
22	C₂×C₁₃	—	9	1	no	—
23	C₂₃	#90865	1	1	yes	characteristic, complemented, Sylow
24	C₃⋊D₃	D₂₉₉	1	1	yes	characteristic
25	C₁₃	C₂₃⋊#157	1	1	yes	characteristic, complemented, Sylow
26	C₃²	Dic₂₉₉	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	2691	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃×C₂₃	C₄
prime radical, cosocle	C₁₃×C₃⋊D₃×C₂₃	C₂
LCS	G ▷ C₃²×C₁₃×C₂₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.