Subgroups — C₂₃×#90646 #23780348

Order 10350.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₂₃×D₁₅	—	3	1	no	maximal
3	C₃×C₅²×C₂₃	D₃	1	1	yes	characteristic
4	C₅×D₅×C₂₃	—	9	1	no	Hall
5	C₂₃×D₁₅	—	3	1	no	—
6	C₅×D₃×C₂₃	—	15	1	no	—
7	C₅²×C₂₃	D₉	1	1	yes	characteristic, complemented, Hall
8	#90646	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₉×C₂₃	—	25	1	no	maximal, Hall
10	C₃×C₅×C₂₃	—	3	1	no	—
11	C₃×C₅×C₂₃	—	3	1	no	—
12	C₂×C₅×C₂₃	—	45	1	no	—
13	D₅×C₂₃	—	9	1	no	—
14	C₅²⋊C₉	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₉×C₂₃	—	25	1	no	Hall
16	C₅×D₁₅	—	3	1	no	—
17	D₃×C₂₃	—	15	1	no	—
18	C₅×C₂₃	—	3	1	no	—
19	C₅×C₂₃	—	3	1	no	—
20	C₃×C₅²	D₃×C₂₃	1	1	yes	characteristic
21	C₃×C₂₃	#3874	1	1	yes	characteristic
22	C₅×D₅	—	9	1	no	Hall
23	C₂×C₂₃	—	45	1	no	Hall
24	D₁₅	—	3	1	no	—
25	C₅×D₃	—	15	1	no	—
26	C₅²	D₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₂₃	#90646	1	1	yes	characteristic, direct product factor, Sylow
28	D₉	—	25	1	no	Hall
29	C₃×C₅	—	3	1	no	—
30	C₃×C₅	—	3	1	no	—
31	C₂×C₅	—	45	1	no	—
32	D₅	—	9	1	no	—
33	C₉	—	25	1	no	Sylow
34	D₃	—	15	1	no	—
35	C₅	—	3	1	no	—
36	C₅	—	3	1	no	—
37	C₃	C₂₃×#3874	1	1	yes	characteristic
38	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	#90646
commutator, cosocle, hypocenter	C₅²⋊C₉	C₂×C₂₃
Frattini	C₃	C₂₃×#3874
Fitting, socle	C₃×C₅²×C₂₃	D₃
LCS	G ▷ C₅²⋊C₉
UCS	C₁ ◁ C₂₃

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