Subgroups — C₅×C₁₁×C₃⋊#261 #22575139

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	C₅×C₁₁×#261	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×C₃⋊#261	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁×D₁₃	D₃	1	1	yes	characteristic
6	C₃×C₁₁×D₁₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₃⋊#261	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₁₃	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₅×C₁₁×Dic₃	—	13	1	no	maximal, Hall
10	C₁₁×#261	—	3	1	no	Hall
11	C₃×C₁₁×C₁₃	C₄×C₅	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	C₅×D₃	1	1	yes	characteristic
15	C₅×#261	—	3	1	no	Hall
16	C₄×C₅×C₁₁	—	39	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	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₁₁×C₁₃	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
21	C₁₁×Dic₃	—	13	1	no	Hall
22	C₅×D₁₃	D₃×C₁₁	1	1	yes	characteristic
23	C₂×C₅×C₁₁	—	13	1	no	—
24	C₃×D₁₃	C₂×C₅×C₁₁	1	1	yes	characteristic
25	C₂×C₃×C₁₁	—	13	1	no	—
26	C₅×C₁₃	C₁₁×Dic₃	1	1	yes	characteristic, complemented, Hall
27	C₅×Dic₃	—	13	1	no	Hall
28	C₅×C₁₁	C₃⋊#261	1	1	yes	characteristic, direct product factor, Hall
29	#261	—	3	1	no	Hall
30	C₄×C₁₁	—	39	1	no	Hall
31	C₃×C₁₃	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₁	C₅×#261	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	—	13	1	no	—
34	D₁₃	C₅×D₃×C₁₁	1	1	yes	characteristic
35	C₂×C₁₁	—	13	1	no	—
36	C₄×C₅	—	39	1	no	Hall
37	C₃×C₅	C₁₁×#261	1	1	yes	characteristic, complemented, Hall
38	C₁₃	C₅×C₁₁×Dic₃	1	1	yes	characteristic, complemented, Sylow
39	Dic₃	—	13	1	no	Hall
40	C₁₁	C₅×C₃⋊#261	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	13	1	no	—
43	C₅	C₁₁×C₃⋊#261	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	39	1	no	Sylow
45	C₃	C₅×C₁₁×#261	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁	C₃⋊#261
commutator, hypocenter	C₃×C₁₃	C₄×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₄
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₁₃	C₄	semidirect
4. C₁₁×C₃⋊#261	C₅	direct (N × H)
7. C₅×C₃⋊#261	C₁₁	direct (N × H)
8. C₅×C₁₁×C₁₃	Dic₃	semidirect
11. C₃×C₁₁×C₁₃	C₄×C₅	semidirect
17. C₃×C₅×C₁₃	C₄×C₁₁	semidirect
18. C₃×C₅×C₁₁	#261	semidirect
19. C₃⋊#261	C₅×C₁₁	direct (N × H)
20. C₁₁×C₁₃	C₅×Dic₃	semidirect
26. C₅×C₁₃	C₁₁×Dic₃	semidirect
28. C₅×C₁₁	C₃⋊#261	direct (N × H)
31. C₃×C₁₃	C₄×C₅×C₁₁	semidirect
32. C₃×C₁₁	C₅×#261	semidirect
37. C₃×C₅	C₁₁×#261	semidirect
38. C₁₃	C₅×C₁₁×Dic₃	semidirect
40. C₁₁	C₅×C₃⋊#261	direct (N × H)
43. C₅	C₁₁×C₃⋊#261	direct (N × H)
45. C₃	C₅×C₁₁×#261	semidirect

Subgroups — C5×C11×C3⋊#261 #22575139

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₁₁×C₃⋊#261 #22575139