Subgroups — C₁₁×Dic₄₆₅ #35205607

Order 20460.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₁₅₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×Dic₉₃	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₁×C₃₁	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₃₁	D₅	1	1	yes	characteristic
7	Dic₄₆₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₁₁×Dic₃₁	—	15	1	no	Hall
10	C₃×C₁₁×C₃₁	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₃₁	C₂×C₁₁	1	1	yes	characteristic
12	C₂×C₁₁×C₃₁	D₁₅	1	1	yes	characteristic
13	C₁₁×Dic₁₅	—	31	1	no	maximal, Hall
14	Dic₁₅₅	—	3	1	no	Hall
15	C₃×C₅×C₃₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	Dic₉₃	—	5	1	no	Hall
17	C₁₁×C₃₁	Dic₁₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₁₁	D₃₁	1	1	yes	characteristic
19	C₂×C₅×C₃₁	D₃×C₁₁	1	1	yes	characteristic
20	C₁₁×Dic₅	—	93	1	no	Hall
21	C₂×C₃×C₃₁	D₅×C₁₁	1	1	yes	characteristic
22	C₃×C₅×C₁₁	Dic₃₁	1	1	yes	characteristic, complemented, Hall
23	C₅×C₃₁	C₁₁×Dic₃	1	1	yes	characteristic, complemented, Hall
24	C₁₁×Dic₃	—	155	1	no	Hall
25	Dic₃₁	—	15	1	no	Hall
26	C₂×C₅×C₁₁	D₉₃	1	1	yes	characteristic
27	C₃×C₃₁	C₁₁×Dic₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₁	D₁₅₅	1	1	yes	characteristic
29	C₂×C₃₁	C₁₁×D₁₅	1	1	yes	characteristic
30	Dic₁₅	—	31	1	no	Hall
31	C₅×C₁₁	Dic₉₃	1	1	yes	characteristic, complemented, Hall
32	C₄×C₁₁	—	465	1	no	Hall
33	C₃×C₁₁	Dic₁₅₅	1	1	yes	characteristic, complemented, Hall
34	C₃₁	C₁₁×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₅	C₁₁×D₃₁	1	1	yes	characteristic
36	C₂×C₁₁	D₄₆₅	1	1	yes	characteristic
37	Dic₅	—	93	1	no	Hall
38	C₃×C₅	C₁₁×Dic₃₁	1	1	yes	characteristic, complemented, Hall
39	Dic₃	—	155	1	no	Hall
40	C₁₁	Dic₄₆₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	C₁₁×D₉₃	1	1	yes	characteristic
42	C₂×C₃	C₁₁×D₁₅₅	1	1	yes	characteristic
43	C₅	C₁₁×Dic₉₃	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	465	1	no	Sylow
45	C₃	C₁₁×Dic₁₅₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₁₁×D₄₆₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₄₆₅
commutator, hypocenter	C₃×C₅×C₃₁	C₄×C₁₁
Frattini	C₂	C₁₁×D₄₆₅
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁×C₃₁	C₂
cosocle	C₂×C₃×C₅×C₃₁	C₂×C₁₁
LCS	G ▷ C₃×C₅×C₃₁
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₃₁	C₄	semidirect
7. Dic₄₆₅	C₁₁	direct (N × H)
8. C₅×C₁₁×C₃₁	Dic₃	semidirect
10. C₃×C₁₁×C₃₁	Dic₅	semidirect
15. C₃×C₅×C₃₁	C₄×C₁₁	semidirect
17. C₁₁×C₃₁	Dic₁₅	semidirect
22. C₃×C₅×C₁₁	Dic₃₁	semidirect
23. C₅×C₃₁	C₁₁×Dic₃	semidirect
27. C₃×C₃₁	C₁₁×Dic₅	semidirect
31. C₅×C₁₁	Dic₉₃	semidirect
33. C₃×C₁₁	Dic₁₅₅	semidirect
34. C₃₁	C₁₁×Dic₁₅	semidirect
38. C₃×C₅	C₁₁×Dic₃₁	semidirect
40. C₁₁	Dic₄₆₅	direct (N × H)
43. C₅	C₁₁×Dic₉₃	semidirect
45. C₃	C₁₁×Dic₁₅₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×C₁₁×C₃₁	2
C₁₁×Dic₁₅₅	3
C₁₁×Dic₉₃	5
Dic₄₆₅	11
C₁₁×Dic₁₅	31

Subgroups — C11×Dic465 #35205607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×Dic₄₆₅ #35205607