Subgroups — C₉×C₂₃⋊#261 #24924485

Order 10764.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃⋊#261	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₂₃⋊#261	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic
7	C₉×Dic₂₃	—	13	1	no	maximal, Hall
8	C₂₃×D₁₃	C₂×C₉	1	1	yes	characteristic
9	C₉×#261	—	23	1	no	maximal, Hall
10	C₂×C₉×C₂₃	—	13	1	no	—
11	C₁₃×C₂₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×Dic₂₃	—	13	1	no	—
13	C₉×D₁₃	D₂₃	1	1	yes	characteristic
14	C₉×C₂₃	#261	1	1	yes	characteristic, complemented, Hall
15	C₃×#261	—	23	1	no	—
16	C₂×C₃×C₂₃	—	13	1	no	—
17	C₉×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
18	Dic₂₃	—	13	1	no	Hall
19	C₃×D₁₃	C₃×D₂₃	1	1	yes	characteristic
20	C₃×C₂₃	C₃×#261	1	1	yes	characteristic
21	#261	—	23	1	no	Hall
22	C₂×C₂₃	—	13	1	no	—
23	C₃×C₁₃	C₃×Dic₂₃	1	1	yes	characteristic
24	C₄×C₉	—	299	1	no	Hall
25	D₁₃	C₉×D₂₃	1	1	yes	characteristic
26	C₂₃	C₉×#261	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	13	1	no	—
28	C₁₃	C₉×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	299	1	no	—
30	C₉	C₂₃⋊#261	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	13	1	no	—
32	C₄	—	299	1	no	Sylow
33	C₃	C₃×C₂₃⋊#261	1	1	yes	characteristic
34	C₂	—	13	1	no	—

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