Subgroups — C₁₃×C₂₃×C₂²⋊C₉ #24924496

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	C₉×C₁₃×C₂₃	—	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	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₂₃	—	3	1	no	—
8	C₁₃×C₂²⋊C₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₃×C₂₃	C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₃×C₂₃	C₃×C₁₃	1	1	yes	characteristic
11	C₉×C₂₃	—	4	1	no	Hall
12	C₂²×C₃×C₁₃	C₃×C₂₃	1	1	yes	characteristic
13	C₂×C₃×C₂₃	—	3	1	no	—
14	C₉×C₁₃	—	4	1	no	Hall
15	C₂²×C₂₃	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₃	—	3	1	no	—
17	C₃×C₂₃	A₄×C₁₃	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	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₃	—	3	1	no	—
23	C₂₃	C₁₃×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₁₃	C₂₃×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	C₃×C₁₃×C₂₃	1	1	yes	characteristic
26	C₉	—	4	1	no	Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	C₉×C₁₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	A₄×C₁₃×C₂₃	1	1	yes	characteristic
30	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₂₃	A₄
commutator, hypocenter	C₂²	C₉×C₁₃×C₂₃
Frattini	C₃	A₄×C₁₃×C₂₃
Fitting, socle, prime radical	C₂²×C₃×C₁₃×C₂₃	C₃
cosocle	C₂²×C₃	C₃×C₁₃×C₂₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₃×C₂₃

Complements

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

N	H ≅ G/N	type
4. C₂²×C₁₃×C₂₃	C₉	semidirect
6. C₂₃×C₂²⋊C₉	C₁₃	direct (N × H)
8. C₁₃×C₂²⋊C₉	C₂₃	direct (N × H)
9. C₁₃×C₂₃	C₂²⋊C₉	direct (N × H)
15. C₂²×C₂₃	C₉×C₁₃	semidirect
18. C₂²×C₁₃	C₉×C₂₃	semidirect
21. C₂²⋊C₉	C₁₃×C₂₃	direct (N × H)
23. C₂₃	C₁₃×C₂²⋊C₉	direct (N × H)
24. C₁₃	C₂₃×C₂²⋊C₉	direct (N × H)
28. C₂²	C₉×C₁₃×C₂₃	semidirect

Subgroups — C13×C23×C22⋊C9 #24924496

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₂₃×C₂²⋊C₉ #24924496