Subgroups — C₃×C₄₃×Dic₅₅ #43248763

Order 28380.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×Dic₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₁×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄₃×Dic₁₁	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₁×C₄₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₄₃	D₅	1	1	yes	characteristic
7	C₃×Dic₅×C₄₃	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₄₃×Dic₁₁	—	5	1	no	Hall
10	C₃×C₁₁×C₄₃	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₄₃	D₁₁	1	1	yes	characteristic
12	C₂×C₁₁×C₄₃	C₃×D₅	1	1	yes	characteristic
13	Dic₅×C₄₃	—	11	1	no	Hall
14	C₃×Dic₅₅	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₄₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄×C₄₃	—	55	1	no	Hall
17	C₁₁×C₄₃	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₄₃	C₃×D₁₁	1	1	yes	characteristic
19	C₂×C₃×C₅×C₁₁	C₂×C₄₃	1	1	yes	characteristic
20	C₂×C₃×C₄₃	D₅₅	1	1	yes	characteristic
21	Dic₅₅	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
22	C₅×C₄₃	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
23	C₄×C₄₃	—	55	1	no	Hall
24	C₃×C₅×C₁₁	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
25	C₃×Dic₁₁	—	5	1	no	Hall
26	C₃×C₄₃	Dic₅₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₁₁	C₂×C₃×C₄₃	1	1	yes	characteristic
28	C₂×C₄₃	C₃×D₅₅	1	1	yes	characteristic
29	C₂×C₃×C₁₁	D₅×C₄₃	1	1	yes	characteristic
30	C₃×Dic₅	—	11	1	no	Hall
31	C₅×C₁₁	C₃×C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
32	Dic₁₁	—	5	1	no	Hall
33	C₄₃	C₃×Dic₅₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₃×C₁₁	Dic₅×C₄₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	D₁₁×C₄₃	1	1	yes	characteristic
36	C₂×C₁₁	C₃×D₅×C₄₃	1	1	yes	characteristic
37	Dic₅	—	11	1	no	Hall
38	C₃×C₅	C₄₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
39	C₃×C₄	—	55	1	no	Hall
40	C₁₁	C₃×Dic₅×C₄₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	C₃×D₁₁×C₄₃	1	1	yes	characteristic
42	C₂×C₃	C₄₃×D₅₅	1	1	yes	characteristic
43	C₅	C₃×C₄₃×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	55	1	no	Sylow
45	C₃	C₄₃×Dic₅₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₄₃×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₃	D₅₅
commutator, hypocenter	C₅×C₁₁	C₃×C₄×C₄₃
Frattini	C₂	C₃×C₄₃×D₅₅
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁×C₄₃	C₂
cosocle	C₂×C₅×C₁₁	C₂×C₃×C₄₃
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₃×C₄₃

Complements

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

N	H ≅ G/N	type
2. C₄₃×Dic₅₅	C₃	direct (N × H)
3. C₃×C₅×C₁₁×C₄₃	C₄	semidirect
8. C₅×C₁₁×C₄₃	C₃×C₄	semidirect
10. C₃×C₁₁×C₄₃	Dic₅	semidirect
14. C₃×Dic₅₅	C₄₃	direct (N × H)
15. C₃×C₅×C₄₃	Dic₁₁	semidirect
17. C₁₁×C₄₃	C₃×Dic₅	semidirect
21. Dic₅₅	C₃×C₄₃	direct (N × H)
22. C₅×C₄₃	C₃×Dic₁₁	semidirect
24. C₃×C₅×C₁₁	C₄×C₄₃	semidirect
26. C₃×C₄₃	Dic₅₅	direct (N × H)
31. C₅×C₁₁	C₃×C₄×C₄₃	semidirect
33. C₄₃	C₃×Dic₅₅	direct (N × H)
34. C₃×C₁₁	Dic₅×C₄₃	semidirect
38. C₃×C₅	C₄₃×Dic₁₁	semidirect
40. C₁₁	C₃×Dic₅×C₄₃	semidirect
43. C₅	C₃×C₄₃×Dic₁₁	semidirect
45. C₃	C₄₃×Dic₅₅	direct (N × H)

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×C₄₃	2
C₄₃×Dic₅₅	3
C₃×C₄₃×Dic₁₁	5
C₃×Dic₅×C₄₃	11
C₃×Dic₅₅	43

Subgroups — C3×C43×Dic55 #43248763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃×Dic₅₅ #43248763