Subgroups — C₃×C₁₁⋊#63118 #22575133

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	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃×Dic₅₅	—	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	D₁₁	1	1	yes	characteristic
13	C₂×C₃×C₅×C₁₁	—	13	1	no	—
14	C₁₁×D₁₃	C₃×D₅	1	1	yes	characteristic
15	#63118	—	11	1	no	Hall
16	Dic₅₅	—	13	1	no	Hall
17	C₃×C₅×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×C₁₁	#261	1	1	yes	characteristic, complemented, Hall
19	C₃×#261	—	55	1	no	Hall
20	C₁₁×C₁₃	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
21	C₃×Dic₁₁	—	65	1	no	Hall
22	C₅×D₁₃	C₃×D₁₁	1	1	yes	characteristic
23	C₂×C₅×C₁₁	—	13	1	no	—
24	C₃×D₁₃	D₅₅	1	1	yes	characteristic
25	C₂×C₃×C₁₁	—	13	1	no	—
26	C₅×C₁₃	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
27	C₃×Dic₅	—	143	1	no	Hall
28	C₅×C₁₁	C₃×#261	1	1	yes	characteristic, complemented, Hall
29	#261	—	55	1	no	Hall
30	Dic₁₁	—	65	1	no	Hall
31	C₃×C₁₃	Dic₅₅	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₁	#63118	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	—	13	1	no	—
34	D₁₃	C₃×D₅₅	1	1	yes	characteristic
35	C₂×C₁₁	—	13	1	no	—
36	Dic₅	—	143	1	no	Hall
37	C₃×C₅	C₁₁⋊#261	1	1	yes	characteristic, complemented, Hall
38	C₁₃	C₃×Dic₅₅	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₄	—	715	1	no	Hall
40	C₁₁	C₃×#63118	1	1	yes	characteristic, complemented, 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	—	715	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×C₁₁×C₁₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₄
LCS	G ▷ C₅×C₁₁×C₁₃
UCS	C₁ ◁ C₃

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
8. C₅×C₁₁×C₁₃	C₃×C₄	semidirect
11. C₃×C₁₁×C₁₃	Dic₅	semidirect
17. C₃×C₅×C₁₃	Dic₁₁	semidirect
18. C₃×C₅×C₁₁	#261	semidirect
20. C₁₁×C₁₃	C₃×Dic₅	semidirect
26. C₅×C₁₃	C₃×Dic₁₁	semidirect
28. C₅×C₁₁	C₃×#261	semidirect
31. C₃×C₁₃	Dic₅₅	semidirect
32. C₃×C₁₁	#63118	semidirect
37. C₃×C₅	C₁₁⋊#261	semidirect
38. C₁₃	C₃×Dic₅₅	semidirect
40. C₁₁	C₃×#63118	semidirect
43. C₅	C₃×C₁₁⋊#261	semidirect
45. C₃	C₁₁⋊#63118	direct (N × H)

Subgroups — C3×C11⋊#63118 #22575133

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₁⋊#63118 #22575133