Subgroups — C₉×Dic₂₉₉ #24924472

Order 10764.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₉₉	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic
5	Dic₂₉₉	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	C₂×C₁₃×C₂₃	C₂×C₉	1	1	yes	characteristic
9	C₉×Dic₁₃	—	23	1	no	maximal, Hall
10	C₂×C₉×C₂₃	D₁₃	1	1	yes	characteristic
11	C₁₃×C₂₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×Dic₂₃	—	13	1	no	—
13	C₂×C₉×C₁₃	D₂₃	1	1	yes	characteristic
14	C₉×C₂₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
15	C₃×Dic₁₃	—	23	1	no	—
16	C₂×C₃×C₂₃	C₃×D₁₃	1	1	yes	characteristic
17	C₉×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
18	Dic₂₃	—	13	1	no	Hall
19	C₂×C₃×C₁₃	C₃×D₂₃	1	1	yes	characteristic
20	C₃×C₂₃	C₃×Dic₁₃	1	1	yes	characteristic
21	Dic₁₃	—	23	1	no	Hall
22	C₂×C₂₃	C₉×D₁₃	1	1	yes	characteristic
23	C₃×C₁₃	C₃×Dic₂₃	1	1	yes	characteristic
24	C₄×C₉	—	299	1	no	Hall
25	C₂×C₁₃	C₉×D₂₃	1	1	yes	characteristic
26	C₂₃	C₉×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	D₂₉₉	1	1	yes	characteristic
28	C₁₃	C₉×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	299	1	no	—
30	C₉	Dic₂₉₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×D₂₉₉	1	1	yes	characteristic
32	C₄	—	299	1	no	Sylow
33	C₃	C₃×Dic₂₉₉	1	1	yes	characteristic
34	C₂	C₉×D₂₉₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉	D₂₉₉
commutator, hypocenter	C₁₃×C₂₃	C₄×C₉
Frattini	C₂×C₃	C₃×D₂₉₉
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle, prime radical, cosocle	C₂×C₃×C₁₃×C₂₃	C₂×C₃
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₃×C₂₃	C₄	semidirect
5. Dic₂₉₉	C₉	direct (N × H)
11. C₁₃×C₂₃	C₄×C₉	semidirect
14. C₉×C₂₃	Dic₁₃	semidirect
17. C₉×C₁₃	Dic₂₃	semidirect
26. C₂₃	C₉×Dic₁₃	semidirect
28. C₁₃	C₉×Dic₂₃	semidirect
30. C₉	Dic₂₉₉	direct (N × H)

Subgroups — C9×Dic299 #24924472

Conjugacy classes of subgroups

Complements

Subgroups — C₉×Dic₂₉₉ #24924472