Subgroups — C₂₃×C₂²⋊(C₁₃⋊C₉) #24924497

Order 10764.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₃×C₂₃	C₃	1	1	yes	maximal, characteristic
2	C₂₃×C₁₃⋊C₉	—	4	1	no	maximal, Hall
3	C₂×C₃×C₁₃×C₂₃	—	3	1	no	—
4	C₂²×C₁₃×C₂₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₂₃	A₄	1	1	yes	characteristic
6	C₂₃×C₂²⋊C₉	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₂₃	—	3	1	no	—
8	C₂²⋊(C₁₃⋊C₉)	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₃×C₂₃	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₃×C₂₃	C₁₃⋊C₃	1	1	yes	characteristic
11	C₉×C₂₃	—	52	1	no	Hall
12	C₂²×C₃×C₁₃	C₃×C₂₃	1	1	yes	characteristic
13	C₂×C₃×C₂₃	—	3	1	no	—
14	C₁₃⋊C₉	—	4	1	no	Hall
15	C₂²×C₂₃	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₃	—	3	1	no	—
17	C₃×C₂₃	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
18	C₂²×C₁₃	C₉×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₂₃	—	3	1	no	—
20	C₃×C₁₃	A₄×C₂₃	1	1	yes	characteristic
21	C₂²⋊C₉	—	13	1	no	Hall
22	C₂×C₁₃	—	3	1	no	—
23	C₂₃	C₂²⋊(C₁₃⋊C₉)	1	1	yes	characteristic, direct product factor, Sylow
24	C₁₃	C₂₃×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₃	C₂₃×C₁₃⋊C₃	1	1	yes	characteristic
26	C₉	—	52	1	no	Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	C₂₃×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₂₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
30	C₂	—	3	1	no	—

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