Subgroups — C₃×C₁₁×#63118 #22575131

Order 8580.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#63118	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×#261	—	5	1	no	maximal, Hall
5	C₅×C₁₁×D₁₃	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₁×D₁₃	D₅	1	1	yes	characteristic
7	C₃×#63118	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₁×Dic₅	—	13	1	no	maximal, Hall
10	C₁₁×#261	—	5	1	no	Hall
11	C₃×C₁₁×C₁₃	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×D₁₃	C₂×C₁₁	1	1	yes	characteristic
13	C₂×C₃×C₅×C₁₁	—	13	1	no	—
14	C₁₁×D₁₃	C₃×D₅	1	1	yes	characteristic
15	#63118	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₁₁×Dic₅	—	13	1	no	Hall
17	C₃×C₅×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×C₁₁	#261	1	1	yes	characteristic, complemented, Hall
19	C₃×#261	—	5	1	no	Hall
20	C₁₁×C₁₃	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄×C₁₁	—	65	1	no	Hall
22	C₅×D₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
23	C₂×C₅×C₁₁	—	13	1	no	—
24	C₃×D₁₃	D₅×C₁₁	1	1	yes	characteristic
25	C₂×C₃×C₁₁	—	13	1	no	—
26	C₅×C₁₃	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₃×Dic₅	—	13	1	no	Hall
28	C₅×C₁₁	C₃×#261	1	1	yes	characteristic, complemented, Hall
29	#261	—	5	1	no	Hall
30	C₄×C₁₁	—	65	1	no	Hall
31	C₃×C₁₃	C₁₁×Dic₅	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₁	#63118	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₅	—	13	1	no	—
34	D₁₃	C₃×D₅×C₁₁	1	1	yes	characteristic
35	C₂×C₁₁	—	13	1	no	—
36	Dic₅	—	13	1	no	Hall
37	C₃×C₅	C₁₁×#261	1	1	yes	characteristic, complemented, Hall
38	C₁₃	C₃×C₁₁×Dic₅	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₄	—	65	1	no	Hall
40	C₁₁	C₃×#63118	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	13	1	no	—
43	C₅	C₃×C₁₁×#261	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	65	1	no	Sylow
45	C₃	C₁₁×#63118	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₁	#63118
commutator, hypocenter	C₅×C₁₃	C₃×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₄
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×#63118	C₃	direct (N × H)
3. C₃×C₅×C₁₁×C₁₃	C₄	semidirect
7. C₃×#63118	C₁₁	direct (N × H)
8. C₅×C₁₁×C₁₃	C₃×C₄	semidirect
11. C₃×C₁₁×C₁₃	Dic₅	semidirect
15. #63118	C₃×C₁₁	direct (N × H)
17. C₃×C₅×C₁₃	C₄×C₁₁	semidirect
18. C₃×C₅×C₁₁	#261	semidirect
20. C₁₁×C₁₃	C₃×Dic₅	semidirect
26. C₅×C₁₃	C₃×C₄×C₁₁	semidirect
28. C₅×C₁₁	C₃×#261	semidirect
31. C₃×C₁₃	C₁₁×Dic₅	semidirect
32. C₃×C₁₁	#63118	direct (N × H)
37. C₃×C₅	C₁₁×#261	semidirect
38. C₁₃	C₃×C₁₁×Dic₅	semidirect
40. C₁₁	C₃×#63118	direct (N × H)
43. C₅	C₃×C₁₁×#261	semidirect
45. C₃	C₁₁×#63118	direct (N × H)

Subgroups — C3×C11×#63118 #22575131

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₁×#63118 #22575131