Subgroups — C₅×Dic₁₂₂₁ #37567494

Order 24420.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₄₀₇	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₂₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×C₃₇	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₃₇	C₂×C₅	1	1	yes	characteristic
7	C₅×Dic₁₁₁	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₃₇	Dic₃	1	1	yes	characteristic, complemented, Hall
9	Dic₄₀₇	—	3	1	no	Hall
10	C₃×C₁₁×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₃₇	D₁₁	1	1	yes	characteristic
12	C₂×C₁₁×C₃₇	C₅×D₃	1	1	yes	characteristic
13	C₅×Dic₃₇	—	33	1	no	Hall
14	C₅×Dic₃₃	—	37	1	no	maximal, Hall
15	C₃×C₅×C₃₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
16	Dic₁₁₁	—	11	1	no	Hall
17	C₁₁×C₃₇	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₃₇	D₃₃	1	1	yes	characteristic
19	C₂×C₃×C₅×C₁₁	D₃₇	1	1	yes	characteristic
20	C₂×C₃×C₃₇	C₅×D₁₁	1	1	yes	characteristic
21	C₅×Dic₁₁	—	111	1	no	Hall
22	C₅×C₃₇	Dic₃₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₁	Dic₃₇	1	1	yes	characteristic, complemented, Hall
24	Dic₃₇	—	33	1	no	Hall
25	Dic₃₃	—	37	1	no	Hall
26	C₃×C₃₇	C₅×Dic₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₁	D₁₁₁	1	1	yes	characteristic
28	C₂×C₃₇	C₅×D₃₃	1	1	yes	characteristic
29	C₂×C₃×C₁₁	C₅×D₃₇	1	1	yes	characteristic
30	C₅×Dic₃	—	407	1	no	Hall
31	C₅×C₁₁	Dic₁₁₁	1	1	yes	characteristic, complemented, Hall
32	Dic₁₁	—	111	1	no	Hall
33	C₃₇	C₅×Dic₃₃	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₁	C₅×Dic₃₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	D₄₀₇	1	1	yes	characteristic
36	C₂×C₁₁	C₅×D₁₁₁	1	1	yes	characteristic
37	C₄×C₅	—	1221	1	no	Hall
38	C₃×C₅	Dic₄₀₇	1	1	yes	characteristic, complemented, Hall
39	Dic₃	—	407	1	no	Hall
40	C₁₁	C₅×Dic₁₁₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	D₁₂₂₁	1	1	yes	characteristic
42	C₂×C₃	C₅×D₄₀₇	1	1	yes	characteristic
43	C₅	Dic₁₂₂₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	1221	1	no	Sylow
45	C₃	C₅×Dic₄₀₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₅×D₁₂₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₂₂₁
commutator, hypocenter	C₃×C₁₁×C₃₇	C₄×C₅
Frattini	C₂	C₅×D₁₂₂₁
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁×C₃₇	C₂
cosocle	C₂×C₃×C₁₁×C₃₇	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₃₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₃₇	C₄	semidirect
4. Dic₁₂₂₁	C₅	direct (N × H)
8. C₅×C₁₁×C₃₇	Dic₃	semidirect
10. C₃×C₁₁×C₃₇	C₄×C₅	semidirect
15. C₃×C₅×C₃₇	Dic₁₁	semidirect
17. C₁₁×C₃₇	C₅×Dic₃	semidirect
22. C₅×C₃₇	Dic₃₃	semidirect
23. C₃×C₅×C₁₁	Dic₃₇	semidirect
26. C₃×C₃₇	C₅×Dic₁₁	semidirect
31. C₅×C₁₁	Dic₁₁₁	semidirect
33. C₃₇	C₅×Dic₃₃	semidirect
34. C₃×C₁₁	C₅×Dic₃₇	semidirect
38. C₃×C₅	Dic₄₀₇	semidirect
40. C₁₁	C₅×Dic₁₁₁	semidirect
43. C₅	Dic₁₂₂₁	direct (N × H)
45. C₃	C₅×Dic₄₀₇	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×C₃₇	2
C₅×Dic₄₀₇	3
Dic₁₂₂₁	5
C₅×Dic₁₁₁	11
C₅×Dic₃₃	37

Subgroups — C5×Dic1221 #37567494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₁₂₂₁ #37567494