Subgroups — C₃×Dic₂₆₃₉ #44539719

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₆₃₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₃₇₇	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×Dic₂₀₃	—	13	1	no	maximal, Hall
8	C₂×C₃×C₁₃×C₂₉	D₇	1	1	yes	characteristic
9	Dic₃₇₇	—	7	1	no	Hall
10	C₂×C₃×C₇×C₂₉	D₁₃	1	1	yes	characteristic
11	C₃×C₁₃×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₃×Dic₉₁	—	29	1	no	maximal, Hall
13	Dic₂₀₃	—	13	1	no	Hall
14	C₂×C₁₃×C₂₉	C₃×D₇	1	1	yes	characteristic
15	C₃×C₇×C₂₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₇×C₁₃	D₂₉	1	1	yes	characteristic
17	C₂×C₇×C₂₉	C₃×D₁₃	1	1	yes	characteristic
18	C₁₃×C₂₉	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
19	Dic₉₁	—	29	1	no	Hall
20	C₃×Dic₂₉	—	91	1	no	Hall
21	C₃×C₇×C₁₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
22	C₇×C₂₉	C₃×Dic₁₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	C₃×D₂₉	1	1	yes	characteristic
24	C₂×C₃×C₂₉	D₉₁	1	1	yes	characteristic
25	C₃×Dic₁₃	—	203	1	no	Hall
26	Dic₂₉	—	91	1	no	Hall
27	C₇×C₁₃	C₃×Dic₂₉	1	1	yes	characteristic, complemented, Hall
28	C₃×C₂₉	Dic₉₁	1	1	yes	characteristic, complemented, Hall
29	C₃×Dic₇	—	377	1	no	Hall
30	C₂×C₃×C₁₃	D₂₀₃	1	1	yes	characteristic
31	C₂×C₂₉	C₃×D₉₁	1	1	yes	characteristic
32	Dic₁₃	—	203	1	no	Hall
33	C₂×C₃×C₇	D₃₇₇	1	1	yes	characteristic
34	C₃×C₁₃	Dic₂₀₃	1	1	yes	characteristic, complemented, Hall
35	C₂₉	C₃×Dic₉₁	1	1	yes	characteristic, complemented, Sylow
36	Dic₇	—	377	1	no	Hall
37	C₂×C₁₃	C₃×D₂₀₃	1	1	yes	characteristic
38	C₃×C₇	Dic₃₇₇	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	C₃×D₃₇₇	1	1	yes	characteristic
40	C₁₃	C₃×Dic₂₀₃	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	2639	1	no	Hall
42	C₇	C₃×Dic₃₇₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	D₂₆₃₉	1	1	yes	characteristic
44	C₄	—	2639	1	no	Sylow
45	C₃	Dic₂₆₃₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×D₂₆₃₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₆₃₉
commutator, hypocenter	C₇×C₁₃×C₂₉	C₃×C₄
Frattini	C₂	C₃×D₂₆₃₉
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₃×C₂₉	C₂
cosocle	C₂×C₇×C₁₃×C₂₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₂₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₂₆₃₉	C₃	direct (N × H)
3. C₃×C₇×C₁₃×C₂₉	C₄	semidirect
6. C₇×C₁₃×C₂₉	C₃×C₄	semidirect
11. C₃×C₁₃×C₂₉	Dic₇	semidirect
15. C₃×C₇×C₂₉	Dic₁₃	semidirect
18. C₁₃×C₂₉	C₃×Dic₇	semidirect
21. C₃×C₇×C₁₃	Dic₂₉	semidirect
22. C₇×C₂₉	C₃×Dic₁₃	semidirect
27. C₇×C₁₃	C₃×Dic₂₉	semidirect
28. C₃×C₂₉	Dic₉₁	semidirect
34. C₃×C₁₃	Dic₂₀₃	semidirect
35. C₂₉	C₃×Dic₉₁	semidirect
38. C₃×C₇	Dic₃₇₇	semidirect
40. C₁₃	C₃×Dic₂₀₃	semidirect
42. C₇	C₃×Dic₃₇₇	semidirect
45. C₃	Dic₂₆₃₉	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×C₇×C₁₃×C₂₉	2
Dic₂₆₃₉	3
C₃×Dic₃₇₇	7
C₃×Dic₂₀₃	13
C₃×Dic₉₁	29

Subgroups — C3×Dic2639 #44539719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₆₃₉ #44539719